https://infogram.com/share-of-world-gdp-throughout-history-1gjk92e6yjwqm16

Over very long periods, different countries take on economic leadership roles. One economy’s decline provides opportunity for another. What does very long-term data tell us about the value of diversifying across economies as well as asset classes? What are the implications for US investors as its reserve currency status weakens?

Disclaimer: nothing in this article is meant as financial advice. I am not a licensed financial advisor. I am a financial analyst looking at multiple sources of historical data, building asset allocation models for educational purposes only.

The Challenge of Modeling Economies

I arrived at this economic diversification conundrum when my original 55-year asset allocation study recommended putting zero allocation into developed markets Ex-US. This unexpected result spawned some deep reflection:

Wondering if the result had to do with the US being the world’s reserve currency and largest economic power, I found a dataset stretching much further back in time. My past three articles have investigated the very long-term performance of assets found in that database.

Note that the GDP share chart at the top of this article shows that the US share of world GDP has been declining since peaking around 1950.

Risk vs. Return for Each Asset

I developed US and Ex-US indices for four different asset classes using the JST dataset: Equity (stocks), housing, bonds, and bills. The plot below shows annual return vs. average risk (measured by average annual drawdown) for each asset.

Equity looks about as I expected. The historical risk levels for Ex-US bonds and bills are larger than I expected because they are measured in US dollars, and the World War I / Great Depression / World War II period led to some extreme drawdowns in US dollar terms.

But what’s going on with housing? Is the risk of housing as a long-term investment really that low?

Housing Drawdown vs. Equity Drawdown

Real Estate causes definitional disagreements for asset allocation research. Among other issues, major research firms disagree strongly on the size of the overall real estate market, as I explored in an earlier article:

The JST dataset features a much broader definition of housing than just tradable Real Estate Investment Trusts (REITs). It combines returns from rents with returns from property value appreciation. But it’s important to note that property values are not marked to market daily like stocks. Look at the drawdown chart for US housing:

Based on the JST housing data, there was essentially no drawdown in housing from the end of World War II to the Global Financial Crisis of 2008. I’m sorry, but I don’t find that credible. Owning a house is not without risk, local markets boom and bust, and rental properties sit vacant and need repairs from time to time.

Dallas Fed housing price data shows regular drops of 10%+ during housing busts.

https://www.dallasfed.org/research/economics/2026/0115

Maybe the difference is real vs. nominal returns, with drops in housing prices hitting as inflation spikes. I don’t know for sure.

Ex-US housing data from JST shows regular drawdowns in US Dollar terms.

Even this Ex-US data looks suspect to me for asset allocation. Does housing risk really look much closer to bonds than stocks?

Is Housing a Liquid Investment?

I think the problem is lack of liquidity, leading to lack of price markdowns. Much like private equity, housing is not repriced on a daily basis. People stay in their homes for many years and prefer to sell into market strength unless there truly is a major crisis forcing them out onto the street.

To me, this annual housing data is simply not on the same risk basis as stocks, bonds, and bills that are priced and traded daily. Therefore, I will be leaving housing out of my asset allocation optimization. Otherwise, the optimizer would just load up on housing, which is not the answer I’m seeking for a liquid investment portfolio. But it does make a strong argument for holding a major stake in real estate in addition to a diversified portfolio of securities, which is what most homeowners in the US do in practice.

Efficient Frontier for Stocks, Bonds, and Bills

Putting together the efficient frontier for stocks, bonds, and bills looks just as expected. Stocks100 is 100% US stocks; 60_40 is 60% US stocks + 40% US bonds.

Diversification enables stock-like returns for substantially less risk.

Allocations vs. Risk Appetite

Here are the asset allocations moving along the efficient frontier:

The tradeoff between stocks and bonds is clear and as expected. Bills play a role for the safest allocations.

Note, however, that the only Ex-US component on the efficient frontier is from stocks. Ex-US bonds and bills are too risky in US Dollar terms to make it to the efficient frontier.

The big insight I see from this chart is that even though only Ex-US stocks are included, they are providing diversification for both US stocks and US bonds. US stocks ramp down more rapidly than Ex-US stocks as US bonds ramp up.

Ex-US Equities Diversify the US Economy, Not Just Stocks

Let’s look at the ratio of Ex-US stocks to US stocks for the optimal allocation. Along nearly the whole frontier, the less risky portfolios deploy more capital outside the US stock market. Ex-US stock allocations are near parity at the risky end but 1.6 to 1.9x as much as the US for less risky portfolios.

Thus, it’s important to keep in mind that Ex-US stocks not only diversify stock exposure but also diversify overall economic exposure. Ex-US stocks provide diversification to US stocks and US bonds in combination, such as the classic 60/40 portfolio.

What About Emerging Markets?

It’s unfortunate that the JST dataset includes no coverage of emerging markets.

Here’s another long-term GDP plot, like the chart at the top of this article. This one includes Latin America. Note that it uses the same Maddison Project GDP data underlying the GDP figures in the JST dataset.

https://bradjballard.com/2016/05/01/percent-of-global-gdp/

As the GDPs of the US and Europe have shrunk, the GDPs of China and India have grown. Latin America grew for a long time but then stumbled in the 1980s.

The problem for asset allocation is that Emerging Market stocks simply were not investible before the 1980s. Heck, you couldn’t even get a US stock market index fund in the 1970s. Therefore, any recommendations for modern investing need to take into account the completely different structure of markets prior to the 1970s.

Now What?

Now I need to reconcile a 55 yr-study showing zero allocation to Ex-US stocks with a 121-yr study showing an allocation to Ex-US stocks on par with the US for risky portfolios and relatively larger for lower-risk portfolios. Let me sit with that for a while. I’d love to hear your thoughts in the comments.

Leave a comment

Subscribe now

How does becoming the world’s reserve currency affect returns for domestic vs. foreign bonds and bills? How does the impact of foreign exchange risk make diversification across countries more or less attractive? Are some developed countries competing for capital more effectively than others? Are some real estate markets more attractive than others as multi-generational investments? Let’s dig into 120 years of asset returns across 16 countries to find out!

120 Yrs of Developed Country Asset Returns

Last week’s article presented and discussed 120+ years of stock market returns from 16 countries, as reported in the JST dataset:

Other than the collapse at the end of World War II, the stock market data were fairly complete. The JST dataset also includes returns for housing, bonds, and bills. These additional datasets have more holes than the stock market returns. Rather than attempting to fill the various single-country holes, I’m treating those missing returns as zero but leaving those countries out of the GDP-weighted Ex-US index returns when they have no data.

All these asset class returns are reported in nominal local currencies, which I then convert to USD given each country’s annual exchange rate. As I’ve continued working with this JST dataset, I’m seeing the importance of examining the FX returns themselves, which are common to all the Ex-US asset classes. The major collapses show up more strongly in FX than in local currencies.

FX Rates

The chart below calculates the GDP-weighted cumulative foreign exchange (FX) returns for the 15 non-US countries.

GDP-weighted FX returns fall by 90% (!) vs. the US Dollar for the full Ex-US index. The first collapse comes from WW I and its aftermath; the second collapse coincides with WW II. During the postwar rebuild, the Ex-US index moderately out-performs the US dollar in aggregate, though it never regains the ground lost in the two world wars.

The USA emerged from these world wars as the unquestioned world reserve currency, a status put in place officially by the Bretton Woods Agreement of 1944 where major world currencies pegged themselves to the US Dollar within some range, while the US dollar was theoretically pegged to gold. That peg to gold broke in 1971. Note the flatness of the chart above from 1944 to 1971.

https://www.federalreservehistory.org/essays/bretton-woods-created

Looking at individual countries reveals some more extreme situations.

Japan’s currency collapsed over 99% when World War II ended in defeat. Post Bretton Woods, the Japanese Yen showed more strength than the US Dollar.

Australia is a more typical situation, dropping a bit into the Bretton Woods era and then trading more freely post 1971.

Germany’s FX situation was even worse than Japan’s. Post World War I, the Weimar Republic led to hyperinflation of 12 orders of magnitude (falling by 90% twelve times in a row). Following that experience, the German currency simply went to zero after World War II. The FX rate goes up after that recovery as the German FX index resets to 1 after going to literally zero.

The Weimar Republic hyperinflation is known for people using wheelbarrows to transport their nearly worthless currency to shop. Legend has it that one shopper had his wheelbarrow stolen while the thief left the mound of currency behind.

https://coinandempire.com/money-systems/currency-system-behind-hyperinflation

France got hit hard as well by the two wars, but its currency held its ground after each wartime drop vs. the US dollar.

Comparing the UK, US, and Switzerland sheds light onto how reserve currency status gets passed from one country to the next. The British Pound drops after World War II, but not as much as most other currencies. After Bretton Woods, it slowly devalues vs. the USD.

Switzerland shows just the opposite result. Neutral Switzerland, which avoided wartime devastation, saw its currency rise because of its safe haven status.

https://www.swissinfo.ch/eng/swiss-financial-sector-must-sink-or-swim/8441076

Post Bretton Woods, the Swiss Franc was the only currency of the 15 to appreciate significantly vs. the US Dollar. The Swiss Franc outpaced the US Dollar by more than the US Dollar outpaced the declining British Pound.

Most Northen European currencies held fairly steady. Finland dropped the most post each war, while Belgium suffered from the horrific trench warfare along the Western Front during World War I.

Southern European currencies showed much less strength. Italy dropped the most, as it was a defeated Axis power in WW II. Portugal dropped more in WW I than in WW II. Spain got hit by the Spanish Civil War of the 1930s. After the Bretton Woods Agreement fell apart, all these Southern European currencies declined further.

Bills

Short-term bill returns in USD are tied very closely to the risks of their FX rates. Based on these 120 years of historical returns, there has not been much reason to hold bills outside the US if you’re a US citizen, as the short-term returns simply do not outweigh the currency risks.

Not surprisingly, the big losses come with each of the World Wars. The Ex-US index losses would be even greater if we had returns for all the years for all the defeated countries. As currently constructed, the Ex-US index simply leaves out the countries with missing data and grosses up the contributions of the remaining countries. In essence, this is an active Ex-US index that excludes broken economies. Even so, the only period showing outperformance vs. the US is the postwar rebuild during the Bretton Woods era.

German bills get hit hard but not as badly as the currency itself as interest rates must have been quite high. France keeps up with the US during the postwar period.

UK bills do not keep pace with US bills, largely because of the currency risk.

Looking at bill returns, the Swiss give back some of their currency strength with negative short-term rates starting in 2015. Yes, from 2015 to 2022, you had to pay interest to keep your money in a Swiss Bank.

https://www.reuters.com/business/finance/swiss-national-bank-cuts-interest-rates-zero-2025-06-19/

Bonds

Bonds add duration risk on top of the interest rate risk and FX risk.

The full Ex-US index history shows that bonds add risk during the wartime period but offer additional return during the postwar recovery. The collapse of Bretton Woods brought Ex-US bonds closer to parity with total US bond returns, leading to similar performance after that.

German bunds collapsed to worthless during the Weimar republic. Post WW II, West Germany looked much like France from a bond perspective.

Swiss bonds added to the outperformance of the Swiss currency. UK bonds also kept closer to US bond returns than did the British Pound itself.

Northern European bonds show much the same pattern as the underlying currencies. Danish and Swedish bonds outperformed for most of the period.

Southern European bond interest rates mitigated some of the currency risk, but none of them were great long-term investments compared to US bonds.

Real Estate

The JST dataset is perhaps best known for its very long-term real estate returns. They define real estate returns as rent + capital appreciation. Going forward, it may be hard to find ETFs to replicate this return series as only a tiny fraction of real estate is publicly traded as some form of a security. But it’s interesting to see real estate represented more accurately as an asset class than just commercial property REITs.

Unlike bills and bonds, Ex-US real estate shows solid outperformance vs. the US over the full period. European land has high productivity, desirability, and value. However, this is not an index that buys and holds all countries in all periods; recall that certain countries are excluded when they have missing data, thereby sidestepping some big losses.

Some of the Ex-US index outperformance comes from simply excluding losses on Japanese land for most of the early history. But once post-war appreciation kicks in, Japan drives much of the Ex-US index performance. Growing up in the 70s and 80s, the stories about the value of Japanese land were legendary, including how multiple generations managed to live so closely packed in together in tiny apartments.

Australia’s full history looks closer to the US than I expected given the stories I’ve heard regarding outrageous rates of return on housing in Australia. The housing returns no doubt look higher denominated in Australian Dollars rather than USD.

France rebuilt effectively after World War II and caught up with US real estate returns. Germany would look worse if we had meaningful data for the WW II period and post-partitioning years. Again, Germany gets excluded from the Ex-US index during this missing data period.

Swiss real estate tracks the US more closely than its currency, bills, and bonds. My understanding is that it’s harder for outsiders to invest in Swiss real estate than in many other countries.

I’m a little surprised to see how much UK real estate trails the US considering the outrageous value of London trophy real estate. Perhaps this is because ownership is structured differently in the UK than in the US. I’m well outside my expertise here but I think feudalism left an echo in current land ownership patterns and home ownership is more like a long-term lease from the nobility. If any of you can explain the nuances of UK real estate vs. US real estate to me, let me know in the comments!

Leave a comment

Northern European real estate returns follow the same basic pattern as their respective FX returns.

Southern European real estate outperforms FX because of the extreme desirability of the Mediterranean climates of Italy, Portugal, and Spain. These are some of the most attractive estates on the planet in terms of climate, food, and lifestyle. Southern European real estate has also likely benefitted from the increased ability of Europeans to move around freely within the EU.

Putting it All Together

What’s hiding in this data is what happens if/when the US is no longer the global reserve currency. It will slip behind, as the UK has gradually slipped behind the US. And some other country will pull ahead, much as Switzerland has.

Next week’s article looks at asset allocation across these four asset classes, US and Ex-US. We will see how those learnings provide a new perspective on the 55-yr monthly study for guidance on US vs. Ex-US stock allocation.

Subscribe now

https://www.oerproject.com/OER-Materials/OER-Media/Images/WHP-Maps/1945-layer-3

The economic rise and fall of individual countries may span centuries, but when major changes occur, they can come quickly. Looking at 120 years of data yields significant insight into both the opportunities and existential risks of investing in single-country stock indices. What can we learn from the empire leadership transfer from the UK to the US? How much damage did the World Wars and Great Depression inflict, and which countries suffered the worst? How fast did recovery come, and how big did the Japan bubble get? Let’s find out.

Investment Biker

My interest in the rise and fall of single-country economies started with my reading of Investment Biker by Jim Rogers, published in 1994, which I fittingly picked up on a road trip at Powell’s City of Books in Portland, Oregon. The book tells the story of Jim Rogers and his girlfriend riding custom motorcycles across every continent, the long way, to research the global economy firsthand.

https://www.drvijaymalik.com/book-review-investment-biker-around/

I’ve always been a geography nerd, but this book was the first to introduce me to the storied history of the Silk Road as well as the allure of Uluru in the Australian Outback.

Jim Rogers would visit the black market currency exchange as his first stop to get a pulse on the local economy. The greatest long-term investment opportunities occurred in the countries that were bottoming out and preparing for a multi-decade rebuild.

This book was the first time I heard some famous quotes from Baron Nathan Rothschild that enabled him to build multi-generational wealth.

Emulating Baron Rothschild

Jim Rogers was a big believer in “buy on the sound of cannons and sell on the sound of trumpets.” War-torn, chaotic economies provided generational entries on multi-decade compounders that ultimately become the new blue chips in the country.

https://www.linkedin.com/posts/vishal-baxi-cfp%C2%AE-qpfp%C2%AE-b9440530_finance-wealthmanagement-mindset-activity-7434115052519051264-IEOO/

Having seen the repeated wartime devastation of his own European homeland, Baron Rothschild is also known for saying “buy when there is blood in the streets, even if it is your own.”

Diving Into the JST Dataset

Last week’s article introduced a “JST Dataset” going back to 1870 for sixteen countries, mostly in Europe.

Interestingly, that start date coincides with the Franco-Prussian War connected to the unification of Germany. This is the war that motivated my great grandfather’s family to flee Alsace-Lorraine for America. Different brothers were born either French or German in the same house depending on who won the most recent battle.

https://en.wikipedia.org/wiki/Franco-Prussian_War

Some Countries Go to Zero

Over this extended period, we see that some countries’ stock markets do indeed go to zero. One European war followed another, and then another. World War II caused the most disruption. Data are problematic around 1945-46 for Germany and Japan.

In Japan the stock market was closed for several years and the JST research team elected to leave the returns blank. In Germany, losses (of surviving companies) were large in both local stock market and foreign exchange terms. For my purposes, from the perspective of a US-based investor, I’m considering both Germany and Japan a total loss in USD in 1945 and then re-investing during the annual rebalance when the stock exchanges opened again.

The German returns going forward post 1945 are for West Germany following the partitioning of Germany, until reunification in 1990. The good news is how well both Germany and Japan perform after the post-war reconstruction. As Jim Rogers and Baron Rothschild pointed out, buying surviving enterprises in a country at the bottom after a complete wipeout can yield massive long-term returns.

GDP Weighting

The JST dataset has some well-known problems with units for nominal GDP. Based on local sources, the units can vary over time and are not well documented. The best practice for most research on these long-term returns is to use GDP per capita * population. The per capita numbers are based on the Maddison Project Database which adjusts for purchasing power parity. I had never heard of this project before, but apparently, it’s popular with macro economists.

https://www.rug.nl/ggdc/historicaldevelopment/maddison/

Recall from last week’s article that Northern Europe had much better returns than Southern Europe over the full 150 years. GDP weighting leans into this outperformance when constructing an Ex-US stock returns index.

https://www.visualcapitalist.com/mapped-europes-gdp-per-capita-by-country/

US vs. Ex-US Performance

Although the dataset starts in 1870 for some countries, we don’t get consistent data across all 16 countries until 1900. This gives 120 years of consistent returns.

Over the full period, US and GDP-weighted Ex-US track each other fairly well. Ex-US suffers bigger drawdowns for the World Wars, while US got hit a bit harder in the Great Depression of the 1930s.

Crisis and Recovery Performance

Zooming in on the biggest global crisis period (WW I, Great Depression, and WW II), it’s fascinating that by the depth of the Depression in the mid-1930s, the US and Ex-US indices fall right on top of each other. With the World Wars largely being fought off US soil (other than Pearl Harbor), the Ex-US countries absorbed significantly more wartime damage both times.

With rebalanced investment in 1948, Ex-US economic and stock market recovery outperforms the US, peaking with the top of the Japan bubble in 1989, also coinciding with the fall of the Berlin Wall.

Ex-US Index vs. EAFE

How does the GDP-weighted 15-country Ex-US index compare to MSCI’s EAFE Index, launched at the end of 1969?

Until 1989, both Ex-US and EAFE track each other quite closely. From that point onward, EAFE steadily trails this GDP-weighted Ex-US index. Both outperform the US index over this initial 19-year period.

Post the Japan Bubble peak of 1989, the US consistently outperforms, though the gap narrows around the time of the Global Financial Crisis of 2008.

As the specific countries in the EAFE index and their weightings change, its performance vs. these GDP-weighted 15 Ex-US countries steadily declines. This could be from the countries added and subtracted as well as cap weighting and other risk exposures.

Individual Countries

Let’s look at the individual countries now. The spread of returns across the 16 is quite large over the full 120 year period without rebalancing. Tracking the full period separately for each country, the US comes out on top. I’ve included the US for visual reference on all the regional plots that follow. Most countries fall far below the annually rebalanced Ex-US index and EAFE.

The JST dataset features only two countries outside the US and Europe: Australia and Japan. Australia tracks the US quite closely over the full period. Japan’s economy is utterly devastated by World War II, but the post-war recovery is just as remarkable. After catching up with the US in 1989 at peak valuation, Japan slipped behind steadily.

France and Germany show the importance of assumptions in rebalancing. Like Japan, Germany goes to zero in US Dollar terms and then gets reset at 1. Germany falls again as the nation is partitioned (unlike Japan), followed by a strong recovery of West Germany.

France never goes to zero, but the destruction to the stock market lasted for decades. Without a reallocation of funds at the end of WW II, France lags behind every other country. Rebalancing details matter.

Switzerland and the UK fared much better and follow similar trajectories until their recent divergence. 1900 was around the peak of the British Empire, and over the full period, the UK continued to fall behind its former colonies the United States.

Some of the best performing countries are in Northern Europe, particularly Scandinavia. The US pulled ahead of all these countries in the 1950s and 60s, but Denmark closed the full gap by 2020. Norway lags its Scandinavian peers, with Belgium coming in at the rear of the Northern Europe pack.

Southern Europe performs poorly as a regional cohort. Italy, like France, was a major WW II battleground and lost several decades. Spain has stayed ahead of Italy while Portugal has lagged behind.

Pre-1900 Performance

Although the history for about half the countries starts in 1900, several countries go back to 1870. Both the US and UK have currency-adjusted returns available beginning in 1872.

Comparing the UK and the US from 1872-1900, it’s clear that the UK is the established economy and the US is the emerging market. US stock market returns are higher over the full period, but substantially more volatile.

What was going on in those early years? The Panic of 1873 caused global economic disruption much like the Global Financial Crisis of 2008, but without government bailouts. 100+ years ago, banks and businesses simply failed during these major busts. The stories you see dramatized in those early black and white movies were based on actual bank panics. In 1873, many railroads, the speculative Internet companies of their day, went bankrupt. The crisis continued through 1879.

https://home.treasury.gov/about/history/freedmans-bank-building/financial-panic-of-1873

Looking at the full 150 year period, the US took the lead from the UK after this early financial crisis and never looked back. The Great Depression of the 1930s caused more volatility in the US than in the UK, but not enough for the US to give back its lead.

