July 7, 2020
Written by Nathan Erickson, CFA®, CAIA, Managing Partner and Chief Investment Officer
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You’ve probably never heard of Ed Thorp. He’s a pioneering mathematician who has run several successful hedge funds built around applications of probability theory. While massively successful as an investor, his original claim to fame was a book he wrote about how to win at Blackjack called “Beat the Dealer”.
For those of you unfamiliar with Blackjack, it also goes by the name “21”. The object of the game is to turn over cards that total as close to 21 as possible, without going over, and to have a higher total than the dealer. While most cards represent their actual values, there are four face cards (ten, jack, queen, and king) that are all worth ten points. Players bet on each hand and, if they have more points than the dealer and don’t go over 21, they win and are paid an amount equal to what they bet. If the dealer wins, the player loses his or her bet. There are a few more rules, but they are superfluous to this discussion.
In the late 1950s, while he was a mathematics professor, Ed Thorp began researching probability theory as it relates to Blackjack. Probability theory refers to the branch of mathematics that deals with the analysis of random outcomes. In those days, dealers used a single deck and did not reshuffle the deck until the full deck was used. Thorp learned that, as cards were dealt, the expected probability of future cards changed. For example, if there are only 16 face cards (four each of ten, jack, queen, and king), and eight of them are dealt in the first 20 cards, the probability of seeing a face card on the next hand given there are 32 cards left is different than when starting with the entire deck. The probability of a face card is lower. In that instance, a player might bet less to minimize his or her losses given the low probability. If in the first 20 cards very few face cards have been turned up, a player might increase his or her bet knowing the probability of seeing a face card is increased.
As it relates to investing, this is similar to the concept of mean reversion. At some point, as a dealer goes through a deck, all of the face cards must be dealt. So, if many face cards are dealt early on, it makes sense that they would be less frequent going forward, but eventually they will all be dealt. Asset classes that have experienced high returns for a period of time are less likely to continue to have high returns, given that they will end up at an average level over time. We have seen examples of this in the S&P 500 historically. While the long-term average is near 10%, the market tends to outperform or underperform, and then reverts back to the average:
Ed Thorp’s probability theory worked extremely well in Blackjack. He made millions of dollars in casinos, and his book sold over 700,000 copies, which is unheard of for such a nuanced topic. The theory worked so well that, eventually, casinos had to change how they operated the game. Instead of dealing a single deck nearly all the way through, they shuffled the deck before all the cards had been dealt. The casino then went a step further and added multiple decks so that probabilities would have to be calculated on more than 150 cards versus 52. While the theory still worked, it became substantially harder to calculate probabilities. More importantly, it became very difficult to size bets appropriately, as the length of time the cards worked against you had increased dramatically due to multiple decks. If you bet too big early on, you potentially run out of money before the probabilities work in your favor.
Investing involves much of the same probability theory. The term “buy low and sell high” is an execution of probability theory. An asset class that has performed poorly and is priced low has a higher probability of doing better in the future, so an investor should overweight it. Conversely, an asset class that has performed well and is priced high has a higher probability of performing poorly in the future, so an investor should underweight it. Of course, investors use many other factors to make decisions, but the general application of probability theory has a desired outcome of winning more often than losing.
Despite a brief but violent decline in March and April brought on by the COVID-19 pandemic, the U.S. stock market continues to outperform all other equity markets. Prudent investing would recommend diversification in any environment but, particularly after the decade-long run of the S&P 500, the probability that small cap stocks, international stocks, or emerging market stocks would outperform would surely have increased. Yet here we are at the middle of 2020 with the S&P 500 down just 3% year to date, and all other markets are down 10-13%.
Looking back, diversification seems to have failed and, along with it, probability theory. The odds have been against the S&P 500, and yet it keeps winning. It is as though we are halfway through the deck and haven’t seen any face cards, and we lost several hands to the dealer. Over the last year, there has been a 10% performance gap between the S&P 500 and all other markets and, over the last three years, diversifying outside of the S&P 500 has cost investors 8% annually! Even more challenging, over the last ten years, international equities have underperformed the S&P 500 by 8-10% annually. That is a long time to underperform.
A possible explanation may be that the probabilities are different because the game has changed. Like the casino shuffling more frequently and adding additional decks, investors have had to deal with massive government and federal reserve bank intervention in good times and bad. Even before the multi-trillion-dollar combination of fiscal stimulus and fed support, we saw a tax cut in 2018 when the economy was in its eighth year of a bull market. We only recently experienced higher interest rates after nearly ten years of recovery, only to see them plummet once again with the onset of COVID-19. Since the financial crisis, no other developed economy has provided the level of fiscal and monetary stimulus that the U.S. has.
It is also possible that, as U.S. investors, our view is biased to our local market. Coming out of the financial crisis, no economy reached the level of growth typical of recovery. We have spent nearly a decade at 0% interest rates and, in other countries, negative interest rates. Debt levels have grown, demographics are a headwind, and we’re now in the midst of a global pandemic. Perhaps the low- to mid-single digit stock market returns the rest of the world has experienced over this time is more reflective of reality, and the U.S. market has been the outlier. Rather than being disappointed that the rest of the portfolio hasn’t kept pace with the U.S., investors should appreciate the excess return that exposure to U.S. markets has provided, given the challenging economic environment we have experienced.
We don’t believe the probabilities of diversification working and markets mean reverting have been eliminated. We cannot ignore that monetary and fiscal stimulus has had a material impact on the U.S. economy or, at the very least, on the behavior of the U.S. large cap equity market. While a casino can change the frequency of shuffling the deck and add additional decks with no consequence, we don’t believe the same is true for providing massive levels of fiscal and monetary stimulus. At some point, there are likely consequences of growing federal debt and increasing the Fed balance sheet.
If the market’s outperformance had happened without fiscal or monetary stimulus, perhaps there could be an argument for continued outperformance. Instead, we are likely to see a shift in leadership in the future, as we have in the past. The challenge for investors is continuing to persist with a strategy that doesn’t feel like it is working, when the urge exists to take what appears to be the easy path of investing in the S&P 500. Looking at the below chart of rolling ten-year annualized returns, investors need only to expand their history beyond the recent past to see that we have been here before with high returns in the S&P 500, and they don’t last forever. Furthermore, high returns are often followed by low returns, for periods even greater than a decade. Probability theory would suggest that, even with more cards in the deck, at some point what has been doing well will stop doing well, and what has been doing poorly will do better. In every environment, a prudent investor remains diversified and accepts a more consistent level of return rather than believing that the outlier is really the norm and will continue indefinitely.