Eugene Fama and Ken French examined the volatility of the three equity premiums we have been discussing in their December 2017 study “Volatility Lessons,” which covered the period July 1963 through December 2016. In addition to finding high volatility of stock returns, they also found:
- Skewness of returns is -0.53 for monthly equity premiums, so the distribution of monthly premiums is skewed to the left. (If a distribution is symmetric about its mean, Skew (the third moment about the mean, divided by the cubed standard deviation) is zero.) However, Skew is positive (0.25) for annual premiums and increases a lot for longer return horizons, to 3.78 for 30-year premiums. Increasing right skew means more of the dispersion is toward good outcomes (good news).
- Monthly equity premiums are “leptokurtic,” which means there are more extreme returns than we would expect with a normal distribution (the tails are fat). Kurtosis (the fourth moment about the mean, divided by the standard deviation to the fourth power) is 3.0 for a normal distribution, and 4.97 for monthly equity premiums. Kurtosis falls to 3.19 for annual premiums but then rises strongly for longer return horizons, to 32.37 for 30‑year returns. The combination of right skew and kurtosis means that outliers are primarily in the right (good) tail.
- The standard deviation of equity premiums increases with the return horizon, from 17% for annual premiums to 2551% for 30-year premiums.
- In general, the distribution of premiums moves to the right faster than its dispersion increases. For example, the median increases 231-fold, from 6% for annual premiums to 1390% for 30-year premiums. Together, increasing kurtosis and right skew for longer horizons spreads out the good outcomes in the right tail more than the bad outcomes in the left.
Fama and French noted that while most of the news about equity premium distributions for longer return horizons is good, there is bad news. They used the realized monthly returns from the period their study covered to construct long-horizon simulation returns, and found that for the three- and five-year periods that are often the focus of professional investors, negative equity premiums occur in 29% of three-year periods and 23% of five-years periods of simulation runs. Even for 10- and 20-year periods, negative premiums occur in 16% and 8% of simulation runs, respectively.
Fama and French found similar results for the size and value premiums, and concluded that this is simply the nature of risk—if you want to earn the expected (the mean of the distribution of potential outcomes) premiums, you must accept the fact that you will experience losses, no matter how long your horizon. Said another way, if you can’t stand the heat, get out of the kitchen.
They concluded: “The high volatility of stock returns is common knowledge, but many professional investors seem unaware of its implications. Negative equity premiums and negative premiums of value and small stock returns relative to Market are commonplace for three- to five-year periods, and they are far from rare for ten-year periods. Given this uncertainty, investors who will abandon equities or tilts toward value or small stocks in the face of three, five, or even ten years of disappointing returns may be wise to avoid these strategies in the first place.”
Myopic Behavior Kills Returns
In my more than 20 years of providing investment advice, I’ve concluded that most investors —both individual and institutional—believe that when it comes to evaluating investment returns, three years is a long time, five years is a very long time and 10 years is an eternity. However, financial economists know that the historical evidence demonstrates that 10 years can be nothing more than noise and thus should be treated as such.
Most investors lack the discipline required to do so. Thus, they end up being subject to recency, which results in buying after periods of strong performance (when valuations are high and expected returns are low) and selling after periods of weak performance (when valuations are low and expected returns are high). That’s not a prescription for investment success. It is also why Warren Buffett says his favorite investment horizon is forever.