The transition between reserve currencies has historically taken multiple decades and involves changes in relative volatility as well as returns.

Next Steps

I’m planning to explore the other major asset classes in this rich multi-national dataset. I’ve never looked at country-by-country returns for real estate. Next week’s article will compare US and Ex-US indices on real estate, bills, and bonds over 100+ years.

Subscribe now

https://www.macrohistory.net/

What do you do when 55 years of historical returns suggest that it’s just not worth investing in stocks outside the US? You broaden the frame of the question. If the result comes from the US being the world’s reserve currency, how did ex-US stocks perform before the US became the world’s reserve currency? To answer this question, I’ve found a much longer historical data set, going back 150+ years to 1870. What can we learn from this much extended history? What happened to the UK as their empire faded? Are there any countries that consistently outperform the US?

Appraising an Incomplete Model

My most popular article to date, “Does it still make sense to invest in stocks outside the United States?” asked more questions than it answered.

Based on 55 years of historical stock market data, I was unable to make the empirical case for investing outside the US. But what about the next 55 years?

Expanding the Model Frame

As a professional model builder, it seemed clear to me that the correct, even “optimal,” amount to invest in Ex-US stocks is not zero going forward. The next logical question is what does the initial model miss because of its framing?

My asset allocation strategy is built around ETFs, so the first idea that occurred to me was to look at the geographic distribution within global factor ETFs. Unfortunately, global factor ETFs are rare, with nothing compelling listed with the United States. I also realized that index providers and ETF constructors might be normalizing to match cap weighting or some other artificial constraint. I could build my own quant factor funds, but I’m not signing up for that project right now and would not have the data license to redistribute recommendations anyway.

I asked Grok a few questions about typical ways asset allocators override historical optimizer results and got reminded of approaches like Bayesian shrinkage, Black-Litterman (including personalized forecasts), and creating synthetic data. But where would I be getting those forward-looking estimates and synthetic data, other than just making stuff up?

Then I thought, if I don’t have reliable forecasts, what if I go back further in time? Over long enough periods, even the mightiest empires rotate into and out of power.

Why Look at 100+ Year Old Data?

One of the best analogies for what might happen to US dominance is what happened to UK dominance, as the UK was the global reserve currency most recently before the US. UK stock market data happens to be some of the easiest to get and highest quality, precisely because they were the dominant global power before the US.

For those of you who weren’t paying attention in history class or have forgotten, there was a long period when sun never set on the British Empire:

https://www.britannica.com/place/British-Empire

Going back 100 to 150 years takes us to the peak period of the British Empire.

Where to Get 100+ Years of Data?

I already knew some places to check for long-run stock data. For each source, there’s some catch.

• Ken French: US stock factor data go back to 1926, but Developed Ex-US International only starts in 1990 with some countries back to 1975

• The best known Ex-US index, EAFE from MSCI, starts in 1969

• Ibbotson Stocks, Bonds, Bills, and Inflation (SBBI) US coverage starts in 1926; international data matches the MSCI EAFE launch date

• One of the oldest global mutual funds, Templeton Growth Fund, only goes back to 1954, with the more pure-play Ex-US Templeton Foreign Fund launching in 1982.

• Global Financial Data has great data back hundreds of years, back to the 1200s in Europe, but I can’t afford their institutional investor data license prices.

• DMS/UBS Yearbook has great global coverage but they’re not providing the full dataset for free

Then Grok pointed out this dataset to me:

The JST Dataset

https://www.macrohistory.net/database/

Jordà, Schularick, and Taylor put together a very long-term international database covering similar ground to the well-known Stocks, Bonds, Bills, and Inflation (SBBI) Yearbook, but available for free and going back 150 years. What a fantastic contribution to academic and independent research. Thank you!

The team became known for their paper “The Rate of Return on Everything”: Òscar Jordà, Katharina Knoll, Dmitry Kuvshinov, Moritz Schularick, and Alan M. Taylor. 2019. “The Rate of Return on Everything, 1870–2015.” Quarterly Journal of Economics, 134(3), 1225-1298.

I hadn’t heard of the team or the paper until just recently. Institutional investors already have access to sources such as Global Financial Data and DMS. My earlier searches for this kind of data did not turn up this database, possibly because it’s better known for its housing and other macroeconomic data than for its stock and bond returns.

I downloaded a free version of the paper from the National Bureau of Economic Research website.

http://www.nber.org/papers/w24112

What’s Great About This Dataset?

This dataset is potentially great for asset allocation research because it has four core assets (bills, bonds, equity, and housing) across 16 countries, compiled in a consistent manner across a relatively consistent timeframe.

It’s simple to download in one clean Excel spreadsheet, containing many other columns such as GDP and exchange rates vs. the US. Since the paper was published, the dataset has been updated with two additional countries: Canada and Ireland.

What’s Missing?

The JST dataset does not have much on Developed Asia, but Japan and Australia are a great start. Hong Kong has been trading stocks since at least the 1890s. The Singapore stock exchange only goes back to the 1970s. For that first 100 years, it seems Hong Kong is the main omission for Developed Asia.

The JST dataset has nothing on Emerging Markets, but that’s fine for my purposes as my post-1971 study does make a small allocation to Emerging Markets. What I’m really looking to explore in detail is US vs. Developed Ex-US and this JST dataset appears spot on for that purpose.

Some Highlights from the Return of Everything

Average real equity rates of return have been increasing, from 6.67% for the full period to 8.30% post 1950 to 10.78% post 1980.

In USD terms, the big equity winner by far is Finland, returning 12.08% in nominal terms beyond US inflation. The worst performer in USD terms is France, at only 5.16%.

Here’s the rank order of risky returns by country, combining both equities and housing, putting the USA in the middle of the pack:

The Nordic countries really dominate the list of risky returns, with Southern Europe accounting for much of the bottom.

The study classifies stocks and real estate as the risky assets. Housing shows much lower volatility, but the housing market is far less liquid.

Australia barely edges out the USA in terms of equity Sharpe ratio, with Finland having higher risk to go with its higher returns.

The “safe” assets, bonds and bills, do not always provide safety. During both WW I and WW II the returns for both bonds and bills went negative in real terms.

I find it interesting how the authors break out monetary regimes:

• Gold standard: 1870-1913

• Amended gold standard: 1919-1938

• Bretton Woods: 1946-1973

• Floating exchange rates: 1974-2015

Note that these periods leave out WW I and WW II, analyzing those separately.

Equity returns (geometric mean) are within 1% across these regimes, though volatility has increased as all currencies have been debased.

Additional Long-Term Data Available in USB DMS Yearbook

There are other very long-term studies of developed countries, most notably the Dimson, Marsh, Staunton dataset from UBS.

https://www.ubs.com/global/en/investment-bank/insights-and-data/articles/global-investment-returns-yearbook-2026.html

“Coverage of the full Yearbook: In the full 310-page Yearbook, Professor Paul Marsh and Dr. Mike Staunton from London Business School and Professor Elroy Dimson from Cambridge University assess the returns and risks from investing in equities, bonds, cash, currencies and factors in 35 countries and in five different composite indexes since 1900. The Yearbook has 13 chapters.”

The challenge for me is that I can’t quote any of this data “without express written permission from the authors.” So, if you’d like to see it, you’ll need to download the yearbook summary yourself.

I found Figure 8 to be interesting, showing the evolution of relative GDP over time. You can see China shrink and then expand again. The Japan bubble of 1989 is on full display. Interestingly, the US share of global GDP appears to peak around 1950.

Looking at the 8-10% GDP share of the bottom 23 countries, I think it’s actually more valuable to have the JST returns going back an additional 30 years to 1870 than to add a handful of smaller countries since 1900.

Figure 94 gives a nice overview of equity factor returns since the 1920s. Momentum wins over all years, followed by low volatility, value, size, and income. Clearly, momentum is not a new phenomenon.

Next Steps

Here are my plans for this 150 year history of multi-national equity returns:

1. Build an Ex-US index for comparison, based on GDP weightings

2. Look for periods of outperformance for Ex-US vs. US and seek explanations

3. See what happened to the UK over time and if there are any analogies to what might happen to the US

I’d also like to build an efficient frontier from this 150 year dataset, showing optimal allocations to bills, bonds, equities, and housing. I’ll be able to break each into US and Ex-US components. Comparing the results to my 55-year study should yield some insight into very long-term Ex-US investing.

Please subscribe to follow along with the new long-term investment insights!

Subscribe now

“If I go, there will be trouble
And if I stay, it will be double”

Strategic Asset Allocation seeks to increase risk-adjusted return by providing effective diversification during stock market crashes. Yet some investors strive to do better, following a Tactical Asset Allocation approach to time market downturns and aggressively rotate in and out of large stock allocations. What are the most common methods for adapting asset allocation to differing market conditions? Do the potential gains outweigh the model risk, transaction cost, and psychological challenges?

Disclaimer: this post is a partial review of tactical and adaptive asset allocation strategies and is not meant to provide specific financial advice. Please consult a licensed financial advisor if you seek advice for your own personal situation.

Team Stick: Self-Adapting Allocations

Even the typical fixed allocation approaches are not completely static allocations. At the very least, fixed allocations benefit from regular rebalancing and dollar cost averaging (DCA). Glidepath approaches used by target date retirement funds move along the efficient frontier to reduce risk as retirement approaches. Risk parity adapts to changing volatilities and correlations. More advanced antifragile portfolio sleeves seek to benefit from sudden crises.

DCA, Value Averaging and Rebalancing

It’s easy to find DCA calculators online. More advanced versions also take market conditions into account, increasing buying at more attractive prices. For instance, the ThinkOrSwim website site compares various approaches: DCA, value averaging, signal based, and VIX adjusted, explaining the pros and cons of each. There are circumstances in which each strategy wins. Not surprisingly, paying attention to market conditions adds a bit of an edge to blind buying.

https://tosindicators.com/research/dollar-cost-averaging

All these strategies are examples of volatility pumping: taking advantage of the natural ups and downs of the market to get better entries in the long term. Periodic rebalancing enhances DCA buying with regular profit taking. My Volatility Pumping article explores this phenomenon in more detail.

Vanguard: Glidepath Target Funds

Traditional asset allocation teaches that those with long investment horizons should take more risk than those nearing or already in retirement. Most large wealth management firms have established a “glidepath” that guides recommended allocations from 90/10 stocks bonds to 60/40 over time. Here’s the glidepath for the Vanguard institutional target date funds. You can see the specific allocations at critical transition ages on the website.

https://workplace.vanguard.com/investment/strategies/tdf-glide-path.html

Since this concept was introduced long ago, many analysts argue that older investors need to take more risk now than would have been recommended 50 years ago. More advisors are starting to agree that 60 year old investors may need to take more risk than 60/40 given the inflation and currency debasement pressures we’re facing, along with the prospect of much longer lifespans and more active retirement lifestyles.

Ray Dalio: All-Weather Portfolio

Allocations can be set by adaptive algorithms rather than by pre-determined percentages. Perhaps the best known of these approaches is risk parity, which seeks to allocate the same amount of risk to each asset rather than equal weighting the allocations themselves. Risk parity also accounts for correlations among the asset classes, using some kind of risk model.

Here’s a quant website that demonstrates risk parity and compares it with simpler strategies like weighting by inverse volatility:

https://quantdare.com/risk-parity-versus-inverse-volatility/

Ray Dalio’s All Weather Portfolio has established an outstanding historical track record using risk parity. However, one important observation regarding the historical success of risk parity is how it specifically benefitted from 40 years of higher allocation to bonds as interest rates were coming down from their Volcker-era highs near 20%.

Chris Cole: Artemis 100-Year Dragon Portfolio

The main drawback of a fixed allocation portfolio is its inability to respond to sharply shifting economic conditions. One creative, yet hard to implement, solution to this problem is adding a portfolio sleeve that strongly benefits from the economic chaos that descends every decade or two.

Chris Cole and the team at Artemis sought to build a 100 year portfolio. Where would you put your family’s multi-generational money if you couldn’t touch it for 100 years, other than regular rebalancing? The resulting story is far more interesting than the typical dry quant whitepaper, full of mythological metaphors (“The Hawk and the Serpent”) regarding the repeated destruction and recreation of economic models, much along the lines of the Fourth Turning. This video interview is well worth watching in full. You can download the accompanying whitepaper for your own reference, but they don’t give permission to cite it directly.

Like many other quant funds, the Artemis team puts a large allocation into commodity trend following to provide robust diversification. They also include gold to fight currency debasement. The most novel and mysterious sleeve is called “long volatility.”

Long volatility seeks to benefit from what Nassim Nicholas Taleb calls antifragile. What strategies and assets thrive on chaos? Tail risk funds work in the short term, but the insurance costs are too high for a 100-year hold. I explored the pros and cons of tail risk funds in this article:

I frankly don’t know the specifics of what Artemis is holding in this long volatility sleeve but suspect there is some heavy financial engineering involving options strategies.

Passive antifragile assets are hard to find. One of my main long-term quests as an ETF investor is to find some ETF that provides antifragile returns but doesn’t bleed back all those gains (and more) during normal periods. If you’ve seen anything like this, please let me know!

Leave a comment

Team Switch: Top-Down Global Macro and Bottom-Up Momentum

The more common approach to addressing economic cycles and occasional chaos is to attempt to modify the portfolio based on prevailing economic conditions. These approaches fall into two broad camps: top-down macro and bottom-up momentum.

GMI: Macro Investing Tool

Followers of Real Vision on YouTube are familiar with hedge fund advisors Raoul Pal and Julien Bittel, alumni of Goldman Sachs and Swiss private bank Pictet. For decades they’ve been selling a newsletter called Global Macro Investor. One of the core offerings is a Macro Investor Tool that identifies macro regimes and investments that most benefit from those regimes.

Several macro indicators determine the macro “season.” Different countries can be in different macro seasons at the same time. Various correlation tools determine what assets and tradable instruments benefit the most from each season.

Each report comes with dozens of pages of correlation charts. The part that worries me, based on my own training in predictive modeling at MIT and Stanford, is how they arbitrarily fit a different lead or lag to each chart to get the maximum correlation. To me, this smells of data snooping. On the other hand, I’m delighted they are so happy to rely upon the Thomson Reuters Datastream tool I used to sell to quants.

The GMI team has made a lot of money from their newsletter business. There are many global macro hedge funds around the world using similar approaches, so the macro rotation idea works well enough to persist across multiple economic cycles.

Stansberry Rotation Model

Other newsletters targeting self-directed investors offer similar macro rotation approaches. Doc Eifrig at Stansberry Research developed an “intelligent retirement model” that uses top-down indicators to flip between various model portfolio conditional allocations. Their tagline for the approach is “Don’t time. Tilt.” The publicly disclosed track record covers a very short time horizon.

https://stansberryresearch.com/health-wealth-bulletin/you-can-do-better-than-conventional-investing-wisdom

As a subscriber to the full suite of newsletters, I have personal access to the model. I would not characterize the changes between the model portfolios as mere tilts. There are times when they recommend selling all stocks to move to cash. That’s more like market timing to me than tilting. The sudden rotations are too aggressive for me to shift my core portfolio allocations that much, particularly using a system someone else designed.

Meb Faber Tactical Asset Allocation

For a better disclosed example of how these kinds of shifting allocations work, let’s review Meb Faber’s approach, which he has been gracious enough to share in full for free with the general public via his website. I’ve frequently discussed Meb’s Global Asset Allocation book. This is his Tactical Asset Allocation study. There’s real beauty in rules this simple, as they’re less likely to be overfit to past data.

https://mebfaber.com/wp-content/uploads/2016/05/SSRN-id962461.pdf

That certainly smooths out the drawdowns. He’s got another strategy that uses trend following on five assets, each of which is either fully invested or in cash.

The question, once again, is if the potential drawdown reductions merit the movement of a full portfolio out of stocks and into cash based on trailing 10 month performance. The next study explicitly accounts for those considerations.

Adaptive Asset Allocation Book

The book Adaptive Asset Allocation comes from the quant team at ReSolve Asset Management. Like Meb Faber, they clearly demonstrate that asset momentum outperforms and can underpin a successful tactical asset allocation strategy. In the figure below, they enhance six-month asset momentum with a min vol weighting and then account for transaction costs.

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2328254

This paper and the broader book detail one of the most realistic quant studies of adaptive asset allocation I’ve seen in broad public circulation.

I had the great fortune to meet one of the authors, Rodrigo Gordillo, at a conference. I asked him if they were getting much customer traction with the adaptive asset allocation approach, and he said some, but most people don’t want to be switching up their portfolios so much. The ReSolve team is currently more focused on marketing a concept they call return stacking than on rotation strategies, even after writing one of the best books on adaptive asset allocation.

Return stacking uses mild leverage to enable “free” exposure to commodity trend following on top of more traditional holdings like stocks and bonds. Once again, we’re seeing the wealth management market voting for fixed exposure to commodity trend following rather than attempting aggressive rotation of allocations.

Pros and Cons of Switching

Between the top-down macro and bottom-up momentum approaches, my personal quant background favors the long-term momentum backtests from Meb Faber and the ReSolve team. I personally don’t have faith in the underlying data required to follow the macro indicators and lead/lag correlations underpinning top-down macro season rotation strategies.

What Makes Backtesting Rotation Strategies Hard?

There are a limited number of observations involving huge crashes of the stock market. They average about once per decade, but the wait can be much longer or shorter. Some bear markets grind on for many years, while others end quickly. It’s so easy to overfit a model to the particulars of an individual cycle.

Why is it Hard to Execute Rotation in Practice?

Beyond model risk, it’s a huge ask to completely sell a large stock portfolio to 100% cash because a model flipped. Transaction costs are real, both financial and psychological. For taxable accounts, there are also capital gains taxes to pay. Frequent churning turns long-term buy-and-hold gains into short-term trading gains at higher marginal tax rates.

Trend-following systems are full of incorrect whipsaw trades, as I’ve shown in earlier posts. Getting caught two steps behind is disastrous for the mental health of an investor and may lead to abandoning a system or engaging in highly destructive revenge trading.

Case Study: the Bitcoin Cycle

Let’s look at the Bitcoin 4-year cycle as an example. Bitcoin has a halving every four years baked right into the code, so that’s a pretty strong rationale for cyclical behavior. A 4 year cycle is also much shorter and more regular than the typical stock bear market cycles with 50% drops at highly irregular intervals. But does trading the Bitcoin 4-year cycle work in practice?

Even though “everyone knows” there’s a four-year cycle, few people profitably trade on it. Selling out and buying back are separate decision points, and it’s possible to get the timing of both wrong on any given cycle.

The large suite of “Bitcoin top indicators” that had been overfit to previous cycles did not fire at the last peak, leading the indicator builders to deny that the cycle ended, yet the bull market finished just like clockwork from a timing perspective. I would not be surprised at all of many/most of the “bottom indicators” fail as well this time. I’ve seen more people lose money than make money trying to time the Bitcoin cycle.

My Plans

For my own portfolio, I’ve found it’s easier to operate a core-satellite approach where the core follows a robust fixed allocation and various satellite portfolios aim to take advantage of macro conditions. I don’t have access (yet) to any magic “antifragile portfolios,” but I do have a long track record of extracting upside from different asset classes as they rotate into favor.

For now, I’m planning in my core retirement portfolio to stick with an allocation until and unless I can convince myself that the effort, cost, and additional risk of switching are clearly merited.

Subscribe now

A decade before Lady Gaga dialed in from the dancefloor, I had a front row seat at the Telecom Bubble. We all had a sense that broadband Internet and wireless phones were about to transform our lives, and the next twenty years indeed proved to provide profound change.

As I was a telecom analyst living in Silicon Valley and consulting with major telecom companies while the Internet and Telecom Bubbles peaked, you would think I had my investment portfolio impeccably sorted. As it turns out, I bought the very top of a generational bubble. Fortunately, position sizing discipline stopped me from going all in and protected most of my capital.

This week I share my top-buying experience as a guest author at Mental Mosaic. Thanks to for inviting me to be a Mosaic Minds Contributor. Please check out the post to see how today’s AI stocks may have some traits in common with the telecom darlings that dropped 98%+ from their bubble peak.

Mental Mosaic

Mosaic Minds #5: Thinking of buying an AI stock?

Elon Musk became the world’s first trillionaire – for around a few days until he dropped down to billionaire status again, then back up to trillionaire, again. And who knows where he’ll end up when this piece is published…

Read more

a month ago · 3 likes · 1 comment · Hari A. and Stephen Malinak

https://www.gwcindia.in/gigapro/blog/value-investing-vs-momentum-investing-key-differences/

Both Value and Momentum factors beat their underlying benchmarks consistently. The very long track record (55+ years) suggests that Value adds returns with lower risk than Momentum. Looking over the most recent period, and indeed the past 40 years, the tables have turned strongly in favor of Momentum. What is going on here, and will this phenomenon persist?

Factor Investing

If you’ve been following my asset allocation research, you’ve seen that stock factor ETFs significantly outperform their underlying cap-weighted indices.

Looking over the full 55-year period since 1971, Value increases returns by 1-2% while reducing average drawdowns by 1-2% as well. Based only on those stats, any investor should prefer value stocks to the base index, regardless of their personal trade-off between risk and return.

Over the same period, Momentum adds significantly more returns, 4-5%, but also increases the average drawdown by 4-5%. Thus, based on the long-term track record, Momentum represents a trade-off of increased returns for increased risk.

These very long-term results align with the general preference of academic researchers and institutional investors for Value over Momentum. But what happens when we dig deeper?

What is Value?

Value is complex to measure and comes in two major variations: intrinsic and relative. Intrinsic value requires dozens or hundreds of assumptions to calculate a robust discounted cash flow model. When I was a fundamental analyst, I spent months building intrinsic value models for single companies (or even individual business units).

