Triumph of the Optimists
Warren Buffet says his wealth came from “a combination of living in America, some lucky genes, and compound interest.”
Last week, I discussed my journey from Zimbabwe to the American free-market economy. Like many immigrants and citizens of this country, I feel very lucky to be here. This week, I would like to focus on the third component of Buffet’s quote: the power of compounding. Specifically, what can investors expect from compounding their capital over long periods of time going forward?
In our view, markets compensate investors for bearing risk. That function is important because we live in an uncertain world—the last century was marked by two World Wars, a Great Depression, and a Global Financial Crisis. The news always seems to be full of new things to be afraid of.
Holding equities for the long term requires optimism in the face of the crises of the day. And if there is one lesson I have observed from studying the long-term history of markets, it’s that, over long periods of time, the optimists have won. Since 1900, US equities have compounded at 10% per year, far outpacing inflation and bonds.
Figure 1: Cumulative Return on US Asset Classes in Nominal Terms, 1900–2000
Source: Elroy Dimson, Paul Marsh, and Mike Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns, Princeton University Press (2002)
The historical base rate of US equity returns suggests a 10% annual rate of return, doubling your money every 7 years and thus creating exponential increases in wealth over decades. The evidence from international markets suggests a similar rate of increase.
Figure 2: Nominal and Real (Net of Inflation) Global Equity Returns, 1900–2000
Source: Elroy Dimson, Paul Marsh, and Mike Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns, Princeton University Press (2002)
But the reason it requires the heart of an optimist to win in the stock market is because of the annual volatility. Equities have a large standard deviation of returns, around 20%. And this volatility is catnip for our worst psychological biases: our loss aversion drives us to sell stocks when prices drop, our desire to see patterns in randomness drives us to attempt to time markets, and our availability heuristic primes us to overweight the probabilities of the bad things on the news actually happening to us.
We believe the best way to counteract these biases, and to win in equity markets, is to hold for longer time periods. Because of compounding, the distribution of expected outcomes places the odds in favor of investors achieving their goal of increasing wealth over time. Specifically, the probability of losing money in equities is lower over longer time horizons.
Figure 3 illustrates this point using simulations that are based on monthly US market returns from 1965 to 2016. In each case, the gray bars reflect the proportion of negative outcomes (losing money over the time horizon) and the blue bars reflect the proportion of positive outcomes. Notice that while both distributions in Figure 3 are centered on a 10% annualized return, there is a wider range of annualized returns over a one-year horizon relative to a ten-year horizon.
Figure 3: Simulated US Market Returns over One- and Ten-Year Horizons
Sources: Ken French data library and Verdad research. For illustrative purposes only. See note on methodology below.
Based on this data, it appears that investors are more likely to increase their wealth over a ten-year horizon than a one-year horizon. And while the probability distribution is extremely favorable, the psychological burden of holding for a decade can be substantial. Just think of all the wars, crises, economic turmoil, and short-term panics that occur in markets over any given decade. Base rates favor equity investors, and compounding shifts return distributions further to the right over time, which makes achieving the goal of increasing wealth more likely over longer horizons. (It is for this reason that Verdad’s funds have longer lock-ups than the rest of the industry).
However, the optimists have more than the broad market portfolio to be excited about. Academic research shows that there are segments of the market that are expected to outperform the overall equity market over long periods of time. These premiums are attributable to small companies (the size premium), cheap companies (the value premium), and profitable companies (the profitability premium).
Figure 4 illustrates the expected return distribution of US small value equities over time horizons ranging from one year to 20 years. The distributions are simulated from monthly US small value index returns between April 1965 and September 2016. As suggested in Figure 4, the small value segment has an expected return of around 15% per year, and investors are more likely to achieve a positive return over longer horizons.
Figure 4: Simulated Annualized Returns of US Small Value Index Over Time Horizons
Sources: Ken French data library and Verdad research. For illustrative purposes only. See note on methodology below.
The market segment we pursue at Verdad—leveraged small value equities—incorporates the size, value, and profitability premiums within a universe of leveraged companies that are paying down the debt on their balance sheet.
The benefits of holding small, cheap, leveraged companies over long horizons are well known to private equity managers. That is why long horizons are embedded within the private equity structure, where the typical lifespan of a fund can be 10 years or more.
Our research suggests that public market investors can capture the premiums that drive private equity returns—at lower cost and with more transparency—if they are willing to look past short-term volatility in the stock market and maintain a long-term perspective. At the end of the day, investors cannot eliminate the uncertainty that is inherent in financial markets. But they can place themselves in a better position to capture the premiums that markets offer.
The triumph of the optimists resonates with me on a personal level. Growing up in Zimbabwe, I lived through the worst hyperinflation in history since the Weimar Republic in the early 1920s. I began my career on Wall Street during the depths of the global financial crisis. Through it all, equity markets have recovered over time and rewarded investors for bearing risk. It’s hard to overstate the importance of a long-term perspective when it comes to investment success.
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Note on Methodology
The bootstrap simulations shown in Figure 3 and Figure 4 are based on monthly returns of the US market index and US small value index from April 1965 to September 2016. Monthly index returns were sourced from Ken French’s data library. The charts represent the distribution of 10,000 random draws (with replacement) of annualized returns from the historical data over various time horizons. This provides 10,000 independent estimates of annualized returns at each time horizon. An annualized return is an annual rate of return which allows investment performance over different time horizons to be compared in the same units.
In Figure 3, the Y-axis, “Frequency,” represents the number of simulated returns that fell within a particular range of the distribution. The “proportion of positive returns” represents the proportion of 10,000 simulated returns that were above zero. This reflects the estimated probability of realizing a return above 0% over each time horizon.
The percentiles in Figure 3 and Figure 4 reflect the 90% of simulated returns (9,000 returns) that were between the 5th percentile and the 95th percentile of the distribution. Returns outside of this range are possible and have occurred historically. Each percentile represents one percent of the 10,000 simulated returns. For example, in Figure 4, the 5th percentile of simulated one-year US small value returns is -20%. That means five percent of the simulated one-year returns (500 returns out of 10,000) were below -20% and ninety-five percent of one-year returns (9,500 returns out of 10,000) were above -20%. Similarly, the 50th percentile (median) of US small value returns is 15% per year across all time horizons so half of the simulated returns were below 15% per year and half were above 15% per year.
Bootstrap simulations are a standard statistical tool that involve random sampling with replacement from the historical data in order to form an expectation of future distributions. “With replacement” means that each random draw of an observation from the historical data is thrown back into the ‘bucket’ of data before the next observation is drawn. Therefore, it is possible to draw the same observation multiple times. Within the context of estimating expected returns, the bootstrap approach allows researchers to simulate thousands of alternative outcomes in order to estimate the distribution of expected returns. This approach ensures that the 10,000 samples of long-horizon returns are independent of each other (i.e. they are uncorrelated). The bootstrap approach is better than using rolling windows to estimate long-horizon returns because rolling windows provide fewer independent samples over longer horizons. For example, over the 52 years between 1965 and 2016, there are only five non-overlapping ten-year windows from which to estimate the distribution of ten-year returns.
The key underlying assumption behind bootstrap simulations is that the distribution of historical returns is indicative of the distribution of expected returns (that may be realized in the future). In order to increase the validity of this assumption, we use a long series of historical returns from 1965 to 2016.