Relative value can be calculated by looking at several different valuation ratios. Our highly alpha-producing StarMine Relative Value (RV) model combined Price/Book, EV/Sales, EV/EBITDA, Price/Earnings, Price/Cashflow, and Dividend Yield + Buybacks. All of these considered both historical data (past 12 months) and forecasts for the next 12 months.

Valuation camps have splintered much like religious factions. Theoretically they have similar beliefs and are all trying to achieve the same end goal, but the infighting on methodology details can get intense. For example, it’s hard to convince hardcore dividend investors to take stock buybacks into consideration. Meb Faber and other analysts have repeatedly demonstrated that Shareholder Yield (combining dividends and buybacks) beats straight dividend yield, but the empirical results often fall on deaf ears.

https://www.osam.com/pdfs/research/_35_commentary_mar12.pdf

Given a long enough time horizon, value models beat their benchmarks. The problem is the opportunity cost. Value models will never recommend investing in high growth stocks like the Mag7 that offer much higher returns than value stocks.

https://www.yardeni.com/charts/us-stock-market/stock-market-investment-styles/magnificent-7

Quants have shown that revenue and earnings growth rates, on their own, are not reliable alpha factors. But Momentum consistently backtests well. Fund managers who successfully load up on growth stocks typically pick the same stocks favored by different variations of Momentum investors.

What is Momentum?

As Bitcoiners would say, Momentum means Number Go Up.

Momentum is preferred by growth investors, traders, and technical analysts. Again, there are variations in the details, but the main camps are trend following and price momentum.

Trend followers look at charts and draw various patterns and indicators to determine what is going up, what is going down, and what is chopping sideways. Quants build price momentum factors by looking at total return over various lookback periods and ranking stocks on relative price performance.

Value Strategies vs. Momentum Strategies

Many years ago, the higher upside from growth investing finally clicked for me when I read a column by the two brothers behind Motley Fool. I can’t track down the exact column I read, but I’ve found some interviews covering similar ground. Tom, the value-oriented brother, beat the S&P 500 by 7.8% per year. David, the growth-oriented brother, outperformed by 13.2% over the same period.

https://www.fool.com/investing/2018/10/22/200-stock-advisor-picks-6-conclusions-no-1-weve-do.aspx

What explains the long-term outperformance of growth picks vs. value picks? When you’re right on a value stock, you double or triple your money as it recovers to fair valuation. When you’re right on a momentum stock, you get a 10- to 100-bagger if the explosive growth continues. But more of these growth stocks go to zero as well, particularly if they burn too much cash too quickly.

Early stage growth takes this to an extreme. Most venture capital investments go to zero. But the top investments more than pay for all the losses, and the most successful VC-funded companies follow a power law distribution. I explored this in an article comparing digital assets to venture capital investments.

I’ve seen value vs. growth stock picking play out live as a subscriber to the full suite of Stansberry Research newsletters for several years. The top 10 Hall of Fame board is full of recommendations from the growth guys, but some growth analysts do so poorly over extended stretches that their newsletters get shut down. The value newsletters plod along more steadily, avoiding spectacular losses while posting less spectacular gains.

“Value and Momentum Everywhere”

Looking at huge numbers of investments in different asset classes all around the world over very long periods, quants find that both Value and Momentum strategies work and are typically complementary to each other. A paper called “Value and Momentum Everywhere” by the quants at AQR makes this case strongly across 8 combinations of asset classes and geographic regions.

https://www.aqr.com/Insights/Research/Journal-Article/Value-and-Momentum-Everywhere

We replicated similar results at StarMine in building our top-performing Value-Momentum model. The Value side combined Intrinsic Value and Relative Value. The Momentum piece combined Price Momentum with Analyst Revisions. Val-Mo was more robust to a wider variety of economic conditions than any of its underlying components.

The Methodology Debate

Although most quants recognize the symbiotic relationship of Value and Momentum, typical human fundamental and technical analysts prefer to stay in their own lanes in a somewhat stubborn human way. Fundamentalists seek certification as Chartered Financial Analysts (CFA) while technical analysts have their own Chartered Market Technician (CMT) credential.

Academics and fundamental analysts trained in business schools tend to prefer valuation approaches based on financial statements. Warren Buffett made a strong institutional investment case for Value, drawing upon influences such as Benjamin Graham who learned from the wreckage of the Great Depression in the 1930s.

Momentum is preferred by traders and technical analysts, many of whom are not taken seriously by the devotees of value. It’s easy to find insults being thrown each way on social media.

Here’s the primary source of the conflict: the best Momentum stocks often have horrifyingly high valuation ratios as they 2x, 10x, 50x, then 100x in price. This irritates the Value guys immensely while justifying to the chartists that “fundamentals don’t matter.” Short selling fundamentalists can get absolutely rekt as “markets can remain irrational longer than you can stay solvent.”

It took Professors Fama and French until 1992 to convince The Journal of Finance that (small) Size and Value led to outperformance. They did not include Momentum, but several other researchers quickly did. Fama and French have begrudgingly acknowledged the success of Momentum after admitting embarrassment that other researchers have repeatedly proven it works.

https://alphaarchitect.com/quantitative-momentum-research-embarrassing-the-ff-3-factor-model/

For 30 years I’ve been told that Momentum historically crashes harder than Value, or at least that’s the reputation in academic and many institutional investing circles. AQR posts a nice discussion of Prof. Fama’s views on Momentum here and goes into several detailed rebuttals:

https://www.aqr.com/Insights/Perspectives/Fama-on-Momentum

But is it really true that Momentum crashes harder than Value? I sat down today to investigate the riskiness of Momentum strategies. What I found is the opposite of what I expected, and that has me rethinking 30 years of received wisdom from Value managers.

What do Post-1971 Data Say?

When I charted my own full factor history, I saw a regime shift happening fairly early on. Eyeballing the 55-year chart, I detected a clear performance shift from Value to Momentum in the middle of 1986.

1971 to mid-1986 worked as I expected based on the long-run historical record of Value vs. Momentum as had been taught to me in the early 1990s. On both large cap and small cap US stocks, Value clearly outperforms the cap-weighted benchmark. Momentum stocks are much more volatile and significantly trail over this 15 year period.

Since mid-1986, Momentum has absolutely trounced Value. It’s not even close. Value hardly works on large cap and provides mild outperformance on small cap. The performance of Momentum over these past 40 years has been outrageous.

Basically, the charts below represent out-of-sample performance compared to what I learned in grad school, right around when Fama and French released their seminal Cross-Section of Expected Stock Returns paper in 1992, calculated from many decades of historical data.

Furthermore, Value gets hit with bigger drawdowns than Momentum. The drops in 2000 (dot-com crash) and 2008 (Global Financial Crisis) are visibly bigger for Value than Momentum. Even the 1987 crash hits Value stocks harder.

Frankly, these charts surprised me. I’ve spent much of my quant career looking at long-short returns, so maybe that explains some of the difference.

This got me scratching my head as the biggest drivers of the Internet Bubble in 1999 were Momentum plays. And yet somehow Momentum indicators reacted quickly to dump those same stocks fast enough to soften the drawdown. The stock market crash of 2000 pushed me into trend following commodity futures markets, so at some level I got the message about the shift to Momentum as it was happening.

Return vs. Risk Since 1986

After looking at these post-1986 performance charts, I decided to update the return vs. risk plots for just that 39.5 year period. Check this out:

Value adds about 2% returns for small cap, while losing half a percent for large cap. But look at the outrageous performance for Momentum! Momentum adds 8.7% annually for large cap and 11.9% for small cap, while reducing average risk by 3.8% to 3.9%.

US Small Cap Momentum shows total returns of 21% over the full period. Feel free to review my math on this one: Compound Annual Growth Rate (CAGR) = (Final Value / Initial Value) ^ (1 / # Years) – 1 = ($1,876,358.02 / $1,000) ^ (1/39.5) – 1 = 21.02%. That’s nearly 40 years of sustained 21% compound growth. If I were asked to place a bet on those 21% returns happening again for the next 40 years, I’d take the under on that bet. Unless the US Dollar collapses, which could happen.

Momentum Drives Technology and Thematic Strategies

Having lived through the period before and after 1986, one of the biggest differences is technology. The home computer became popular around that time, and personal computers took over the workplace. By the time we got to the 1990s, Silicon Valley was booming. After the dot-com bust, technology took off even more strongly with Web2 to create the online world we live in today.

All this technological momentum led to the rise of thematic funds like Cathie Wood’s ARK Invest. My recent quant work, post 2020, has shown strong performance for Momentum oriented strategies. Thematic funds capture momentum even better than sector momentum.

https://insight.factset.com/harnessing-thematic-momentum-in-portfolio-rotation-and-alpha-generation

Macro Also Drives Momentum

Some macro factors are also driving the outperformance of Momentum. Currency debasement leads investors to chase higher returns to compensate for inflation. The first big inflation shock in the 1970s hit Momentum stocks hard. But the money printing since then has worked more in favor of driving stock prices up, something we saw explicitly during the Covid stimulus.

US dominance, through a combination of currency strength and technology leadership, could be another driver of Momentum performance. I showed in an earlier paper that factors like Value and Momentum are struggling outside the US.

Could it be Arbitrage?

It’s been observed by quants that when a new factor gets widely recognized as a legitimate factor, typically when the first major paper gets published, that factor stops working going forward. This is one reason why quants are so secretive about their work and why they seek specialized data not available to most people. Financial statements are freely available to the general public.

It’s possible that decades of academic research and massive institutional money flows have arbitraged away much of the long-term performance of Value. Fama and French came out with the Value factor in 1992, relatively soon after Value’s outperformance peaked around 1986. Enough institutional money chasing Value stocks by looking at the same fundamentals ultimately puts a floor on the prices of those stocks and becomes a self-fulfilling prophecy.

What Comes Next?

I wish I knew.

It’s hard to ignore the strength of Momentum if you’re going for high returns. 21% returns for decades can really help play catch-up in a retirement account. Momentum investors would say to ride the trend until it ends, and so far, we have no evidence of the impending end of that trend.

Long-term Value investors would say value is due for a comeback over the “long term,” a sentiment that could be classified as a tautology. Value investors are by definition contrarian, so an extended period of underperformance is less likely to dissuade them.

My 55 year asset allocation study makes a strong case for allocating to Value stocks, but the past 40 years put that into some question. Whatever events drive the next major stock market drawdown will shed more light onto relative performance of Value and Momentum.

What do you think? Let me know in the comments section below!

Leave a comment

Share

Subscribe now

https://www.morningstar.com/economy/what-weve-learned-150-years-stock-market-crashes

The main driver of asset allocation is to provide diversification during stock market downturns. As shown in prior articles, the Self Sovereign Wealth Fund™ model portfolios provide higher returns with lower risk over a 55-year backtest period. How well do they navigate the largest bear markets since 1971? Looking at the biggest stock market crashes shows that the Conservative and Moderate portfolios provide strong protection while the Aggressive portfolio recovers faster and outpaces the stock market.

Disclaimer: Past results of theoretical backtests do not guarantee future performance. I am a quantitative analyst, not a licensed financial advisor, and nothing in this post or on my Substack should be regarded as financial advice.

Review of SSWF Model Portfolios

Last week’s article showed how the Self-Sovereign Wealth Fund™ model portfolios trace out a new efficient frontier with much higher returns, yet lower risk, than the traditional efficient frontier that consists largely of varying combinations of cap-weighted stock and bond indices.

The SSWF Conservative, Moderate, and Aggressive portfolios represent differing trade-offs between risk and return. The improvements to the efficient frontier come from incorporating quant factors on the stock indices, diversifying with commodity trend following, and adding gold and/or Bitcoin to combat currency debasement. If you want to see what specific ETFs are in these portfolios, and why they outperform traditional combinations such as 60/40, check out this article:

Purpose of Event Studies

An event study lines up different tradable instruments or portfolios at a start date tied to some event and tracks their relative performance to a stop date. For these event studies, the start date is the month when the US stock market (represented by the S&P 500) peaked before a bear market (a drop of 20% or more), and the end date is the month when the US stock market had fully recovered from its drawdown.

Event studies enable quick answers to these questions:

• How do different portfolios react to the same events?

• How deep is the drawdown?

• How fast is the recovery?

• How much higher is a portfolio vs. its benchmark reference portfolio once the bear market has ended?

Sampling Different Varieties of Bear Markets Since 1971

Here is a representative list of long-lasting, deep, and quick bear markets over the past 55 years. There are other crashes and events of interest, but these six span the range reasonably well to compare the bear market performance of portfolios.

• 1973/74 Oil Embargo Bear Market

• October 1987 Crash

• Internet Bubble Bust in 2000

• Global Financial Crisis of 2008

• Covid Crash of 2020

• Inflation-Driven 60/40 Bear Market of 2022

1973/74 Oil Embargo Bear Market

The 1973/74 oil embargo bear market came hot on the heels of the collapse of the Gold Standard in 1971. Stocks fell 46.5%, while 60/40 fell 30.7%. Commodity prices took off in dollar terms, as did gold prices. It’s therefore not surprising that the Conservative and Moderate portfolios, with their heavy exposure to gold, benefitted from this crisis, ending 30-34% higher by the time stocks recovered. These portfolios also hardly fell below their starting values.

The event drawdown in the table is measured from the high point of stocks. Measuring from the high point of the SSWF portfolios would put their drawdowns up into the 10-20% range and that definition of drawdown is used in the 55-year study.

The Aggressive portfolio looks similar to 60/40 on the chart. It’s hard to get a clean comparison in the 1970s as the commodity trend following funds had not entered the picture yet, so the difference comes largely from gold exposure, which the model increases in the 1970s to cover for the missing commodity trend following piece.

October 1987 Crash

The sudden crash of October 1987 cleanly showcases the protective ability of the SSWF portfolios. Stocks fell 29.9% and 60/40 fell 17.9%. Even the Aggressive portfolio beat 60/40, falling only 15.3%, which Moderate fell 7.2% and Conservative dropped a mere 3.5%. The recovery patterns on the chart are very clear in this example. Aggressive falls faster, then passes Moderate and Conservative by the end of the event. This particular event study clearly shows the tradeoff between risk and return in a typical bear market.

Internet Bubble Bust in 2000

The Internet Bubble crash was brutal for stocks both in terms of drawdown (44.7%) and duration. 60/40 provided significant protection, cutting the drawdown in half (21.5%). The three SSWF portfolios, on the other hand, hardly noticed the bear market in stocks. Measured from the stock market peak that starts the event, they only dropped 1-3% below that starting point and kept moving up. By the time stocks had fully recovered in 2006, the Conservative portfolio had pulled ahead by 66%, Moderate was up 88%, and Aggressive posted whopping gains of 102% while stocks were just treading water for 6 years.

Global Financial Crisis of 2008

The differences in portfolio performance during the Global Financial Crisis of 2008 are stark. Stocks drop 50.8% while 60/40 drops 29.5%. The Conservative portfolio only falls 1.5% below its starting value, though the full drawdown is bigger because it peaks after stocks peak. But it’s still down only 1.5% from the point at which stocks peaked. Even the aggressive portfolio drawdown stops at 22.7%, much less than 60/40. By the time stocks fully recovered in 2012, the Aggressive portfolio had pulled ahead of stocks by 47% while even the Conservative portfolio had pulled ahead by 34.7%.

Covid Crash of 2020

The Covid crash of early 2020 was sharp with a very fast recovery. Technically, it registered just under a full 20% bear market, but stock investors certainly felt the drop. The Conservative portfolio outperformed 60/40, though the Moderate portfolio dropped a bit more. Covid hit the Aggressive portfolio harder than stocks, largely because of Bitcoin exposure. 60/40 ended this period higher than any of the other portfolios, by a couple of percentage points. Gold handled this crash better than Bitcoin, leading the Conservative portfolio to outperform the Aggressive portfolio.

Inflation-Driven 60/40 Bear Market of 2022

2022 was one of the worst bear markets for the 60/40 portfolio and got more people thinking about ways to improve diversification. Both the Conservative and Moderate portfolios handily beat 60/40, cutting the drawdown by more than half. The Aggressive portfolio dropped within 1.8% of stocks, but it pulled 12% ahead of stocks by the time 60/40 recovered.

Summary Findings

Different bear market events play out differently, but some overall patterns are clear. The SSWF Conservative and Moderate portfolios provide consistent protection across all these events, driven by stock quant factors that reduce drawdowns and gold plus commodity trend following to provide macro level diversification. The SSWF Aggressive portfolio provides some protection most of the time but can drop harder than stocks in return for its strong long-term outperformance driven by Bitcoin exposure. The most risk-averse investors will strongly favor Conservative or Moderate over Aggressive.

Looking over the full 55-year test period, the Moderate portfolio provides protection close to the Conservative portfolio while seriously cranking up the average return (12% CAGR vs. 9%). The aggressive portfolio adds another 3% CAGR for a total of 15%, but it adds substantially more risk as well. An argument could be made for any of these portfolios along the efficient frontier depending on personal willingness and ability to tolerate larger drawdowns to get larger returns.

Implications for Modeling

It’s hard to approximate the historical impact of Bitcoin before it exists. The Aggressive portfolio will be too heavily loaded to Bitcoin for many people. Adding 2026 Bitcoin bear market returns will crank down the optimal allocation, though it may overcompensate if the four year cycle continues and 2027 takes off like a rocket again.

Preparing for the Next Crash

The next bear market is always somewhere ahead on the horizon. If you’re all-in on stocks, are you prepared for a sudden 20-50% drop? Would you then sell the bottom or buy the dip? How much easier would it be to ride out a much more diversified portfolio that still delivers stock-like returns? Let me know your reaction in the comments.

Leave a comment

Share

Subscribe now

https://www.leevalley.com/en-us/shop/tools/hand-tools/marking-and-measuring/rules/115845-veritas-12-aluminum-bench-rule

The Internet is full of model portfolios for asset allocation. Most lie along the same classic efficient frontier traced out by the glidepath from 100% stocks to 60% stocks / 40% bonds to ultra-conservative all-weather portfolios. How do the Self-Sovereign Wealth Fund™ core portfolios along the new efficient frontier measure up vs. the famous competition? The answer may really surprise you. Hint: they’re better than Awesome.

Disclaimer: I am not a licensed financial advisor and nothing in this article is intended as financial advice. I am a financial analyst with 30 years of experience researching my own long-term investment strategy and sharing my findings for educational purposes. Please do your own research before investing in any of the model portfolios discussed here.

Meb Faber’s Free(!) Global Asset Allocation Book

Wealth manager and podcaster Meb Faber put out a long-term study of asset allocation about ten years ago. It’s available on his website for free in e-book form.

https://mebfaber.com/wp-content/uploads/2016/04/GAA-Book-1.pdf

Meb famously keeps suggesting that giant pension fund CalPERS fire their entire investment team and replace them with a handful of low-cost ETFs to improve their performance. He finds that simple buy-and-hold allocations beat many well-regarded fund managers over long periods.

https://mebfaber.com/2023/11/08/should-calpers-fire-everyone-and-just-buy-some-etfs/

Comparing Efficient Frontiers

I sampled several of the famous portfolios in Meb’s book and measured their returns and drawdowns over the same 55-year period as my asset allocation study, using monthly data. The differences are stark. The portfolios from the book sketch out an “inefficient” frontier that is consistently lower return and higher risk that what I’m finding in my modernized and expanded asset allocation study.

Whatever the risk level of the famous portfolio, there is a spot on the Self-Sovereign Wealth Fund™ efficient frontier with less risk and/or far more return. I’ve highlighted three SSWF portfolios as Conservative (9%), Moderate (12%), and Aggressive (15%) based on their locations along the efficient frontier. Both the Conservative and Moderate portfolios beat the Awesome portfolio: SSWF Conservative has much lower risk and slightly higher return, while SSWF Moderate has much higher return and slightly lower risk.

What Drives the Outperformance of the SSWF™ Efficient Frontier?

The higher efficient frontier comes from the inclusion of assets left out of the other portfolios. My SSWF asset allocation study has 24 assets; Meb’s book includes 13. Naïve even weighting of these 24 assets shows lower risk than 60/40 and higher returns than 100% stocks.

Gold and commodity trend following provide risk reduction. Factor-based stock portfolios and Bitcoin enable return expansion. For a full explanation, please check out last week’s article:

Meb gives a nod to both smart beta factors and trend following on page 81 but then defers coverage of them to different books, articles, and podcasts, leaving them out of his long-term asset allocation study.

Approximating Portfolios

Some of these target portfolio allocations are fixed, while others drift over time (particularly the Global Market portfolio). For consistency, I implemented these portfolios as fixed allocations approximating those specified in Meb’s book. These allocations may or may not exactly match the online graphics shown below in the descriptions of each portfolio. Seeing how these portfolios all line up along the same frontier suggests my approximations are good from a modeling perspective.

I’m focusing this comparison on truly liquid portfolios that can be formed easily using low-cost ETFs, so I’m leaving out the Yale portfolio and its Ivy Endowment cousins that rely heavily on illiquid investments with high fees and 10+ year lock-up periods which require high-end private market access that you and I don’t have.

Dillian’s Awesome Portfolio

Jared Dillian recently released a book about his Awesome Portfolio. True to its name, this one has one of the best ratios of return to average drawdown. That’s pretty awesome indeed. He used to call it the strategic portfolio. It’s remarkably conservative and designed to be easy to hold for decades through the full range of market conditions.

https://www.jareddillianmoney.com/strategic-portfolio-details

I met Jared Dillian in person at a couple of investment conferences, and he’s got a large following in the self-directed investor community. He also DJs.

DJ Stochastic

Harry Browne’s Permanent Portfolio

The Permanent Portfolio seeks to benefit from the full spectrum of macroeconomic conditions. Some wealth advisers have adopted it as a cornerstone of their approach. Doing some basic math, I see that it’s the same as Jared Dillian’s Awesome Portfolio but minus the real estate. Dropping real estate from the mix lowers returns but decreases risk even more, leading to the highest ratio of return to risk among all these famous portfolios.

https://www.nbfwm.ca/advisor/the-filipiuk-group/our-approach.html

There appear to be other variations of the Permanent Portfolio, as the allocations in Meb’s book do not match most of what I’m seeing online for the Permanent Portfolio and follow a more complex variation with slightly higher return and higher risk. Meb’s formulation just moves the Permanent Portfolio a bit farther along the classic efficient frontier.

Dalio’s All-Weather Portfolio

Ray Dalio is one of the world’s most famous and successful investors, and the all-weather portfolio is a core holding for his Bridgewater Associates hedge fund. Using risk parity leads to an outsized allocation to low-volatility bonds.

I would argue, as several other people have, that the all-weather risk parity approach benefitted from decades of tailwinds from interest rate cuts that will not be repeated over the next 30-50 years from our current starting point.

https://www.optimizedportfolio.com/all-weather-portfolio/

Note: the above website has detailed analyses of several of these famous portfolios. Feel free to check them out. I am not affiliated with any of these websites; I am just pointing out information that is readily available on the Internet.

Global Market Portfolio

The best-known benchmarks for stocks and bonds are simple market cap weighted representations of the entire asset class. Extending that thinking, why not just market cap weight all the world’s asset classes and use that as an asset allocation benchmark?

https://investorpolis.com/the-global-market-portfolio-is-the-investor-starting-point-central-allocation-north-or-lighthouse-for-investments/?lang=en

There is certainly a strong argument for using market weights as a true asset allocation benchmark. The problem is that no one can agree on the sizes of each market and therefore the relative percentages. There are also disagreements about what to do with illiquid and semi-liquid investments that might account for billions to trillions of dollars in value.

Specifically, in my opinion, real estate is vastly understated in the great majority of “global market portfolios” I see online. Please check out my earlier article on this topic showing the wide range of calculations:

Talmud Portfolio

Some investment wisdom is very old. One famous book, The Richest Man in Babylon, came out 100 years ago but set itself a few thousand years earlier. The Talmud portfolio draws upon this kind of ancient economic wisdom. Note that this one is the same as the Awesome Portfolio without cash and gold.

http://investorhome.com/talmud-portfolio.htm

William Bernstein Portfolio

Some of the first asset allocation books I read were written by retired physician William Bernstein. Many other physicians and self-directed investors seem to like his ideas as well. I’m a doctor, but not that kind of doctor. This portfolio is a 75% stocks / 25% bonds portfolio with stock market diversification across size and geography.

https://thephysicianphilosopher.com/lazy-portfolio/

Buffett’s 90% Stocks Portfolio

The most aggressive portfolio on this list is Warren Buffett’s 90/10 stocks/bonds allocation. Some financial advisors that I know are happy to take the final step to 100% stocks and then talk soothingly to their clients about buying the dip when the inevitable bear market hits. Many self-directed investors struggle with those stock market drawdowns and end up selling the bottom only to buy back the top.

https://robberger.com/portfolios/the-warren-buffett-portfolio/

Interestingly, Buffett leaves out Ex-US (“foreign”) stocks and just goes with the S&P 500. US Stocks have certainly outperformed over the past 55 years.

What Have We Learned?

Based on a 55-year monthly rebalancing backtest, it’s easy to find target return funds that strongly outperform any famous portfolios constructed from a subset of assets that sandbag the true efficient frontier. Both the Conservative and Moderate SSWF™ portfolios have higher return AND lower risk than the Awesome portfolio.

Here’s your chance, as a self-directed investor, to beat CalPERS and many of the institutions at their own game. Which location along the SSWF™ efficient frontier appeals the most to you?

Long-term investors can achieve far higher returns than a 100% stock allocation at risk levels lower than the classic 60/40 stocks/bonds. Balancing value and momentum factors trounces the cap-weighted stock benchmark, while Bitcoin, gold, and commodity trend following add diversification and substantially reduce risk. I’m refining this 15% target return portfolio to serve as the Self-Sovereign Wealth Fund™ Core Portfolio.

NFA Disclaimer: Nothing in this article is meant to provide financial advice, and I am not a licensed financial advisor. This information is provided for educational purposes only and is believed to be historically accurate. If you seek specific financial advice for your personal situation, please contact a licensed financial advisor.

Continuation of Asset Allocation Study Series

This is the latest update of an ongoing series of articles on asset allocation. The previous installment added Bitcoin, an additional trend following approach, and introduced value and momentum stock factors in the US.

New Assets

This model version increases the total number of asset alternatives from 16 to 24 by adding:

• Treasury Inflation Protected Securities (TIPS)

• The Société Générale CTA Index, with live representation from the CTA ETF

• Developed Markets Ex-US Stocks Value and Momentum Factors

• Emerging Markets Stocks Value and Momentum factors

• US Stocks Value and Momentum Factors, both Large Cap and Small Cap (replacing All Cap versions)

Constructing History for TIPS

Treasury Inflation Protected Securities were introduced in mutual fund format in 2000 and as an ETF in 2003. When I first added TIPS into the asset allocation mix, the optimizer liked them so much that the suggested allocation seemed unrealistic. I determined it would be a better test to approximate how TIPS would have performed over the full backtest period going all the way back to 1971.

Some economists at the Federal Reserve simulated how TIPS would have worked back in the 1970s given Fed data:

https://www.federalreserve.gov/pubs/feds/2008/200805/200805pap.pdf

With the help of my AI coach, I dove into the nuances of turning these Fed data sources into a timeseries of monthly nominal total returns for TIPS. I was surprised to find out how well the simulation approach matches actual returns during the period of overlap when TIPS funds started trading live.

That’s a great approximation for an investment instrument that did not previously exist. I fiddled with the various parameters to trade off best-fit slope and correlation. R-squared is 88% and the correlation of monthly returns is 92%.

Total return is slightly conservative compared to TIP ETF because the regression slope is 0.95. The match between the simulated and actual total return curves is better than I’ve seen for some of the stock factors and trend following approaches I’m using in this 55-year study.

TIPS Allocation

TIPS now dominate the bond allocation along the lower-risk end of the efficient frontier. I capped all asset allocations at 20% to avoid too much concentration and optimizer misbehavior, topics explored below in the commodity trend following section.

The least risky allocations naturally rely heavily on T-bills. 10-Yr treasuries ramp up as stocks ramp down. Corporate bonds play a small role in the mid-range of risk and return.

SG CTA Index and CTA ETF

To complement the AQR and MLM trend following histories, I have added a Commodity Trading Advisor (CTA) history that starts around the same time as the other two. This history chains together three timeseries: BTOP50 (Jan 87), SG CTA (Jan 00), and the CTA ETF (Mar 22).

Here are the official index definitions from the source, BarclayHedge:

https://portal.barclayhedge.com/cgi-bin/indices/displayHfIndex.cgi?indexCat=Barclay-Investable-Benchmarks&indexName=BTOP50-Index

https://portal.barclayhedge.com/cgi-bin/indices/displayHfIndex.cgi?indexCat=SG-Prime-Services-Indices&indexName=SG-CTA-Index

https://www.etf.com/CTA

BTOP50 and the SG-CTA index follow each other very closely, until CTA diverges upward a bit in 2009. The CTA ETF underperformed soon after it went live and then caught up with the SG-CTA index.

Comparing this spliced CTA series to the other two trend-following approaches, CTA starts stronger in the late 1980s, then falls behind by 1995. It rallied recently to catch up with MLM. The spliced CTA history has notably lower drawdowns relative to the other trend following indices, which is interesting as the CTA index is derived from live performance of CTA funds and is not simulated. It most likely has some survivor bias in it, particularly in those early high-return years. Getting rid of all survivor bias in trend following track records is nearly impossible.

Tying Together Trend Following Allocations

I sought a third trend-following history because there are so many different varieties of approaches and none of the histories are terribly reliable. I was interested to see how the optimizer treated their quirks. Not surprisingly, it overreacted to the differences between them.

Here’s the original optimizer output, uncapped and unconstrained. Allocating over 35% to a single trend-following approach is unrealistic and not robust to sensitivity analysis.

The optimized allocations, when capped at 20%, look a lot more reasonable and the 20% cap forces more funds into the other two trend followers in that 15-16% target return range. Overall returns for the top end of the efficient frontier dropped once I capped Bitcoin at 20% as well.

Studying the definitions of each trend following approach, looking at the pattern of historical returns, and observing the dispersion of ETF live performance all undermine my willingness to favor one approach above another. For a 55-year asset allocation study, I think the most robust approach is to allocate the same amount to each alternative and let the optimizer focus on the aggregate allocation.

Once I add this additional constraint, the 20% cap no longer kicks in as the allocation to each of the three funds stays below 13%. The other two trend following allocations are tied with the purple one and hiding behind it visually.

Here’s the latest version of the same allocation sweep plot, after I updated the US stock allocations to include more diversified high return stock factor formulations.

Gold allocation goes up to compensate for higher stock volatility in the 1970s, before the trend following histories begin. Trend following allocation goes down to a more reasonable 10% per fund because stocks now show higher returns across the full history. The various moving parts across all 24 assets interact with each other.

Value and Momentum History

As the US value and momentum factors were the top performers with history going all the way back to 1971, I wanted to see how the small cap and large cap subdivisions have performed. Earlier I had just combined the small and large histories from Ken French’s database into a single average; now I’m looking at them separately and pairing them with live ETFs for both large and small cap.

Large cap momentum fund SPMO has been amazing over the past five years. Small cap XSMO has trailed. My investigation of SPMO was inspired in part by this delightful Substack article from a few weeks ago.

Asymmetric Radar

The “Hidden” ETF That Quietly Crushed the S&P 500 This Decade

There’s an S&P 500 ETF that has quietly beaten the classic index by several percentage points per year over the last decade, and almost nobody talks about it. I’m not talking about some exotic small‑cap fund or a leveraged product; it lives inside the same large‑cap U.S. universe most people already own…

Read more

4 months ago · 62 likes · 25 comments · Asymmetric Radar

DFA small cap value has beaten IJS, which has handily beaten both the Russell 2000 (small cap) and S&P 500 since inception. Large cap value IVE has trailed the S&P 500 recently after outperforming through 2020.

Risk/Return Comparison

There is a clear progression along the frontier from bonds to value stocks to momentum stocks to Bitcoin: all with increasing returns and increasing risk.

Adding value and momentum factors was not enough to convince the optimizer to allocate anything to Developed Markets Ex-US, as explored in last week’s article:

Emerging Markets value factor far outperforms Emerging Markets momentum, and it’s close enough to US stock factor returns to show up at the riskier end of the efficient frontier.

Tying Together Stock Factor Allocations

Left to its own devices, the optimizer played the same crazy games with value and momentum as it did with trend following. See, for instance, the wild thrashing between large and small cap value at target returns of 10 and 11%.

Tying together large and small cap value, along with large and small cap momentum, shows a much more stable allocation and clear pattern of risk vs. return. The highest returns require riskier momentum stocks.

Capping Bitcoin Allocation at 20%

Once I added additional constraints to balance out overloading on individual stock and trend following funds, the main impact of the 20% cap is now on Bitcoin. Obviously, each individual investor has their own opinion on a proper cap for Bitcoin, and many would place that at 0%.

Still, more asset allocators and financial advisors are warming up to Bitcoin, and the start of the next Bitcoin bull market may awaken more people to the importance of Bitcoin in an era of increasing currency debasement.

It’s fascinating to me that the unconstrained optimizer is putting very similar weights on gold and Bitcoin in the middle part of the efficient frontier. That says something about their complementarity. Clearly gold wins at the safe end and Bitcoin dominates the high returns, even when capped.

Top-Level Allocations

Putting all these new pieces and additional optimizer constraints in place, the results look quite reasonable to me.

The highest return comes from 80% stocks and 20% Bitcoin. The safest allocation is roughly 50% bonds, 25% stocks, and 25% commodities (gold + trend following). In the middle, around 13% target returns, we see 40% stocks, 40% commodities, 10% bonds, and 10% Bitcoin.

Many people have run these efficient frontier studies over the past 60 years. Few include this much attention to commodities and a rigorous way to incorporate Bitcoin. Take those out and what remains is the typical stock/bond glidepath.

Efficient Frontier

But look at what adding commodities, Bitcoin, and stock quant factors do to improve the efficient frontier. The expansion of return is massive, while reducing risk significantly at the same time.

The blue frontier was the first monthly model, using vanilla stock indices. The green frontier added Bitcoin and US value and momentum factors on stocks. The dark blue frontier on top is this week’s refinement, splitting US factors into large and small cap and refining some optimizer settings for more stability. At this point, it looks like we’ve hit diminishing returns on pushing out the frontier.

Model Portfolios

Here are specific portfolios corresponding to each point along the efficient frontier. I’ve bolded the 15% target return portfolio featured in the risk-return plot at the start of this article.

Each column shows an illustrative ETF to represent that asset class going forward. I will be refining these live ETFs to choose the best representatives for portfolios I’m planning to track.

Choosing the Core Portfolio for my Self-Sovereign Wealth Fund™

The 15% target return portfolio looks like a good trade-off between risk and return to serve as my core portfolio. Earlier I introduced the concept of a core portfolio as the central holding of a Self-Sovereign Wealth Fund™.

This SSWF™ Core Portfolio features a lower average drawdown than 60/40, historically, and far higher returns than 100% large cap US stocks (15% vs. 11.17%). The allocation maxes out on US value stocks, while being loaded 10% each in US large and small cap momentum stocks. Emerging Markets Value gets a token 1.8% allocation. Bitcoin is optimized at 17%, below its 20% cap. The remainder is roughly split between gold (9.8%) and three trend following funds at 3.8% each. These allocations seem about right to me as a starting point for my own tradeoff between risk and return.

Remaining Questions

I’m feeling pretty good about the results I’m seeing at this point. For my own investment purposes, here’s what I need to figure out to bring the study to a close:

• How does this SSWF™ Core Portfolio perform during the biggest bull and bear markets over the past 55 years? How has it held up out of sample in 2026?

• What to do about Ex-US stocks; is it worth moving off the frontier a bit to build diversification?

• What assets are missing? Do high yield corporate or sovereign bonds have a role? (I’m skeptical.) How about hedge fund replication strategies and private equity? (I don’t think the liquid ETF versions are good enough to make the cut.)

• Refining the best ETF to represent each selected asset, or considering multiple ETFs to add diversification

Please subscribe to see the finishing touches on the SSWF™ Core Portfolio!

Subscribe now

https://www.fjwealthmanagement.com/blog/world-market-cap/

The United States accounts for approximately half the global stock market, by market cap. But its dominance over total return is much stronger. US stocks have trounced non-US stocks over the past 19 years, with US stocks returning 4.75x more than non-US stocks. That’s an enormous difference, and it’s hard to ignore. Are we due for a long-awaited mean reversion, or will US stocks continue to steamroll their foreign competition? What are the implications for systematic asset allocators if non-US stocks can find no place on the efficient frontier?

One Step Forward, Two Steps Back

Working on my Ph.D. dissertation at Stanford, I learned that it’s very common in research to take one step forward then be forced two steps back to consider a more fundamental problem that is blocking progress. This week’s article was supposed to showcase the tradeoff between US and non-US stocks using factor indices such as value and momentum. What I found instead is that Emerging Markets value stocks make the cut, but the optimal allocation to Developed Markets Ex-US is precisely zero. Let’s explore some reasons for the underperformance and consider the asset allocation implications going forward.

Politically Correct Geographic Region Terminology

If you live in the United States, what do you call the rest of the world? Most Americans would say international or foreign. Working for global news company Reuters, with offices in 165 countries, gave me a more global perspective. Visting over 50 Reuters offices, I found that I was the “international” visitor and “foreigner” most of the time.

To my surprise, Reuters does not publish a map of offices, so I asked Grok to create one based on the office list on the Reuters website.

Brief sidebar on AI hallucinations: the original map showed no Reuters offices in the UAE, Saudi Arabia, or Norway, but I pointed out to Grok that I had visited Reuters offices in all those locations, to which Grok immediately agreed and tried to update the map. I visited Reuters customers in Oman, but that salesman may have worked from home as a satellite of the Dubai office. Iran used to have offices, but they closed. AI remains untrustworthy, even with basic facts like current office locations for Reuters.

The USA is “foreign” to those living in London. I learned many fascinating things from my London-based colleagues including the glorious concept of faffing about by studying charts such as the one below. Londoners have many geographic terminology challenges in sorting England vs. Great Britain vs. the United Kingdom vs. Commonwealth Realms vs. British Overseas Territories vs. Crown Dependencies.

https://medium.com/@galka_max/the-absurdly-confusing-lands-of-the-british-crown-explained-in-1-chart-30e2d50d1c8a

After traveling most of the world’s financial centers, I learned that the proper term for the full collection of stock markets outside the United States, by consensus of global index creators and the global quant community, is Ex-US.

Quant Obsession with Defining Global Regions

Besides index providers, quants are perhaps the most obsessed about defining regions and benchmarks. Most quant models are based on scoring models using relative ranks, and those ranks can be global, within a region, or across some other benchmark.

For reasons that still mystify me, one of the most widely followed Ex-US indices is the EAFE index from MSCI. EAFE stands for Europe, Australasia, and the Far East EAFE countries include only those marked in green on the map below.

https://www.wiegandfinancial.com/tow/america-is-great-but-it-isnt-everything/

I see many holes in this EAFE map, including several countries where I had customers. I understand not including Russia, but what happened to Canada? US + EAFE leaves out Canadian stocks. Many Canadian companies are cross-listed in the US, but many are not. Canada’s varying status in global benchmarks may underlie its strong reputation as “quant paradise” because there are so many quant factors that work well on Canadian markets.

MSCI also has an All Country World Index (ACWI) which includes ACWI ex-US.

https://www.bankeronwheels.com/best-international-etfs/

ACWI, like MSCI World, combines developed and emerging markets. It’s also less comprehensive, covering only 85% of global market cap. For broader coverage, MSCI offers the ACWI IMI (Investible Market Index) that includes 99% of global market cap.

Developed, Emerging, and Frontier markets have their own definitional issues. What is Developed Europe? Much of the EU, accessible without a passport check, is not considered “Developed Europe.” The UK is frequently carved out as its own region, as supported by Brexit.

What is Developed Asia? Our StarMine quant team defined Developed Asia as 5 island nations: Japan, Hong Kong, Singapore, Australia, and New Zealand. The only foothold on mainland Asia came from the New Territories of Hong Kong. And what’s up with Chinese shares listed on the Hong Kong Exchange?

Because the Japanese market is so large and behaves differently, it’s common to separate Developed Asia into Japan and Developed Asia ex Japan. But as I traveled Asia Pacific, I found that many quant fund managers were trading an Asia Pacific strategy that also included South Korea, Taiwan, Vietnam, and some smaller Emerging / Frontier markets.

https://factsinstitute.com/countries/asia-pacific-countries/

Market Cap Weighting

If the goal is just to maintain broad representative exposure, it’s trivial to hold MSCI ACWI Ex-US or ACWI IMI Ex-US and be done with it.

But the whole point of my asset allocation study is to seek meaningful diversification and ways to reduce drawdowns, so I need to explore relative performance and correlations of regions and factors built upon those regions.

US vs. Ex-US Performance

The primary EAFE ETF (EFA) went live in 2001. It pulled ahead of the S&P 500 until late 2007, peaking at 121% vs. 49% total return, an outperformance of 2.5x.

The aptly named Global Financial Crisis hit EAFE harder than the S&P 500, causing a drawdown of 59% vs. 54%.

Since peaking in 2007, EAFE has trailed the S&P 500, 120% vs. 570%, a 4.75x outperformance for the USA. 19 years is a long time to underperform, and EAFE also trails over its full 25 year history as an ETF.

Given the massive outperformance of the Mag7, how does the rest of the US stock market compare to EAFE? Both equal-weighted S&P 500 (green) and US small cap Russell 2000 (orange) still crush the performance of EAFE, so the outperformance extends well beyond the Mag7 and tech stocks.

Potential Reasons for Ex-US Stock Market Underperformance

As a free market capitalist American citizen, it’s easy for me to hypothesize economic policy reasons for underperformance. Europe and much of Asia have embraced varying degrees of socialism and heavy-handed government regulation of industry and commerce. Some companies are controlled outright by the State. I learned when visiting a Singapore sovereign wealth fund that they were required to hold certain State-owned enterprises like Singapore Airlines.

Currency exposure may be a significant culprit. In the early days of the Euro, I recall a decade of great enthusiasm from my European friends about Europe beating the US economically for the foreseeable future. The Euro peaked in 2008 at $1.58, then fell below USD parity in 2022, a 14-year downtrend. Collapsing currencies hurt returns denominated in USD.

https://www.macrotrends.net/2548/euro-dollar-exchange-rate-historical-chart

I could get into additional European policy challenges but that quickly gets politically confrontational and there’s plenty of discussion of those topics on Twitter/X.

There have been sustained periods of Ex-US stock market outperformance in the past. If you go back far enough, there was around a 30-year period of Ex-US outperformance from around 1985 to 2015.

https://www.justetf.com/en/academy/msci-world-ex-usa-needed.html

But once again, my recollection of the UK business environment under Thatcher looked more like the US than it does now. Lately we’ve seen more emerging and frontier countries embrace free markets while the Europeans add ever more layers of regulations.

US vs. Ex-US Factors

What if, instead of comparing full market cap weighted indices, we use quant factors to pick companies that are either great values or strong outperformers (momentum)?

iShares has offered a comprehensive suite of “smart beta” multi-factor ETFs since 2015. In the US there are large cap (LRGF) and small cap (SMLF) funds. Ex-US developed markets include large cap (INTF) and small cap (ISCF) as well. Emerging markets feature a single multifactor ETF (EMGF). I have held some allocation to this full basket of multifactor ETFs in my personal retirement account for much of the past 10 years.

Interestingly, in the US, we see exactly the opposite performance order that the ETF designers (and I) were expecting based on backtests. Pure market cap > large cap multifactor > small cap multifactor. The alpha factors have been reversed in the US since 2015, largely because of the dominance of the Magnificent 7, which are by no means “value” or “small” companies.

For Ex-US Developed Markets, on the other hand, we see the expected alpha factor ordering: small cap multifactor > large cap multifactor > market cap benchmark. Unfortunately, the total returns are far less than what you see in the US. Adding factors does not turn Ex-US stocks into US factor performance.

Emerging Markets show decent factor outperformance since 2022 but still lag well behind the US.

Successful Mutual Funds

Seeing the struggles of factors on Ex-US markets, I dug deeper to find out how various fundamental fund managers have done. I started with the famous Templeton Foreign Fund that I owned in my first 401(k) plan back in 1991. Further research surfaced the Dodge & Cox International Stock Fund as a leader in its class. Dodge & Cox are renowned for their narrow portfolios and outstanding stock picking ability. Since 2001, Dodge & Cox strongly outperformed EAFE, while Templeton Foreign Fund trailed.

The real surprise was the extremely strong performance of the DFA International Value Portfolio. Dimensional Fund Advisers (DFA) has Nobel Prize winner Eugene Fama on their staff, and I’ve covered them in an earlier article.

In some ways DFA is the procedural opposite of Dodge & Cox, relying heavily on multiple factors rather than fundamental stock picking. They’re also doing something much more sophisticated than a basic one-dimensional value tilt, and the combination of value, profitability, and other fundamental factors nearly keeps up with the Dodge & Cox stock picking pros.

How does DFA International Value compare to the iShares multi-factor ETFs since their inception?

It’s really close. iShares small cap multifactor ISCF took an early lead, but DFIVX made a full comeback after falling into last place. Given its much longer track record, I’d be inclined to pick DFIV as my representative of the class. DFIV is the ETF version of DFA mutual fund DFIVX, launched in 2021.

Risk vs. Return

The vanilla cap-weighted benchmarks show strong US dominance on both risk and return. Adding value and momentum factors significantly improves US returns over the full 55-yr period, even while losing out to the Mag7 over the past decade.

Value works great on Emerging Markets, while momentum gets whipsawed with lower returns and bigger drawdowns. Other researchers have noted this behavior as well. Emerging Markets Value sits in the general vicinity of the US factors and does get picked up by the optimizer for a small allocation along the efficient frontier.

Developed markets Ex-US remain problematic. I tried three long-term histories:

1. Ken French’s website, the same source I used for US value and momentum. Unfortunately, the data set only starts in 1990 rather than 1971.

2. AQR’s website, the same source I used for trend following. Their “value and momentum everywhere” data starts in 1981. The value returns are similar to French, though a bit higher. The AQR momentum returns are much lower than French.

3. Mutual fund history from DFIVX, backfilled with AQR history to extend back to 1981.

The performance improvement from factors is simply not enough for the optimization process to put any Developed Ex-US funds onto the efficient frontier. DFIVX does the best, but it still trails the basic EAFE benchmark over the full period.

It’s not just a return problem; it’s a correlation problem as well. Ex-US pulled ahead of the US from 2001-07 but then crashed harder. Ex-US stocks are just not providing sufficient diversification in terms of drawdown timing.

Some of the shortfall may come from the construction of historical data. The lengthy AQR history only includes England + Continental Europe + Japan. Japan went into a horrific drawdown after 1989. AQR may also be overly conservative with their institutional-grade liquidity filters.

Now What?

Frankly, I’m not sure what to do next. I’d love to get your comments on investing in Ex-US Developed Markets.

Leave a comment

It’s easy to wave your hands and say markets move in cycles, and Ex-US stocks are due for a comeback. But 55 years is a long time to underperform systematically. And going back to my comments on the impact of heavy-handed regulation of Ex-US markets, that regulatory process seems to be accelerating rather than abating.

The next step for me may be to back up even further to think about the optimization process. I could make some adjustments to broaden the history, or I could incorporate some forward-looking expectations. Or I could find out how much including Ex-Us leads to a “sub-optimal” portfolio. I’m not quite ready to file the whole efficient frontier concept in the “all models are wrong” category yet, but some new insights might come from that perspective.

Ideally, I’d like to include a systematic ETF that grabs the best stocks from Developed Markets Ex-US. Maybe DFIV is the answer. I might find different results using different backtest periods.

The biggest risk and opportunity involve what happens if/when the Mag7 melt down, Internet Bubble style. If they don’t 10x from here first. Will Developed Markets Ex-US provide any protection in that scenario, or will they fall even harder than they did in 2008? No one said this was easy.

For now, I’m going to give it some more thought and keep digging into additional data. Please subscribe to see what I find out.

Subscribe now

Financial engineers show how the magic of volatility pumping creates higher returns from combinations of uncorrelated assets. Frequent rebalancing of a diversified portfolio captures this volatility pumping premium. Adding dollar cost averaging (DCA) juices the returns even more by buying whatever is dipping the most in any investment period. Let’s explore how and when volatility pumping increases returns, and under what circumstances it fails.

Investment Science

During my Ph.D. program in Engineering-Economic Systems at Stanford, our department chair David Luenberger created a new class called Investment Science. Prof. Luenberger was an expert on optimization, dynamic systems, and quantitative economics, so this was a math class rather than an introduction to fundamental analysis of businesses.

The main new thing I learned from the class was a concept called volatility pumping, which somewhat magically created a positive expected value outcome from combining multiple zero expected value volatile processes. If you want to see the details, check out Chapter 15 of the Investment Science book or one of many readily available online resources.

https://www.scribd.com/document/1007631685/Investment-Science-David-G-Luenberger?v=0.505

Volatility Pumping

Here’s the canonical two asset example: (1) a stock that either doubles or gets cut in half each period, with 50/50 probability, and (2) a zero return cash investment. Both assets have a zero expected return in any given period. But if you combine them in a portfolio and rebalance each period, the combination grows at nearly 6% per period!

Why does this work? When the stock wins, you harvest half the gain. When the stock loses, you replenish half the capital. Because the gains are bigger than the losses within the same period, the amount harvested from a gain is bigger than the amount that needs to be replenished after a loss. It’s the harvesting that makes the difference—if you just held the volatile stock, the next loss would be the size of the last period’s gain. Repeated endlessly and each period either buys the dip or sells the rally.

What happens if you combine two independent stocks that are equally likely to double or get cut in half each period?

The expected gain is now 11.8% per period. Continual rebalancing creates a nearly 12% gain from 0% expected value ingredients.

https://parrondoparadox.blogspot.com/2011/02/parrondos-paradox-stock-market.html

Rebalancing Exploits Volatility Pumping to Add Returns

Now consider the impact of volatility pumping in asset allocation. The efficient frontier benefits the most from assets that are uncorrelated or even negatively correlated to each other. Each rebalance period engages in volatility pumping across the multi-asset portfolio. Monthly rebalancing pumps volatility more effectively than annual rebalancing. Transaction costs aside, the more frequently you rebalance uncorrelated assets, the more you gain from volatility pumping.

Higher volatility assets also drive more gains from volatility pumping, provided they remain uncorrelated from each other. If all correlations go to one on the downside, ruin can come quickly for a portfolio of highly volatile assets. This is yet another reason why I focus on drawdown as my primary measure of risk, because it captures extended periods of correlated downside much more directly than standard deviation or volatility.

When Volatility Pumping Fails

During the Internet bubble, some colleagues of mine started a fund that rebalanced high volatility stocks on a daily basis, and sure enough, volatility pumping worked as expected. They later ran into serious macroeconomic headwinds that crashed all the holdings at once, pointing out the fragile nature of “independent” assets in the real world vs. a textbook. Old timers know that all correlations go to one in a crisis.

https://medium.com/the-investors-handbook/the-dotcom-bubble-review-of-the-darkest-days-for-the-technology-world-8985af7a1edf

Correlation presents a serious problem for volatility pumping. Textbook examples and toy models can make all the assumptions they want, but financial assets have strong and shifting correlations. The classic crisis scenario where “all correlations go to one” is deadly for volatility pumping, and even more disastrous when volatility spikes at the same time. Thus, much of the work of asset allocation seeks to identify assets that survive or even thrive during crises, which is why gold and commodity trend following get such high allocations along the efficient frontier.

Here’s a chart from renowned hedge fund Two Sigma showing how correlations of 74 securities across four asset classes suddenly spiked on the top three statistical factors in their risk model during the 2008 crisis.

https://www.twosigma.com/articles/asset-class-correlations-return-to-normalcy/

A more subtle problem with volatility pumping is insufficient mean reversion. Volatility pumping exploits timing differences in assets with similar expected values, capturing the gains of one asset to offset the losses of the other. The textbook examples above have expected values of zero for all assets, an extreme mean-reverting process. When the return of one asset strongly dominates the return of another, the gain from volatility pumping can be less than the loss from diluted returns.

I tried setting up a volatility pumping example between Bitcoin and the other assets in my asset allocation study since 2018. Combining Bitcoin with any other asset, even one that’s highly uncorrelated, just diluted the returns of Bitcoin. This is why “Bitcoin maximalists” decide to ride out the drawdowns to capture the full upside of Bitcoin.

DCA Example: Bitcoin

To benefit from the volatility of a single asset like Bitcoin, many people use dollar cost averaging (DCA). The most effective method is to “buy the dip,” but as anyone knows who has tried, frequently the dip just keeps dipping. In the extreme, a naïve DCA approach simply purchases the same dollar amount in each period. There are many calculators online to show how this works; for instance, here’s a Bitcoin DCA calculator from the crypto exchange Uphold.

https://uphold.com/en-us/dca-calculator?dateEnd=2026-06&dateStart=2018-01

The calculator shows how investing $100 per month for 102 months, starting in Jan 2018, yields an ending value of $46,787. The DCA result is much higher than the $10,200 investment.

But what if you had put the full $10,200 into Bitcoin all at once in Jan 2018? Investing $10,200 into Bitcoin at the start of 2018 at a price of $13,880 would buy 0.73487032 BTC. At the end of May 2026, the Bitcoin price was $73,568 for a final portfolio value of $54,063. In this case, you were actually better off buying at the peak monthly price of the 2018 cycle rather than averaging monthly purchases over the following 8.5 years. Although it retraced heavily in 2022, Bitcoin spent very little time below the 2018 peak price at the end of the 2022 bear market.

Once again, like the situation for volatility pumping, simply riding the strong upward drift of Bitcoin creates more gains than the DCA approach of buying all the peaks and dips along the way. This is a case of time in the market beating timing the market. Buying just the dips rather than the peaks would be an even better strategy, but most people have trouble pulling that off in reality.

DCA Enhances Volatility Pumping

In situations where volatility pumping works well, with low/negative correlations and comparable returns across different assets, DCA enhances the benefits. DCA works like rebalancing, but you don’t have to sell; instead, you buy whatever is dipping with fresh cash.

DCA vs. Lump Sum Efficient Frontier

In my 55-year asset allocation study with 16 assets, DCA raises returns across the board relative to lump sum entry in 1971. The addition investment itself shows up as a return relative to the initial investment, so returns are better measured relative to the risk-free rate of return (which also uses DCA). The risk-free return goes up by 1.81%, from 4.40% to 6.21% (where the difference is the additional capital being added each month plus interest earned on that additional capital).

The orange and blue dots compare the same portfolios for DCA (orange) and lump sum (blue). The most volatile portfolio, 100% US large cap stocks, shows the biggest improvement in both risk and return. Realizing that DCA benefits the most volatile portfolios leads influencers to pound the table about using a DCA approach for Bitcoin. But it’s important to observe that the gain in 100% stocks (12.71% - 11.17% = 1.54%) is less than the gain in risk-free T-bills. Like Bitcoin, time in the market beats timing the market as stocks are rising faster than the benefit from DCA.

DCA vs. Lump Sum Allocation

The chart below, though a bit busy, shows that optimal allocations follow the same basic pattern for both DCA (darker shades) and lump sum (lighter shades).

The DCA target return allocations are all shifted to the right, since the efficient frontier moved up by about 1.5%. The bond curve is simply shifted by the target return difference. The DCA Bitcoin curve shifts a little more at the high return end because DCA juices the return. DCA favors stocks a bit more than commodities relative to lump sum.

DCA vs. Lump Sum Drawdown

Looking at drawdowns for a 100% US large cap stock portfolio, the only meaningful difference is in the first bear market of 1973/74.

Basically, you can’t tell the difference after the first big drawdown. The reason is that I haven’t indexed the DCA amounts for inflation. I could fiddle with the monthly amount vs. the initial amount, and I could index for inflation, but I’m not convinced that the extra assumptions would add any more clarity.

When I weigh the modeling complexity against the new insights, I see that the marginal insights are insufficient to merit the additional assumptions and complexity of DCA for this asset allocation study. Not every modeling idea is worth the additional effort to implement. Parsimonious models lead to clearer insights and more direct attribution of the impact of each input.

Conclusions and Next Steps

DCA is a great idea, particularly for investors who have high income relative to their current level of assets. It will likely improve your returns while reducing risk. But moving from a lump sum to DCA approach for this study introduces many new variables while leading to similar results. So, going forward, I’m planning to stick with the basic lump sum approach for the asset allocation study.

Next up, I’ll be refining the candidate asset classes some more to fill some potential remaining gaps in the portfolio.

Subscribe now

This week’s asset allocation update adds four new assets that all push out the efficient frontier. Bitcoin provides powerful thrust to achieve the highest returns with the highest risk. An additional trend-following approach achieves similar allocations to the trend following approach already in the mix. Value and momentum factor US stocks substitute for vanilla US stock allocations while increasing returns and lowering risk. Finally, in the context of these 16 assets, we can now generate an explicit parametric tradeoff between gold and Bitcoin while moving from the safest end of the efficient frontier to the riskiest.

NFA Disclaimer: Nothing in this article is intended as financial advice. I am not a licensed financial adviser. I am a quant researcher performing an asset allocation study for my own portfolio and this model is still a work in progress. If you seek financial advice, please contact a licensed financial adviser.

Adding Four New Asset Class Histories to the Mix

This update increases the asset pool from 12 to 16 asset classes by adding Bitcoin, the Mount Lucas Management (MLM) trend following index, US stocks value factor, and US stocks momentum factor.

Bitcoin becomes a viable asset for the allocation study starting in January 2018, at the very peak of that Bitcoin cycle. Any human being with some interest in investing had heard of Bitcoin by then, and starting at a cycle top handicaps the fastest horse in the race.

The MLM trend following index provides a different take on trend following relative to the AQR index and is matched with a live ETF (KMLM) that follows the same methodology.

Thanks to for sharing a website with monthly returns for the MLM Index going back to 1988. Please check out his note on my Befriend the Trend article for more information.

https://chipstak.substack.com/p/befriend-the-trend/comment/251756079

US stocks value factor and momentum factor histories are both drawn from Ken French’s academic website. These are represented in live trading with the VLUE and MTUM ETFs, both derived from the MSCI USA index.

New Return vs. Risk Plot

Even while handicapped by starting at a cycle peak in January 2018, Bitcoin blows out the top of the return vs. risk plot for all 16 asset classes, coming in at the highest return (26% CAGR) and highest risk.

Both the value and momentum factors strongly outperform US large cap stocks which have a CAGR of 11.2%. The value factor CAGR is 13.6%, while the momentum factor CAGR is 15.5%, and both factors demonstrate lower risk than US large cap stocks.

The MLM trend following index shows both lower return and higher risk than the AQR trend following index, which is exactly what I wanted to see. The multi-year steady path of AQR’s historical returns feel a bit optimistic to me. The timing of the returns and drawdowns are different, so both end up getting allocations along the efficient frontier.

New Efficient Frontier

Adding Bitcoin along with the US stocks value and momentum factors significantly increases the return levels of the entire efficient frontier.

The old frontier (green) peaked at around 12% returns, while the new one (blue) hits 17% returns over the full 55-year period if you are willing to tolerate the wild ride of a large Bitcoin allocation coupled with the ups and downs of heavy exposure to the momentum factor.

Overall Allocation

The high level allocation pattern is quite clear. The lowest risk part of the frontier holds over 40% in bonds, while the highest risk end goes over a 60% allocation to Bitcoin. I suspect most people would avoid both of those extremes, but those are the allocations I expected to see at each end.

The midrange of the efficient frontier favors stocks for higher returns and commodity trend following for risk reduction. Both stocks and commodities get significant allocations along the full length of the efficient frontier.

Bitcoin vs. Gold Allocation

The chart below, showing the explicit allocation tradeoff between Bitcoin and gold, is one I’ve been seeking for the past five years, and I’ve finally produced a quantitatively robust version. This tradeoff is in the broader context of the 16 asset histories incorporated in this study, so the numbers don’t add to 100%.

I’ve seen several efficient frontier studies incorporating Bitcoin, but most of them are out of date by now (missing the most recent cycle) or make some assumptions that I can’t personally justify. Let me know if you’ve seen a recently published study showing a gold vs. Bitcoin allocation sweep in the context of other assets like stocks and trend following.

Leave a comment

Gold allocation remains steady at around 10% for the lower half of the efficient frontier, then trails off with higher return requirements. Bitcoin stays near zero for return targets below US stocks (11%), then ramps up increasingly with higher return targets.

Note: I’m not advocating for a 30%+ allocation to Bitcoin, but the chart does show how much Bitcoin has turbocharged portfolio performance since 2018. Note further that adding the bear market of 2026 will lower the target allocation for Bitcoin. This asset allocation study is still a modeling work in progress.

Trend Following History

Turning to commodities, the MLM trend history shows more volatility than the AQR trend history and better matches with my own personal experience of running a commodity trend following fund. I expect to see huge surges followed by pullbacks, which I see for MLM but not AQR.

The big question that remains is the flatness of both histories over the past 20 years after such strong performance in the early years. Note that being flat during the 2008-9 crisis represents a substantive accomplishment and this explains why trend following gets such a large allocation on the efficient frontier.

Commodity and Trend Following Allocation

Interestingly, MLM index gets a higher allocation than AQR for higher return targets, even though MLM offers both lower return and higher risk. The benefit comes from the timing of the drawdowns. For lower return targets, the allocations are essentially equal.

As mentioned earlier, gold gets an 8-12% allocation at the lower risk end of the spectrum. The GSCI long-only commodity index hangs in there with 1-2% allocation as well on the lower risk part. Whether long-only or trend following, commodities contribute more to risk reduction than return enhancement.

Stock Factor Performance

The outperformance of both the value and momentum factors on US stocks has been quite clear, coming out of the bear market of 1973-74. Momentum has consistently outperformed value for the past 30 years.

Looking at the chart above, it’s easy to see why the optimizer selects both value and momentum over the baseline US large cap stock index.

Value vs. Momentum Allocation

It’s less visibly obvious why value stocks get such a large allocation from the optimizer, but that allocation comes from the lower risk of the value stocks with their less intense drawdowns.

Only the most aggressive target return allocations favor momentum over value; the higher the return target, the greater the reliance on momentum to deliver those higher risk returns.

Once again, the optimizer assigns no weight to emerging markets or ex-US stocks. In a future model version, I plan to include non-US stocks with factor loadings to see if they make the cut with factor exposure.

Bond Allocation

The bond allocation picture is clear: lowest risk portfolios rely on T-bills, mid-risk portfolios make use of higher return corporate bonds, while low-mid risk portfolios employ 10-yr treasury bonds as well.

Any target return portfolios above 14% CAGR leave out bonds altogether.

Low Risk and High Risk Examples Along the Efficient Frontier

Adding these four new assets to the mix leads to some attractive portfolios. The chart below shows a low-risk option in orange that pairs the return of US large cap stocks with lower risk than 60/40. That orange portfolio mostly sidesteps all the big drawdowns, making steady positive returns through the lost decade of the 2000s with a small blip in 2008/9.

For those who are willing to take bigger risks, the blue portfolio achieves 17% returns with essentially the same risk as a 100% allocation to US large cap stocks. That’s nearly 6% points more than the 11.17% large cap stock return.

As a caveat, risk and return are measured over the full 55-year period, with most of the contribution to each coming since the introduction of Bitcoin in 2018. Personally, I would not go this far out the risk curve, but it’s interesting to see what it looks like compared to 100% US large cap stocks.

For the lower risk portfolio, the reduction in drawdown is truly remarkable. US large cap stocks hit 40-50% drawdowns three times. The lower-risk portfolio barely hits 15% drawdowns over the same period, while delivering the same returns.

Next Steps

Results so far look promising. I want to check a few more things before I’m ready to start picking a model portfolio along the efficient frontier and selecting specific ETFs to implement the model portfolio.

I’m now looking at Dollar Cost Average (DCA) weighting to see how that changes things. A DCA approach puts more weight on the recent period which is fully based on live performance of actively traded ETFs.

Seeing the strong performance of value and momentum in the US, I want to add additional factor exposure outside the US.

I may also introduce a third trend following history (such as Société Générale) as a sanity check given the critical importance of trend following along the middle part of the efficient frontier.

Please subscribe to see how these additional inputs improve the robustness of the full portfolio.

Subscribe now

Financial modeling is an art, a science, and an engineering discipline governed by economic considerations. No model is ever perfect, but many are plenty good enough. Often, it’s more insightful to compare several simple models with different perspectives rather than refining a single framework well past the point of diminishing returns. The quest for perfection is so expensive that even professional-grade models are full of known bugs and blind spots, some of which get reclassified as “features.” This week’s article reviews many ways that models go astray and how to fix these shortcomings.

Subscribe now

The Map is Not the Territory

A few months back I wrote about competing models of human behavior, contrasting the views of humanists (focused on that first word), behaviorists (zoomed in on the second word) and rationalists (who model humans like robots).

I guess it’s not surprising that social scientists and technologists who model humans as robots are more likely to believe that robots can achieve consciousness comparable to humans. In much the same way, behaviorists expect humans to behave like animals. Humanists have fundamental disagreements with putting either robots or animals on equal footing with humans.

Each modeling approach brings insights along with accompanying drawbacks. As a polymath, I discover more insight from comparing models based on fundamentally incompatible worldviews. Looking at a model from a completely different framework makes it easier to spot the gaps in the model. These gaps are much harder to detect from within the paradigm.

https://art-verse.com/2017/11/09/the-dialectic-of-innovation/

Philosophers have a name for this process of gaining new insights from opposing models: the dialectic process. Resolving the conflict between thesis and antithesis may open insight into some previously hidden dimension.

Why Are All Models Wrong?

Statistics is a great field to learn about the fragile nature of models, as George Box observed. Mark Twain put it a bit more bluntly.

Any model is a simplification. Statistical models are based on a finite sample of past observations that may not accurately reflect the past, let alone have relevance for the future. Bayesian models based on subjective probabilities are just that, subjective judgments fraught with a long list of behavioral biases.

Data Quality Issues

The perils of statistical reasoning based on past events are accentuated by the rapid adoption of AI. Machine learning models are fancy statistical models dressed up in an aura of new technology. I’ve been hearing about the magical wonders of AI models, specifically neural networks, since completing my senior thesis at MIT in 1989. It took more than 30 years for computational power to overcome long-term skepticism about what these kinds of models can deliver. Unfortunately, many non-technologists can be easily persuaded by a generative AI model that sweet talks them while having no idea what it’s actually talking about.

Those of us who have been testing and competing against these kinds of models for a very long time deeply understand a crucial concept in model building: garbage in, garbage out.

I especially like that rainbow unicorn poo. Can I get that as an emoji on my phone?

Among the many shortcomings of machine learning and AI models, they are completely dependent on their training data. Problem 1: the sum total of all history is still incomplete. Problem 2: the future can and will behave differently. Problem 3: much of what is claimed to be factual in the training data is not accurate. Problem 4: AI model trainers introduce strong biases, knowingly or unknowingly.

Financial data are notoriously poor quality. Many people do not realize how bad their data histories are because they have not compared different sources. This is why I spent so many weeks comparing and validating credible sources of historical data for my ongoing asset allocation study.

Crypto data, representing the wild west of finance, are even worse. I can confirm from direct experience that Grok’s ability to clean messy, incomplete, contradictory, and ever-changing crypto API data feeds is absolutely terrible. Other AI tools may be better at the task, but I’m not expecting to vibe code my way out of data quality problems anytime soon. I’m also hearing reports from professional coders that vibe coded prototypes are much harder to maintain and generally need to be rewritten by competent software architects.

Building Models to Generate Insight

Most people are aware of the problems generated by poor data quality. Fewer people are as familiar with the challenges of proper model framing. Building a robust modeling framework is an engineering-economic decision. Lucky me, I earned my Ph.D. in a unique department called Engineering-Economic Systems at Stanford, where we studied the art of modeling from many perspectives.

https://msande.stanford.edu/engineering-economic-systems-stanford

Models intentionally focus on certain aspects of a situation and leave others out, as time, attention, and resources are not unlimited. Hence, what a model leaves out often accounts for more problems than what the model represents erroneously.

Entering Thru the Coal Chute

The reality of modeling is that you learn as you go. The first attempt at a model leads to new insights and reframings. The final version of the model may bear little resemblance to the first version. This led to the coal chute metaphor made famous by our department’s founder Bill Linvill.

Prof. Linvill explained that building and demonstrating a model is like hunting through a forest to find and renovate an old, abandoned building that has been forgotten for years and overgrown with vegetation. First, you must find the building. Then you check the front door, back door, and windows: all locked or jammed shut. Eventually you trip over a hatchway on the ground that can be pried open (with difficulty) to access a filthy coal chute. If you’re brave enough to slide down that chute, you can begin the process of cleaning and restoring the house. After months of fixing it up, you’re finally ready to open it for visits and charge admission. But that first visitor comes in through the front door that you so thoughtfully restored; you’re not supposed to drag them in through the coal chute the way you arrived.

My Substack blog intentionally violates that principle of professional modeling. I’m giving you the behind the scenes tour of the coal chute to see how industrial-scale financial models get built. This is your chance to learn what gets discussed in quant research team meetings. A normal institutional analyst would spend 6-12 months refining this kind of study before any customers get to see it, so they don’t know about all the frame changes, new directions, unexpected obstacles, and bugs caught along the way. Some of these old shacks in the forest are full of creepy crawly critters.

Defensible Models

While working on my Ph.D., I interned at a strategy consulting company founded by graduates from our department. When we launched new consulting projects, we explained to the client how we used an iterative modeling process, with each new model learning from insights generated by the previous model.

The typical phases were:

• A pilot model put together in a day or two to capture the main drivers of uncertainty and frame the project

• A prototype model, built in the first couple weeks to a month, that attempted to capture about 80% of the problem to refine focus

• A full-scale model, addressing all the key issues well enough to provide clarity of action

• In some cases, where the stakes were especially high or there were stakeholder conflicts, we would continue refining the model for about a year to make the model and its conclusions fully defensible

Most of the time, the 3-month full-scale model did the trick. The purpose of the next 9 months was to deal with objections in a convincing manner. Going back to the coal chute metaphor, the house had been reclaimed and put into basic working order in three months, while redecorating for the grand opening with a red carpet for VIPs might take the rest of the year.

Sensitivity Analysis: Tornado Diagrams

We had a specialized tool to identify the most important variables rapidly. The prototype model would brainstorm all the variables that anyone on the team thought might be important, then we quickly assessed ranges of uncertainty on each. The base case would be the median (equally likely to fall above or below that value), then we had a high case with a 10% chance it could be higher, and a low case set where there was a 10% chance it could be lower. Statistically speaking, these are the 10^th, 50^th, and 90^th percentiles. We would generate a tornado diagram by holding each variable at its base level, other than one, and varying the 10-90 range of that variable to see its impact on the outcome measure of interest.

https://plos.figshare.com/articles/figure/_Tornado_diagram_showing_a_series_of_one_way_sensitivity_analyses_comparing_genetic_testing_and_usual_care_/997919?file=1462825

Tornado diagrams typically show how uncertainty is not symmetric. This is not an exercise in fuzzing up the input numbers +/- 1%. It’s understanding the true asymmetric 10-90 range of uncertainty and how that impacts the final result. This probabilistic thinking has found its way into the field of medical informatics, in part from the influence of my department at Stanford. Many of the tornado diagram examples I found in a quick online search were medically related.

Even when there are 100 variables, most of the time the top 3-5 account for 80% or more of the overall uncertainty. Those variables merit more attention and better modeling to refine the result.

Non-Linear Feedback Effects

When I saw this article about the tar sands of Alberta, I recalled a modeling conundrum I heard about all the way back in 1992.

The Financial Pen

Oil Sands: The Most Important Industry You’ve Never Studied

On Arrakis, the desert planet at the heart of Frank Herbert’s classic science-fiction saga Dune, where rival houses and empires battle for control of the rare substance called spice which fuels space travel and galactic power, strength does not come from prophecy…

Read more

a year ago · 133 likes · 28 comments · The Financial Pen, Strategist, and Architect

A team from our consulting company worked with one of the oil companies for years on their tar sands strategy. Oil prices were around $20 per barrel, and tar sands extraction ranged from around $15 to $24. At the time, in the early 1990s, somebody reasoned this way in a presentation I attended: “Oil should not go over $40 per barrel because at that price, nearly endless amounts of oil can be extracted from the Alberta tar sands.”

https://storymaps.arcgis.com/stories/e926b83706cf495584e03b81da726c35

Getting usable oil out of these tar sands is not an easy process, and there are plenty of controversies around the site. But what the speaker missed was a feedback loop. The price of extracting oil from the tar sands, transporting it to where it was needed, and refining it into usable fuel were all functions of the cost of oil. As the price of oil went up, the cost of extraction, transport, and refining went up as well. That analyst had missed this feedback loop at the time and pointed out the oversight years later in another presentation. The breakeven cost of extraction is now around $40-80 per barrel depending on the specific project. The outstandingly detailed Substack article from explains many technological and transportation breakthroughs that have continued to improve the economics of these tar sands.

No Drafts in Expert Witness Work

By now, it should be clear that there are important relationships and subtleties in models that may take several iterations to surface. This fact does not play well with the legal system. Lawyers can destroy the credibility of an expert witness during cross examination by pointing out contradictions in earlier drafts of their own work. For this reason, no drafts are retained during expert witness work. Each new model overwrites the previous within the same document, and old versions simply disappear.

But non-lawyers don’t know about this trick for hiding contradictory history, and in the real world, drafts exist and persist. For one lost profits case I was sent to find all the historical “business cases” for a failed company at expansive legal offices in the old Sears tower in Chicago. The lawyers started by handing me a thin manila folder with about ten documents. I asked some questions and then a big box came out. I asked a few more questions and a dozen boxes showed up in the conference room. At the end of the meeting, I believe I had identified at least 300 different “business cases” showing hundreds of different internal valuations of the firm. This is why trial lawyers either want to see all the potentially embarrassing drafts or don’t want there to be any drafts depending on which side you’re on.

Building One-Page Models

To minimize the horrific possibility of self-contradiction upon cross-examination, expert witnesses typically keep their models as simple as possible. A one-page model is also far more likely to be understood by a jury with zero technical expertise in the matter.

Here’s an example damages model from the Federal Judicial Center’s “Reference Guide on Estimation of Economic Losses in Damages Awards” by a Stanford professor:

https://www.fjc.gov/sites/default/files/2014/12.econ_loss.PDF

That’s the whole model. My fellow strategy consultants with their multi-thousand line 100-variable probabilistic models would be scratching their heads and clucking about this crude approach, but that’s how it works in the expert witness business.

Auditing Spreadsheets

Even a one-page model can be fraught with peril for an expert witness. My cases nearly always settled before trial, but there was this one time we severely undermined the credibility of the opposing witness in court. This was around 2003, soon after the Internet Bubble Crash sent most small tech company stocks down 99%. He had put together a table of a dozen peers to calculate lost profits based on typical “software industry margins.”

Unfortunately for the opposing witness, his table included Microsoft, which made a ton of profit, and 11 tiny companies that all lost money. The weighted average was essentially Microsoft’s profit margin, which he then used to claim enormous lost profits. Our witness pointed out to the jury that the company in question looked much like the 11 tiny money-losing companies and not at all like Microsoft, and that demolished the lost profits claim, as there would have been no profits to lose.

Looking back, a long-term study a few years later found that only 4.2% of venture-backed Silicon Valley startups were profitable.

https://wordpress.clarku.edu/wp-content/uploads/sites/423/2016/03/SVPerform_EDQ2007.pdf

Excel vs. Python

Each modeling platform brings its own pros and cons, and modeling experts tend to have strong opinions about their platform of choice.

I’ve programmed in Basic, COBOL, Fortran, Lisp, C, C++, C#, Java, and Python, and I still prefer Excel for most cases when I can use it. In Excel, you can see what is going on right in front of you. I find it much easier to graph and interpret spreadsheet data. Perhaps that’s because Excel was my primary tool for the first 12 years of my career and I got to the top 1% of Excel hackers along the way. I’ll never have the patience or desire to achieve that level of expertise with Python.

Over the years, I’ve learned many techniques for catching my own errors. It’s embarrassing to catch them, but better to find them myself. Basic spreadsheet hygiene like calculating cross-sums can reveal many problems. All spreadsheets and all models have some sort of bugs; if the bugs aren’t visible in the underlying data or constructed model, they’re lurking in what’s been left out.

The First Computer Bug

For those of you who haven’t already heard the legendary story, the first “bug” found in a computer program was an actual bug, duly logged by Grace Hopper in her 1947 journal. This is why we call them bugs.

https://www.computerhistory.org/tdih/september/9/

What’s the most surprising bug you’ve found? How have you detected a serious problem in someone’s financial model? Do you ask yourself (and the analyst) what’s missing when presented with a glossy analyst report?

Leave a comment

Go squash those bugs.

This update to my asset allocation model, using monthly historical data since 1971, shows how to get the returns of a 100% stock allocation with a 72% reduction in risk (as measured by average monthly drawdown). If you had a way to get the same returns as the S&P 500, but with less than half the average drawdown, would you take advantage of that opportunity? If you prefer the lower risk of 60/40, why not lower that risk by 64% more to get to the efficient frontier? Read on to find out what creates this massive risk reduction.

Disclaimer: these are simulated returns, based on historical data believed to be accurate. Past performance does not guarantee future results. The asset allocation model remains a work in progress and future articles will continue to refine new insights. This article is provided for educational purposes only. I am not a financial advisor. Please contact a licensed financial advisor if you seek personalized financial advice.

Why Reduce Risk Now?

How much higher do you think this stock market bull market is going to run, seriously? The trend is your friend until the end when it bends, and that bend seems to be right around the bend, so to speak. I’m not calling for a major pullback at a specific time, but I’m preparing to update my personal asset allocation.

Bubble comparison charts are abundant on the Internet right now. Here are a few recent viral posts from X. I’m sure you’ve seen plenty of these on Substack as well, though many momentum fans think it’s still a good time to buy.

Disclaimer: I have no strong opinion on these particular analysts or their specific metrics and arguments other than the stock market is really starting to feel like the late 1990s to me as well.

Would you rather reduce your exposure to stocks too early or too late if an Internet Bubble style crash is headed our way? Maybe this is a good time to take at least some profits from the stock market and stash them away into a safer long-term asset allocation?

To be clear, I’m not talking about hiding in cash. I’m talking about long-term investing in alternative asset classes that provide stock-like returns and protect from currency debasement.

Hybrid Alternatives

Last week’s article explained the concept of a hybrid alternative that gives you the best of both worlds. I wrote that in preparation to present portfolios that offer higher returns than 100% stocks coupled with the lower risk than a 60/40 allocation.

It turns out that asset allocation indeed provides fertile grounds for developing hybrid alternatives that push out the efficient frontier. The gains come not from building a different blend of stocks and bonds but by introducing new, less correlated assets into the mix. Specifically, adding gold and trend following ETFs to the portfolio increases returns while reducing risk. A previous article showed the performance added by gold and trend following based on annual rebalancing.

Model Upgrades

This version of the asset allocation model upgrades from annual to monthly data. A previous article explained the sources of this new monthly data in detail. Notably, the new monthly returns for small cap stocks come from the website of renowned academic Ken French. These revised small cap returns lead to a higher allocation to small cap stocks in this version.

While integrating the new monthly data, I also discovered a bug in how I had been handling assets that came online after 1971. My calculations intended to gross up allocations in earlier years to make sure the total allocation added to 100%. I got this gross-up calculation correct in one place, but missed it in another, leading to understating total returns for portfolios that allocated to post-1971 starting assets. Specifically, the portfolios that included trend following had understated their returns in the earliest years. Fixing this error leads to a higher allocation to trend following along the high-return part of the efficient frontier.

I’ll have more to say about bug hunting and the unavoidable limits of the financial modeling processes in next week’s article. For now, let me reinforce that this whole multi-part asset allocation study is a work in progress, and each model update provides deeper insights that improve upon previous versions. Outsiders rarely get to see these shifting nuances of quant models in progress.

Efficient Frontier

Processing the new monthly asset returns data reveals that a direct hybrid combination of stock returns and 60/40 risk sits well inside the efficient frontier for this 55-year monthly data set. The frontier includes one portfolio with returns that add 0.7% per year (straight up) and another portfolio that cuts average drawdown by 40% (straight left) relative to a theoretical hybrid of 100% stock returns and 60/40 risk.

How do these efficient-frontier portfolios manage to deliver stock-like (or better) returns with so much less risk? Mainly it comes from a significant allocation to gold and trend following. Let’s look at the full range of optimal allocations.

Sweeping the Efficient Frontier

The high-level asset allocation pattern is clear. The lowest-risk portfolios make heavy use of bonds, while the highest-return portfolios allocate nothing to bonds. In this model formulation, commodity allocations are higher than stock allocations all along the efficient frontier.

The return vs. risk profile along the efficient frontier is heavily driven by US small cap stock exposure. The highest returns require heavy exposure to small cap stocks, while the lowest risk portfolios minimize small cap exposure. Real estate allocation peaks in the midrange, with large cap dominating the less risky end of the spectrum. Tech stocks never make it to the efficient frontier, nor do ex-US stocks or emerging markets stocks.

Higher return portfolios benefit from higher risk corporate bonds, while the safest portfolios load up on nearly risk-free T-bills. 10-year treasury bonds play a minor role in the lowest risk portfolios, but only up to a 10% allocation.

Trend following gets a significant allocation across all efficient frontier portfolios, growing from 12% at the low-risk end to over 40% for the highest returns. Gold ranges from 10 to 20%. Only a tiny allocation for the GSCI commodity index creeps in at certain points on the efficient frontier. The annual data frontier never got any GSCI allocation.

If you’re curious about the exact allocations, here are the specific asset weights along the efficient frontier:

These weights are obviously subject to change as I continue to add more assets into the mix. The current efficient frontier depends on the legitimacy of the historical trend-following returns provided by researchers at hedge fund AQR, so those will get more scrutiny going forward.

Performance Over Time

Historical returns for the high-return efficient frontier strategy look really good. Over time, the portfolio captures the upside movements of stocks while greatly reducing drawdowns to provide the smoother ride of 60/40. Performance has visibly tailed off since 2008, which also makes me want to investigate the trend following pre-2008 performance more closely to validate its assumptions.

Here’s the lower-risk version of 60/40 on the efficient frontier, offering the same return with 64% less drawdown risk.

That orange line is incredibly smooth. Owning gold sidesteps the big declines of the 1970s. This low-risk portfolio mostly avoids the crash of 2000 and better handles the Global Financial Crisis of 2009. Performance syncs up with 60/40 over the most recent couple years.

Drawdown Comparison

The 64-72% reductions in risk for the efficient frontier portfolios are easier to see when comparing the drawdowns over time.

The high return efficient frontier strategy does great at reducing the Internet Bubble drawdown but struggles with the Global Financial Crisis. It’s also a bit disappointing in the 2020 Covid crash.

The low-risk efficient frontier portfolio does a better job reducing risk in 2022 but still struggles with the Global Financial Crisis. I’ve kept the drawdown chart on the same scale so you can see how far risk drops relative to the more aggressive portfolios. This lower risk formulation pumps the brakes on the biggest drawdowns somewhere between 10% and 15%. These charts make it clear why I’m going back to the 1970s, as that drawdown was on par with what happened in 2008/9.

Appraising the Model: Next Steps

In preparing to pull the trigger on updating my personal asset allocation, I have a few more topics to explore.

How reliable is the trend following history? What happens if you add different takes on long-term history for different approaches to trend following? I’ve found a couple of competing trend following indices for comparison.

Why no allocation to Emerging Markets and Ex-US Stocks? 55 years of underperformance is a long time. I suppose it’s possible that if the US dollar loses its grip as the world’s reserve currency, we’ll see a snap back in non-US denominated stocks.

What happens if you add value stocks and momentum stocks? Value and momentum are the two most widely applied factors both among investors and on the Substack finance community. Will either of these factor-driven stock portfolios make it to the efficient frontier?

What happens if you add Bitcoin? Does the Bitcoin allocation directly subtract from gold or does it increase the overall allocation to commodities?

Please subscribe and stay tuned to get some answers to these questions.

Subscribe now

What other questions would you like me to explore? Let me know in the comments!

Leave a comment

https://www.caranddriver.com/shopping-advice/a64655267/vehicle-car-truck-suv-body-types-explained/

Trading off competing values can be tricky. But it becomes much easier when you identify an alternative that is better according to each value measure. The economic concept of Pareto Efficiency describes an alternative that dominates another alternative along every dimension of value. My Ph.D. dissertation extended this efficient frontier concept to seek hybrid alternatives that combine the best aspects of two or more other alternatives. This week’s article presents some real-life hybrid strategy case studies from the automotive, computer, and music industries.

Pareto Efficiency

Economics classes make lots of assumptions, and many of them turn out to be untrue in practice. However, the idea of Pareto Efficiency is about as rock solid as an assumption gets. If you care about two things, say quality and affordability, and option B is both higher quality and better affordability in your own opinion than option A, and you only care about those two value dimensions, then you should definitely choose B over A and are quite likely to do so in practice. Another way of describing this situation is that B is a dominant alternative over A.

The beauty of Pareto Efficiency is that it avoids the sticky problem of trading off two competing value measures. It simply doesn’t matter what your tradeoff is between those two values if an alternative is better on both dimensions.

Here’s an example of Pareto Efficiency from a data scientist’s political polling website, using restaurant options.

https://fivethirtyeight.com/features/marco-rubio-and-the-pareto-frontier/

In this example, White Castle is clearly the most affordable option and the worst tasting one as well. The world-renowned French Laundry ranks best on taste but is the least affordable. Between these two we have the much maligned “Italian” chain Olive Garden. (Olive Garden is a mid-market chain restaurant out of Florida, as is the fake Australian Outback Steakhouse.) One reason so many people avoid Olive Garden is that they have relatively high prices and low quality compared to typical locally owned Italian restaurants, such as the Giovanni’s shown here. Therefore, Giovanni’s dominates Olive Garden. There is still a tradeoff with more affordable and better tasting restaurants along the Pareto frontier, but Olive Garden can be stricken from the list of viable options.

Here’s global macro hedge fund advisor Raoul Pal’s video review of Olive Garden, after being pressured for months by his Texan girlfriend to visit:

Markowitz Efficient Frontier

The same Pareto Efficient concept lies behind the Markowitz efficient frontier. The frontier gets flipped right to left because it’s maximizing return while minimizing risk, so the best options lie to the top left.

https://investinganswers.com/dictionary/e/efficient-frontier

My Dissertation: The Value of Searching for Better Alternatives

In grad school at Stanford, while doing research on value tradeoffs, I started thinking about ways to push out the efficient frontier. What if instead of focusing on how to make trade-offs between known alternatives along the current frontier, you instead focused on finding ways to generate new alternatives that pushed out the frontier?

Hybrid Alternatives

I define a “hybrid alternative” as one that combines two different alternatives and achieves the higher value of each one at the same time. Taking cost and quality as the two dimensions, here’s a diagram showing a theoretical hybrid alternative.

In this example, A and B define the original frontier, with A being the bargain option and B providing a luxury alternative. But what if you could find car C that was as cheap as budget car A and as nice as luxury car B? Perhaps car C is on sale, or perhaps you as a buyer put different value tradeoffs on different subjective measures of quality.

Putting forward a theoretical target in multiple value dimensions does not guarantee that such a thing exists. But what I’ve found is that when there are many alternatives, it’s much easier to find some quirky hybrid that pushes out the frontier at least a bit. I’ve seen this framework apply well to:

• Buying a car

• Buying a home

• Choosing a college

• Finding a new job (work-from-home, lose commute)

• Optimizing investment portfolios

These are all situations where alternatives are abundant, with hundreds of potential options.

Hybrid Car Body Type: Lexus RX300 Crossover

A few years after I graduated with my Ph.D., I used this framework when shopping for a new car. We were preparing for the birth of our first child and neither of our small sports cars could easily handle a car seat or baby gear. So, we went to the local auto show to look for some sort of sedan, SUV, or station wagon. This also happened to be the time when the “crossover” body style exploded onto the auto scene.

Being an overly analytic quant, and partly just for laughs, I built a spreadsheet model to rate each vehicle according to many dimensions. The composite “quality” score accounted for everything the table below, as rated by both my wife and me. Both of our fathers were auto mechanics, and both of us were car enthusiasts, so my wife went along for the ride on this 24-point quality analysis, ranking each vehicle 1-10.

Aggregating across all these dimensions, I calculated a single quality score for each vehicle. We fiddled around with the numbers until the rank order and relative distance between each felt about right. Adding costs resulted in the chart below. This is actual data from early 2001, dug up from my computer archives. Car prices have gone up a lot since then.

At the budget extreme, we see the Mazda 626 (blue), the sporty sedan option with four doors for easy car seat access. At the luxury end, we see my wife’s preferred option, the relatively new BMW X5 SUV (red), in its cheapest configuration. The green markers show two tall station wagons we found, the Subaru Outback and the Volvo Cross-Country (XC). These were like traditional station wagons but raised for better clearance and visibility.

Other manufacturers noticed what Subaru and Volvo were doing by raising their station wagons a couple of inches and started jacking up car bodies and making them look more like a truck. Voila: the birth of the crossover. Technically, a crossover is built using a raised car frame but with a more SUV-like shape. A true SUV has a different body-on-frame architecture that better enables true off-roading capability. But automotive engineers are clever and some of these crossovers could scamper over rough terrain. We read an off-roading review in Car and Driver showing how the Lexus RX300 somehow managed to complete all the 4WD challenges while giving off the vibe of a whimpering show poodle.

https://www.caranddriver.com/reviews/comparison-test/a60231831/2001-acura-bmw-infiniti-land-rover-lexus-mercedes-benz-mitsubishi-suv-archive-test/

“Not surprisingly, the Lexus also lost points as it whimpered along our off-road trail: no dedicated low range, no usable engine compression for braking, and passenger-car tires. With the least ground clearance of this bunch, the RX300 had difficulty stepping over a felled tree the others climbed easily. Still, it completed the route, although throughout it resembled a poodle in the midst of a coon-hound trial.”

The Lexus RX300 was based on the Toyota Highlander but with a more premium interior and other upgrades. From a Toyota/Lexus perspective, it was higher cost and higher quality. But it cost less and delivered higher quality than the competing Acura MDX crossover, which was bigger than we needed. The Lexus RX300 was also slightly better for our purposes than the Volvo XC and substantially cheaper. The more trucklike BMW X5 was much larger and much more expensive. BMW later filled this gap in their lineup with the X3 and ultimately the smaller and cheaper X1.

The Lexus RX300 hit a real sweet spot in the market when it debuted. Note how it was priced about the same as the down-market Subaru Outback but brought the upscale feel of the Volvo XC. Based on our own scoring mechanism, the new Lexus entrant pushed out the efficient frontier.

Doug DeMuro, the widely followed automotive YouTuber, concurs that the Lexus RX300 introduced a whole new automotive concept at the time. What happens when you cross a truck with a station wagon? You get a “crossover.” The crossover has become one of the most popular vehicle types 25 years later.

Hybrid Power Train: Toyota Prius

You’re probably more familiar with the term “hybrid” from the hybrid powertrain architecture also made famous by Toyota. The Toyota Prius was a commercial breakthrough as the first large production vehicle that ran on both gasoline and electric powertrains. These, too, were hybrid alternatives in the decision analysis sense, as they provided the convenience of gas-powered vehicles with the fuel efficiency of electric vehicles.

https://global.toyota/en/detail/20209700

A hybrid powertrain overcomes the range challenges of fully electric vehicles and lowers the weight required by the number and size of batteries needed for fully electric vehicles.

Hybrid Laptop: PowerBook Duo

Technology is full of hybrids. Way back in 1992, Apple Computer was trying to strike the right balance between lightweight portable computers and powerful desktop computers. Enter the PowerBook Duo with its docking station that enabled both mobile and desktop modes.

https://sixcolors.com/post/2020/08/20-macs-for-2020-19-powerbook-duo/

The code name for the Duo while it was in development was “Bob W,” which stood for “Best of Both Worlds.” You’ll frequently find this term associated with hybrid alternatives.

Best of Both Worlds in Music

Not only did Van Halen release a hit song Best of Both Worlds, but the band is full of hybrid appeal.

When the rest of VanHalen fell out with original lead singer David Lee Roth, his replacement Sammy Hagar took the band to new heights of fame. People commonly referred to the updated lineup as “VanHagar.”

Decades later, while Eddie VanHalen is no longer with us, fans are still split on which lead singer was best in retrospect. Now there’s a tribute band with members role-playing both lead singers to cover all the hits.

Fans of Hannah Montana (and their parents) may also recall a Best of Both Worlds tour featuring both Hannah songs and Miley Cyrus songs as she was preparing for her ultimate breakaway from Disney.

The central concept of the show was how a girl could have the “best of both worlds” as a famous pop star in disguise and an undercover normal schoolgirl life as well. That fragile duality could only hold on for so long, but it did draw a huge audience.

Finding More Hybrid Alternatives

Where have you seen or created hybrid alternatives? How did they work out for you? Let me know in the comments!

Leave a comment

Subscribe now

Finance professors have obsessed for decades over whether or not it’s possible to “beat the market.” Harry Markowitz proposed “Modern Portfolio Theory” in 1952, eventually leading Eugene Fama to put forward the “Efficient Market Hypothesis” in 1970. Fama won a Nobel Prize for his 1970 EMH work in 2013. But, demonstrating the lengthy delays in academia, Fama and his colleague Ken French had already proven that markets were not efficient in 1993. So, do academics think you can beat the market or not? And how do they gather and process the data they need to make these apparently contradictory claims?

Fama Wins 2013 Nobel Prize for 1970 Work He Disproved in 1993

Eugene Fama gained fame by arguing first for, then against, the Efficient Market Hypothesis. His claim that it’s very hard for investors to beat the market was the justification for his sharing the 2013 Nobel Prize.

https://www.fool.com/investing/general/2013/10/23/eugene-famas-nobel-prize-right-person-wrong-reason.aspx

However, as the article cited above explains, quant researchers associate Fama more closely with his seminal paper showing multiple factors that “beat the market,” specifically size and value.

Fama French Breakthrough

Here’s the trick: call size and value “risk factors” rather than “market inefficiencies.” Then the story becomes how the market rewards people who take on specific risks, rather than saying the market is “inefficient.”

The 1992 and 1993 Fama French papers were a huge deal at the time and are still among the most widely cited papers in finance. I was in grad school at Stanford when these papers were published, and various faculty members were whispering about how the hallowed Efficient Market Hypothesis had just been disproven and that you can, in fact, beat the market. Benjamin Graham, famous value investor and role model for Warren Buffett, knew this back in the 1940s.

Professional fund managers had been operating small cap and value funds for decades before Fama and French blessed these as legitimate “risk factors” in the eyes of academia.

Dimensional Fund Advisors

After refuting the Efficient Market Hypothesis fiction, it was natural to launch market-beating funds based on these Fama French factors. Fama became a director at Dimensional Fund Advisors who put out a series of funds based on quant factors including size, value, and profitability.

Interestingly, DFA still shy away from momentum funds because of drawdown concerns, though nearly every quant has found that momentum outperforms the market over long enough horizons.

Ken French Data Site

Ken French, Fama’s academic partner at the University of Chicago in 1993, has become better known as a data provider for academic researchers. He’s now at Dartmouth and publishes his factor library on the website of the Dartmouth Tuck School of Business.

https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

French’s data has very broad coverage of global markets, going back far in time, calculating his various factors across all these different geographies.

Because of this excellent geographic coverage and decades of history, I’m now using French’s database as my long-term historical record of monthly returns for several equity-related assets in my asset allocation study.

French Data vs. Shiller Data

Robert Shiller, who shared the 2013 Nobel Prize with Fama, also puts out a research site with deep historical monthly data. Shiller is best known for the Shiller CAPE ratio (Cyclically Adjusted Price-to-Earnings Ratio). This is a fancier version of the Fama French value factor that smooths out the business cycle by looking at earnings over 10 years and adjusting for inflation.

Shiller’s data is meant to take a very long view on value across business cycles and is not meant to capture short-term drawdowns. Shiller uses monthly average prices, which reduce volatility compared with month ending prices used by Ken French. The month ending price data matches my purposes much better and aligns with daily pricing of currently active ETFs like SPY and VOO for the S&P 500.

What Happens When People Aggressively Trade on Factors?

Ironically, markets are becoming more efficient as academics continue to find dozens of factors that explain systematic inefficiencies. There were no small cap or value ETFs 100 years ago. And since these were recognized as official market-beating factors, performance has trailed off vs. the back-generated history showing how each factor would have performed 100 years ago when there was no systematic factor trading.

Bid-ask spreads have collapsed over the past 100 years. Now any retail investor with a few dollars can buy broad index funds holding hundreds of stocks for no commission, no transaction cost, and very little price impact through bid-ask spreads.

https://users.nber.org/~confer/2001/si2001/jones.pdf

When factors become well-recognized and easily tradable via systematic strategies and ETFs, the factors become less reliable as they get priced in more aggressively.

The way I’ve seen this work out in the past 20 years is that factors now provide what I call a return on drawdown more than a risk factor. By that I mean that factors work most of the time except when they go into severe drawdowns that give back years of profits. Once people “give up” on a factor and shut down their funds based on that factor, it typically comes roaring back into life. This is one of my motivations for diversifying across factors as well as asset classes.

French Small Cap vs. Damodaran Small Cap

As you go farther back in time, factor performance records tend to overstate historical performance relative to current performance. This overstatement is exacerbated by looking at illiquid pools of stocks that had transactions costs too high to arbitrage away the performance of that factor.

French and other quants attempt to compensate for the liquidity problem by looking at broader groups when calculating their factors. The Fama French size factor, Small Minus Big (SMB), compares the bottom half of stocks to the top half by size. The Fama French Value factor, High Book-to-Value Minus Low Book-to-Value (HML), looks at the top 30% value stocks vs. the bottom 30%.

The Damodaran data I had used for the annual historical small cap returns looked only at the smallest 10% and was equal-weighted, taking the same size position regardless of tiny market cap. It would be hard to achieve the paper returns on microcap stocks when traded on an industrial scale. For my monthly data set, I’m now using the Fama French version of small cap which equates more closely with the widely traded Russell 2000 small cap index.

French Risk-Free Rate vs. Damodaran vs. BIL vs. SGOV

Ken French also provides a monthly risk-free T-bill rate, held one month to full duration. ETFs can’t operate that way on single month-to-month T-bills, as they need more liquidity and therefore must hold multiple overlapping T-bills. The SGOV ETF fits this one month risk-free rate better than BIL. BIL goes significantly more negative in certain months. Because of better correlation to the risk-free rate and less chance of a negative return, I’m now using SGOV as my short-term T-bill ETF.

Calculating Bond Prices from Monthly Yields

I’ve traded commodities and equities for 30 years. I’ve always been much less clear on how fixed income pricing works, particularly funds that include a basket of bonds. After decades of putting it off, I finally sat down and learned how to calculate bond fund returns from a table of changing monthly yields.

As I suspected, the total return calculation based on start-of-month and end-of-month yield is only an approximation. Having AI as a tutor is helpful, as you can interactively ask the AI questions that you can’t ask a book or website. After a few iterations on the duration formula, here’s what I was able to reconstruct for 10-yr US treasures and BAA Corporates using monthly yield data from FRED:

The monthly constructed returns show much higher drawdowns for corporate bonds than what is revealed by the annual returns. Essentially, the annual returns serve as a lower envelope as monthly returns run ahead and come crashing back down. For the purposes of asset allocation based on risk and return, the monthly data are far more appropriate.

I wonder if the drop-off in correlations over time is a sign that markets react more strongly to crisis events than what is captured by simplified monthly bond pricing formulas.

Some Straightforward Monthly Benchmark Updates

For Real Estate, I found monthly history starting from the end of 1971 on the NAREIT website. Given that’s when the benchmark started, I will enable real estate as an investible option starting in Jan 1972.

Spot gold prices are available in TradingView back to the 1920s.

Investing.com shows monthly returns for the Goldman Sachs Commodity Index (GSCI) back to 1971. The GSCI history on Investing.com matched the GSG ETF slightly better than the GSCI index on TradingView.

TradingView has the Nasdaq Composite index back to 7/73. A site called Macrotrends has monthly data for the Nasdaq Composite back to early 1971.

Ken French provides monthly returns for an ex-US universe similar to EAFE and an emerging markets universe similar to MSCI Emerging Markets. To supplement the French data in earlier years, I found monthly returns data on both EAFE and EM indices on an ETF analytics site called LazyPortfolioETF,

AQR provides constructed historical data going back to 1985 on a monthly basis. The correlation to the DBMF ETF drops off significantly when moving from annual to monthly data. The broad AQR benchmark correlates 63% with DBMF, while the commodity AQR benchmark only correlates 28%. On the other hand, DBMF returns are much closer to the lower commodity benchmark than the overall benchmark. Given the large allocation to trend following that resulted from the annual data, I’m keeping with the more conservative commodity benchmark history for now. Clearly, I need to dive more deeply into the nuances of trend following as I refine the study and add more trend following ETF options.

Updated Splice Correlation Table for Monthly Data

The correlations between historical sources and live ETFs show a clear pattern. Any asset with a well defined total return index correlates 97% or higher to the live tradable instrument.

Constructed histories, on the other hand, show much lower correlations. Both 10-year treasuries and corporate bonds use approximate formulas based on start-of-month and end-of month yields that do not quite match the daily performance of live bond ETFs that are also based on larger baskets of bonds. 3-month T-bills line up much better because they have much lower duration and interest rate variability.

Trend following shows the worst match as there are so many different approaches and universes for systematic trend following. This variability could become either a bug or a feature in live performance, as the whole purpose of trend following is to introduce diversification when the performance of all other asset classes go to a correlation of 1 during a crisis.

Please subscribe to see the impact of this monthly data on the efficient frontier and find out the newly refined optimal portfolios!

Subscribe now

https://www.trendfollowing.com/trade_everything/

The main question I’m getting on Substack regarding asset allocation is “what are most people over-allocated to?” For most people, the answer is an overallocation to stocks. For others, it’s cash. The better question is, what are most people under-allocated to? Gold is one clear answer, other than the gold bugs who are already all-in. But the biggest missing piece is some form of commodity trend following. This article introduces trend following into the annual asset allocation model going back to 1971 and finds that both gold and trend following play important and complementary roles.

Disclaimer: This study is meant for educational purposes only and is not financial advice. If you seek financial advice for your personal financial situation, please seek assistance from a licensed financial advisor. Past performance of any asset does not guarantee similar future performance.

Background for Study of Annual Asset Returns

This week’s article provides a more detailed update to the v1 annual study released two weeks ago. That initial model suggested allocating 20-30% to gold but did not include trend following.

Today’s v2 annual model introduces five additional asset classes, bringing the total to 12 asset classes:

• Trend following long-short commodities (DBMF)

• Long-only Goldman Sachs Commodity Index (GSCI)

• Ex-US stocks (based on EAFE: Europe, Australasia, and Far East)

• Emerging market stocks (EEM)

• US Tech stocks (QQQ)

If you want to see why I picked DBMF as the trend following ETF, check out this earlier article:

The Challenge of Partial History

Ten of the asset classes have annual returns starting in 1971. The Emerging Markets stock index launched in 1988, and it was hard to trade a basket of emerging markets stocks before then. For trend following, I currently have returns starting in 1985. The same source provides returns by decade going back farther but I am starting with just the annual history for now. In a future version, I’m planning to add Bitcoin into the asset mix, most likely with a starting year of 2018.

I could handle the missing early years in multiple ways. One approach would be to fill the missing early data with a proxy; for instance, I could backfill emerging markets stocks with EAFE returns prior to 1988, as both are examples of non-US stocks. But I don’t think that either gold or GSCI are good proxies for a long-short commodity trend-following index.

For now, I’m forcing the allocations to non-available asset classes to zero before they launch. I simply gross up the other allocations to 100%, keeping their relative weights consistent before and after the introduction of new assets. At some point down the road, I’ll calculate the sensitivity of the final result to these kinds of assumptions.

Return vs. Risk

The chart below plots annual return vs. average annual drawdown (my preferred measure of risk) for each of the 12 asset classes. I’ve also included an even mix (1/12 to each) and a 60/40 proxy, using the same definition as the v1 study.

GSCI looks terrible over the full 55-year period. This long-only commodity index has both the worst returns and the most risk, which might explain why so few people show interest in allocating part of their portfolio to commodities. Trend following commodity markets, both long and short, vastly outperforms the buy and hold approach.

The updated definition of real estate is based on REITs, which puts their return/risk in the vicinity of other US stocks. Tech stocks have about the same average return but far more risk. Both EAFE and Emerging Markets stocks have returned significantly less than US stocks over the full 55 year period, with higher risk as well.

Efficient Frontier

As in the v1 study, I used the Excel optimizer to find portfolios with the minimum risk for any given level of return. This time, I swept return across a broader range to develop a smooth “efficient frontier.” Returns of 7% can be generated for a near-zero average annual drawdown, while maximum risk portfolios peak at just over 12% annual returns. These are all nominal returns, not adjusted for inflation.

Sidebar on Non-Linear Optimizers

One of the challenges of non-linear optimization is that multiple completely different combinations of inputs can lead to essentially the same level of output. To visualize how this happens, consider a mountain range with multiple distinct peaks that are nearly the same height. The Matlab plot below shows a generic example.

https://www.mathworks.com/products/global-optimization.html

This multipeak phenomenon can cause confusion when comparing two portfolios that have different-looking allocations but generate essentially the same risk-return profile. These annual asset allocation studies have not run into this problem yet, but eventually they will as we add more assets that are strongly correlated to each other (a problem known as “collinearity”). Fortunately, the optimization plots so far show nice smooth transitions as we move along the efficient frontier.

Optimal Allocations vs. Risk

We can move along the efficient frontier by projecting onto either the risk or return axis. Let’s start by looking at risk.

The lowest risk efficient portfolio puts 60% into bonds, 30% into commodities, and 10% into stocks. This is roughly consistent with what we saw in v1. The highest risk efficient portfolio holds 75% stocks and 25% commodities, with no bonds.

Optimal Allocations vs. Return

Moving along the efficient frontier by charting return, we see that bonds get abandoned at a target return level of 10.5% or higher. Higher return targets consistently require higher stock allocations, which makes sense.

Commodity allocations peak in the middle. 60/40 returns about 9.5%, while a 100% stock portfolio returns about 11%. The range between these two return targets might be considered the “sweet spot” for the efficient frontier. This sweet spot of returns is exactly where the commodity allocation peaks, between 45% and nearly 55% commodities. In practice, hardly anyone is doing this: I’ve observed very few widely followed model portfolios put forward by large wealth managers that include such a large allocation to commodities.

It’s possible that this large commodity allocation is an artifact of gold’s recent bull run, but we know that’s tied to the ongoing devaluation of the US dollar, a process that could just as easily accelerate.

Stock Allocations

Now let’s look at optimal allocations within each broad group of assets, starting with stocks. Because of their lower returns, neither EAFE stocks nor Emerging Markets stocks made it to the efficient frontier. This may change when we move from annual data to monthly data and are able to see specific variations within the annual drawdowns.

Not surprisingly, the riskiest portfolios rely on tech. More surprisingly, the small cap benchmark got selected more than large cap for the lower risk end of the efficient frontier, possibly because small-cap stocks are more value oriented and large-cap stocks are dominated by growth stories. The REIT-based real estate index showed the highest risk-adjusted performance and got the biggest allocation. I find that result a bit suspect and will investigate further in the next model version.

Sweeping along the return axis makes the transitions quite clear. Things get a bit noisy at the high end when various stock indices with essentially the same returns compete with each other for the full allocation.

Bond Allocations

The specific bond index allocations are quite straightforward. The lowest risk portfolios rely heavily on T-bills.

10-Year Treasury bonds peak near the middle of the return spectrum, where the classic 60/40 portfolio can be found.

Even though they have the highest returns, corporate bonds get hardly any allocation in v2. In v1, they got the highest allocation among bonds. The introduction of new asset classes led to a reallocation based more on the risk profile of corporate bonds than on the return profile. Also, it’s quite possible that the live ETFs used in recent years led to a restatement of the risk-return profile for some of these asset classes relative to the original Damodaran academic research data.

Commodity Allocations

To me, the commodity allocations are by far the most interesting finding from this v2 annual model. Annual model v1 had allocated 20-30% to gold. That allocation remains in v2, with trend following leading to an even larger allocation to commodities.

The efficient frontier shows us that gold and trend following are complementary assets that can both belong in an optimal portfolio, depending on risk preference.

Trend following is a long/short approach that contributes to risk reduction during strong drawdown periods. Therefore, trend following gets the largest allocation for the lower-risk portfolios. Because trend following puts a drag on returns, it gets de-selected for the very highest return portfolios, ramping down as target returns go over 10.5%.

GSCI never gets any allocation because it offers the lowest returns with the highest risk. The results might be different if we broke out individual commodity groups that peak and crash at different times. It also might make sense to look at other precious metals like silver, given the strong allocation to gold. Adding Bitcoin will also likely eat into the gold allocation.

Example Portfolios from Efficient Frontier

Now let’s see what the updated high return and low risk portfolios look like over time. The 11.1% target return portfolio matches stock market returns at much lower risk.

We still see significant drawdowns in 2008 and 2022. Those drawdowns can be addressed by cranking down target returns to 9.5%, the target for 60/40.

Adding bonds really does smooth out the biggest drawdowns, but at a cost to returns. Adding volatile commodities via gold and trend following brings more smoothness than stocks and bonds alone can achieve. That’s the beauty of diversification. It’s also the direct solution to inflation spurts caused by fiat currency and its accompanying money printing.

Next Steps

I’m now gathering monthly data to compare results with far better granularity on drawdowns. As usual, the deep historical data gathering and cleaning process is taking far longer than updating the analysis will take.

I’m also planning to look at some finer-grained allocations. How does adding Silver and Bitcoin impact the commodity allocation? Is it worth adding high yield bonds and TIPS to the bond allocation? Eventually I’d like to add private equity and other hedge fund strategies but that’s a much more difficult modeling exercise.

We’re getting to the point of specificity that I’m preparing to add paid subscriptions. If you’d like to support my work and find out exactly what I’m putting in my personal portfolio at the end of this research project, please consider pledging to become a paid subscriber. Thanks!

https://joca-cable.com/blog/splicing-wiring/

Financial models are only as good as the data that feed them. To upgrade the annual asset allocation model I introduced last week, I assign current ETFs to match every asset’s history and add some new assets to fill key gaps. Along the way, I investigate the definition of each asset’s benchmark and quality check the match between the history, the current ETF, and the chosen benchmark. This week’s article provides a behind-the-scenes view of how quants investigate competing data sources and decide what makes the cut. You’ll be introduced to some dirty secrets of how financial data vendors rewrite history, rarely discussed with outsiders.

Finding a Mysterious Wharton Dataset

Setting out to find annual data back to 1971 for more asset classes, I came across an archived data set from the prestigious Wharton School of Business that provided annual returns from 1970 to 2009, attributed to Andrew C. Mack.

https://finance.wharton.upenn.edu/~acmack/ret2009.pdf

I asked Grok to investigate the provenance of this data and it seems this table was used for some study or class, but the original context has been detached from the data set. Welcome to the fascinating world of point-in-time historical financial data.

Sidebar on Point-in-Time Data

Few people outside the institutional data industry understand how much data vendors and their suppliers love to rewrite history. “Point-in-time” data refers to data stored precisely as it was first made available at a historical point in time, which may be quite different from current historical records. Data can be changed over time for many different reasons:

• Companies repeatedly restate their earnings, correcting errors or changing definitions

• “Corporate actions” like mergers and acquisitions lead to “pro forma” historical accounts that were constructed after the fact and differ from original reporting

• Survivor bias leads to failed entities being dropped from history, overstating the performance of the group that lived vs. the full cohort including those that failed

• Data vendors—in their zeal to cut costs—discontinue, delete, or lose historical records that were available earlier

Finding stranded old documents like this Wharton .pdf file, frozen in time on a server, often leads to more accurate point-in-time data than looking up current sources. Sometimes there is no other source because the vendor lost or overwrote their own history.

Around the time that global data vendor Thomson Reuters bought our small analytics startup StarMine in 2008, I was introduced to a Point-in-Time (PiT) data vendor called Charter Oak. Their president Marcus Bogue was a world-class expert on how point-in-time data differs from restated data. We spoke together at several conferences, so I got to hear his story many times. He would show how companies like General Motors might restate their earnings nine different times in subsequent financial reports, wreaking havoc upon the relative rankings of companies in backtested quant factors derived from those repeatedly restated numbers.

How did Charter Oak get its point-in-time data? Frequently they gathered physical CDs and DVDs (remember those?) from customers of major data vendors.

These read-only records, including paper copies, were time-stamped and could not be modified. The running joke (and accurate truth) was that being a data CD pack rat provided enough profits for a fancy car collection funded by sales of old data that the original vendors themselves no longer had.

My speaking tour with Dr. Bogue was around 2009, coincidentally the same time this Wharton document got archived. No doubt the mysterious Andrew C. Mack was motivated to gather historical data to study the impact of the Global Financial Crisis.

In an interesting bit of irony, the Charter Oak website itself is now gone, along with the old presentations for quant groups. But I found a snapshot from the Wayback Machine (a site that stores snapshots of websites that are no longer active). A point-in-time record of a point-in-time data collector. If anybody has heard from Dr. Bogue recently, I’d love to catch up.

Adding New Asset Classes

The Wharton .pdf adds two new data sets for my asset allocation study: international stocks and Goldman Sachs Commodity Index (GSCI). It also provides markedly different histories for US small cap stocks and equity REITs. To validate this data and compare it to the Damodaran data, I worked with Grok to figure out what current ETFs most closely corresponded to each of the two academic data sets. Grok has become a knowledgeable intern at this point, on par with recent graduates from top finance programs.

Assigning ETFs to Each Asset Class

Here are the ETFs I picked:

1. Large Cap US Stocks: Vanguard S&P 500 (VOO)

2. Small Cap US Stocks: iShares Russell 2000 (IWM)

3. Ex-US Stocks: iShares MSCI EAFE (EFA)

4. Emerging Market Stocks: iShares Emerging Markets (EEM)

5. US Tech Stocks: Invesco QQQ Trust (QQQ)

6. T-Bills: SPDR Bloomberg 1-3 Month T-Bill (BIL)

7. 10Yr Treasury Bonds: iShares 7-10 Year Treasury Bond (IEF)

8. Corporate Bonds: Vanguard Long-Term Corporate Bond (VCLT)

9. Real Estate: iShares Core US REIT (USRT)

10. Gold: iShares Gold Trust (IAU)

11. GSCI: iShares S&P GSCI Commodity Indexed Trust (GSG)

12. Trend: DBi Managed Futures Strategy (DBMF)

These are the best known, longest running, most widely traded, or cheapest ETFs following the specific indices for which I have surfaced long-term annual returns.

When I start gathering monthly history, I may go back farther and grab earlier ETFs that cover the same indices in some cases. I may have to switch benchmarks to get monthly history; we shall see. The point of iterative modeling is to learn what you can from a data set, then use what you learned to build a better model for the next iteration.

Different Formulations of Small Cap Stock Returns

I chose the Russell 2000 as the most widely followed US stock index. The Wharton .pdf correlates 99.99% with the overlapping annual history for IWM. Prof. Damodaran used an entirely different formulation for small cap, correlating only 88.7% with the IWM annual returns. Damodaran got his small cap data from Prof Ken French’s website at Dartmouth, used to analyze the size factor for the famous Fama/French 3 factor model.

The Fama/French size factor data holds groups of small caps in equal weight portfolios. Equal weight indices require more rebalancing and transaction costs than cap-weighted indices like the Russell 2000. I want my model portfolio to be as easily tradable as possible, so I’m moving forward with the Russell 2000 index and ETF for now. I may revisit this later when I consider size, value, momentum, quality, and other factors to construct an improved equity sleeve for the overall portfolio.

Comparing Real Estate History

Comparing the Damodaran and Wharton data on real estate tells a similar story. The Wharton real estate returns track the FTSE NAREIT Equity REIT Index total returns with dividends reinvested. The USRT ETF follows this same REIT index.

Damodaran’s data set starts with the Shiller Residential Home Price Index prior to 1986, when switches to a private commercial real estate proxy like the NCREIF Property Index. These are unlevered price indices and do not include rental income.

Considering that homeowners are typically overexposed to residential real estate prices, looking at commercial real estate as an investible asset class that includes both normal mortgage leverage and rental income makes more sense to me for an asset allocation study. The fact that the USRT ETF lines up directly with the Wharton data makes that pairing a more logical starting place to me.

The differences in both returns and volatility for the two different real estate benchmarks are quite large.

Avoiding CTA Survival Bias

When I first started this asset allocation project three years ago, I searched for a historical database of Commodity Trading Advisor (CTA) performance to provide a history of returns prior to the launch of trend-following ETFs. The most comprehensive publicly available listing I found was from IASG, an independent advisory group based in Chicago (home of the commodity futures trading pits).

https://www.iasg.com/managed-futures/performance?sortBy=dateInception&pageNumber=1&orderBy=ASC

After spending some time with the database, I determined that it has some pretty serious survival bias problems. I have no reason to doubt the accuracy of what is in the database itself. What concerns me is what is missing from the database. Going back to the discussion of point-in-time data, where are all the failed and otherwise closed CTA funds? This snapshot of the screener shows only 9 funds active as of 1995. I know for a fact, having been a commodity analyst back in 1996, that there were far more than 9 CTA funds back then. Even among the 9, the compound annual rate of return (CAROR) varies from 4.18% to 15.99%. I don’t think taking the average the returns of these survivors would be representative of the typical CTA performance at the time.

AQR Trend Following History

Realizing that every other quant trying to run deep historical studies on asset allocation faces the same problem, I looked around to see what some of the major quant shops are using for deep history in their publications. The most prominent study I have found (so far) is from AQR, a Greenwich CT quantitative hedge fund with a strong reputation. Three of their researchers proposed a time series momentum strategy that could be used to approximate CTA returns going back as far as commodity futures price data allow.

https://www.aqr.com/Insights/Datasets/Time-Series-Momentum-Factors-Monthly

AQR generously provides the history of these time series momentum strategies back to 1985 on their website for people to conduct their own research using the data.

Even this algorithmically constructed dataset shows outrageously strong and smooth performance in the early days. When I plug the baseline TSMOM returns into an optimizer, it loads up allocations to trend following more than I’m comfortable believing can be captured in an ETF. The AQR authors further decompose the signal into commodities, equities, fixed income, and foreign exchange. The DBMF ETF returns (bright green) correlate better with the commodities returns (orange, 95.7%) than the overall TSMOM returns (dark blue, 82.5%), so I’m going with the commodity momentum returns for now.

Emerging Markets History

Neither academic source had deep historical returns for emerging market stocks. MSCI Emerging Markets, the benchmark for EEM, is the most widely followed emerging markets stock benchmark. A little digging around turned up a financial planner’s site called Novel Investor that posted returns going back to 1988 for emerging market stocks. The correlation with EEM returns is 99.8%. Here’s a table Novel Investor put together showing how each asset class has performed since 2011, including an asset allocation mix. These asset class benchmarks line up well with mine, other than the bond indices.

https://novelinvestor.com/asset-class-returns/

Summary Table

The table below summarizes the benchmarks, early history sources, current ETFs for each asset class and ETF start year, as well as the correlation for the overlap period for the historical sources.

10 of the asset classes have overlap correlations of 99% or higher. As explained above, trend following uses an algorithmically constructed benchmark that correlates at 96%. Only the GSCI commodity index has a lower correlation, at 86.4%. Given the variety of commodity futures contract rollover approaches, it does not surprise me to see a mismatch between index performance and ETF performance for a commodity fund. For now, I’ll bookmark this for further investigation.

Stock Charts

Here are the historical charts for the stock asset classes. I’ve included real estate with stocks because this version is based on equity REITs and clearly correlated to other stock indices.

Bond Charts

For the bond asset classes, the tradeoff between risk and return is easily seen.

Commodity Charts

For the commodity asset classes, gold and trend following appear to complement each other nicely. The GSCI long-only index performed about the same as gold in the 1970s, then it has gone sideways since 1980. The strategy of buying and holding commodities suffers from both futures contract rollover issues as well as deflationary pressure from improvements in commodity production over the decades.

Preview of Coming Attractions

I’m currently running these updated asset class histories through the optimization machine to see what I can learn. Please subscribe to find out the results!

Subscribe now

https://worklizard.com/the-power-of-gold-the-history-of-an-obsession/

This article marks the beginning of my quantitative study of asset allocation from 1971-2025. The research period specifically starts when Nixon fully cut off the US dollar from the gold standard in 1971. This first simple asset allocation model, built upon annual returns data compiled by NYU Finance Prof. Damodaran for 7 asset classes, highlights the importance of holding gold in a fiat currency regime. For model v1, the optimal high return portfolio turns out to be 51% stocks, 19% bonds, and 30% gold. The optimal low risk portfolio puts 20% into stocks, 60% bonds and T-bills, and 20% gold. Read on to find out why.

Disclaimer: I am not a licensed financial advisor, and this article does not provide financial advice. I am a long-time quantitative analyst doing research for my own portfolio and sharing work in progress for public comment and discussion. This article is part of an ongoing investigation into asset allocation. Future articles will introduce more asset classes and more granular monthly data, thereby updating the conclusions. Please subscribe if you’d like to follow along with the ongoing research.

The Art of Iterative Modeling

I began my professional career as a financial analyst coming from an engineering background, where we learned the value of starting with simple models, gaining insight from them, and using those new insights to construct better models. In my Decision Analysis Ph.D. program at Stanford, we learned to formulate a decision basis, evaluate its implications, then appraise its value as a model to guide action. We would iterate as long as it took to get commitment to action, putting in effort proportional to the magnitude of the stakes of the decision.

https://en.wikipedia.org/wiki/Decision_analysis_cycle

I’m impressed that one of my advisor’s students posted this 35+ year old classroom graphic on Wikipedia. I can vouch for the accuracy of the article in its representation of what we were taught in the Decision Analysis class at Stanford.

This article is the first simple iteration of my asset allocation study. It took me about a day to build the model in Excel. I wasn’t sure if I needed to go straight to python for the optimization part, but it turns out that the solver optimizer in the current Excel is remarkably good compared to the specialized optimization software I used in grad school 35 years ago.

Purpose of Annual Rebalancing Study with Limited Asset Classes

This study is a first rough attempt to build the backtesting infrastructure and determine what output charts make the most sense. Looking at actual data and initial results has already impacted how I’m going about the optimization process. At first, I thought I wanted to optimize return / risk, but now I’m seeing that I prefer to minimize risk for a given level of target return, as the charts below will show.

This first-pass study uses a consistent set of annual returns from a reliable source (Prof. Damodaran at NYU) who prepared them for long-term studies such as this. Starting with clean, consistent data sidesteps the many challenges of data curation, described in the article linked below. I’ll get to work on those challenges in the next iteration next week.

This study has known gaps in asset classes: no ex-US stocks, no commodities besides gold, no trend following or other alternatives. Future studies will likely lower the gold allocation to spill over into other commodities and/or trend following. Introducing Bitcoin will also likely deplete the gold allocation.

This annual data study also has known gaps in methodology, since annual data suppresses drawdowns within the year. Monthly data will enable better measurement of annual drawdowns and more frequent rebalancing to reduce these drawdowns.

With this framing introduction covered, let’s see what we can learn from Prof. Damodaran’s annual returns data.

Annual Performance for Each Asset Class

Charting the annual asset class data reveals how gold absolutely trounced stocks in the 1970s. I started the study in 1971 because that’s the year when the US fully abandoned the gold standard. The ending years of study also catch the recent strong rally in gold that pulled gold ahead of corporate bonds.

I’m a little surprised to see the low returns from real estate over this 55-year period. I’ve had better luck in my own personal residences, but specific location matters tremendously in real estate, and returns from the choicest locations are diluted in the total real estate index. Next week I’ll compare these real estate returns to some other historical real estate benchmarks.

Return vs. Risk

Plotting returns vs. average drawdown was particularly insightful for me. Gold has a horrible annual average drawdown (over 20%), by far the worst of the seven asset classes, but its strongest upside performance comes at exactly the right time to balance out the biggest drawdowns in other asset classes.

3-month T-bills have precisely zero annual drawdown, making them a truly risk-free rate for this study. It appears these are the returns of buying and holding 3 month T-bills to maturity, so there is no price risk. If I had plotted real returns rather than nominal returns, T-bills would have shown a drawdown, but the assumptions around inflation are hard to estimate and defend. I’ve decided not to adjust for inflation and just look at what nominal prices do from one period to the next.

Based on annual data, corporate bonds completely dominate 10-year US treasuries, as they have both higher returns and lower drawdowns on an annual basis.

Plotting the ratio of return to average drawdown makes the differences more stark. Technically, the T-bills ratio should be infinite, so I just blanked it out. Seeing the infinite ratio for T-bills also made me realize that I’m not trying to optimize this ratio, as I’d clearly rather hold large cap stocks than corporate bonds. There is a tradeoff to be made between return and risk, but that tradeoff is not as simple as taking the highest ratio of return / risk.

These plots also include four combination portfolios:

1. A 60 / 40 combination of 60% large cap stocks and 40% US 10Y treasuries. I realize that different 60 / 40 portfolios are constructed differently, but the S&P 500 and 10Y US treasury bonds seemed like the most natural starting point.

2. An even asset allocation: 1/7 to each of the 7 asset classes. Look at how well that even-weighted approach does on return / risk. This combination is the closest to the risk parity approach of what has been plotted here.

3. A minimum-drawdown portfolio that matches the return of large cap stocks.

4. A minimum-drawdown portfolio that matches this return of the 60/40 portfolio.

You will see on the return vs. drawdown plot how the two minimum-drawdown portfolios (orange dots) line up at the precise return level of their corresponding benchmarks (blue dots). Let’s compare the performance and composition of these two portfolios to their benchmarks.

Min Risk for Large Cap Stock Return

Recalling my recent article on average drawdown as a measure of risk, that approach is working beautifully for the 55-year annual asset allocation study. Look at how well the optimization smooths out drawdowns relative to 100% stocks.

Min Risk for 60/40 Return

Minimizing drawdown relative to 60/40 is not as dramatic and mainly helps in the early years. Note how this set of assets, using annual data, is unable to overcome the recent inflation-driven drawdown of 2022. These optimized portfolios also struggle with the Global Financial Crisis of 2008.

On the other hand, gold (and likely some other commodities, especially oil) beautifully fills the huge bear market of 1973-74.

Sources of Improvement

Gold plays a pivotal role in drawdown reduction for these two portfolios. The large cap stock portfolio allocates 30% into gold, which the 60 / 40 drawdown reduction portfolio puts 20% into gold.

Both portfolios substitute corporate bonds for US 10-year treasuries. As mentioned before, this is a case of dominance in which both return is higher and risk is lower. When one asset dominates another in terms of both risk and return, there is no tradeoff to be made: the better asset simply substitutes for the inferior asset. Going to monthly data and adding more assets may change the result.

Dominance across the full 55-year period does not imply dominance in each year. Large cap stocks are better on both risk and return vs. small cap over this full period. But there are years when small cap stocks do much better. The optimizer saw this and put 16% into small cap and 35% into large cap for the high return strategy.

Finally, note how the risk-reduced version of the 60 / 40 strategy relies on a 7% allocation to 3-month T-bills to achieve that smoothness. But this smoothness comes at a cost to returns. The high-return strategy makes no use of T-bills.

What Does This Mean? And What are the Limits of Those Insights?

I was not expecting the lowest risk, high return strategy to be 51% stocks, 19% bonds, and 30% gold. Were you? Have you seen anybody proposing that as an asset allocation? I haven’t. If you don’t believe the result, feel free to download the annual returns from Prof. Damodaran’s site and build a spreadsheet calculating returns from annual rebalancing using the allocations shown in the chart.

What’s driving this high allocation to gold? Currency debasement is real. Look at the difference between holding gold vs. US 3-month T-bills for 55 years. The importance of gold could go up even more over the next year, or it could come crashing down. This study shows what worked over the past 55 years and makes no guarantees over what will happen in the next 1, 5, 10, or 50 years.

What’s Next?

As mentioned at the start, this is an iterative study meant to get the ball rolling. I’m not immediately putting my portfolio into any of the allocations shown above. Specifically, here’s what I’m doing next:

• Add more asset classes: ex-US stocks, commodity index, trend following

• Pick current ETFs for each asset class and start splicing in annual data back to their starting points

• Review the definitions of each asset class to match the long-term history to what is currently investible via ETFs

It’s common for messing around with data to account for 50-80% of the quant research process, which is why I spent several weeks writing about data curation.

Please subscribe if you want to follow along with the research and support my work. This is a rare opportunity for outsiders to see that goes on inside the sausage factory of quantitative financial modeling. Expect some more surprises along the way.

Subscribe now