Volatility and Premiums in Equity Returns
Understanding volatility is essential for informed investment decisions. A long term perspective is also needed. Fama and French have demonstrated that long time periods are required to be reasonably sure that average equity, size and value premiums will be positive. Tables 1, 2 and 3 make the point concretely.
About Table 1: The Equity Premium
Table 1 shows averages and standard deviations of annual values for the equity (RMRF) premium from 1963 to 2011. For example, the mean of the annual equity premium from 1963–2011 is large, 5.95% per year. This is what attracts investors to stocks. However, the standard deviation of the equity premium is also large—17.85%, or three times the mean. In other words, the yearbyyear values of the premium are volatile. This illustrates the point that investing in stocks is risky.
A normal distribution predicts that the annual equity premium is negative (that is, stocks underperform Tbills) in 37% of the years between 1963 and 2011. But, as the time horizon increases, the standard deviation of the average equity premium drops from 17.85% for a oneyear period to 7.98% for five years, 5.65% for ten years, 3.57% for 25 years, and 2.53% for 50 years. More significantly, the decline in the standard deviation of the average equity premium reduces the probability that the average stock return will fall below the average bill return as the investment period is lengthened. The probability of that happening declines from 37.0% for one year to 22.8% for 5 years, 14.6% for ten years, 4.8% for 25 years, and 0.9% for 50 years.
Years

1

5

10

15

20

25

50


Equity Premium

s(Mean)

17.85

7.98

5.65

4.61

3.99

3.57

2.53

Prob < 0, E(RMRF) = 5.95%

37.00%

22.80%

14.60%

9.90%

6.8%

4.8%

0.9%

Looking to the future, Fama and French estimate there is almost a oneinfour chance that the average premium for a fiveyear period will be negative; that is, Tbills will beat stocks. At 25 years, there is still almost a oneintwenty chance that the realized average equity premium is negative. It takes a long investment lifetime, 50 years, to reduce the probability of a negative realized average equity premium to 0.9%. So even if we know for sure that the true expected value of the equity premium is a healthy 5.95% per year, there is still a 0.9% chance that an investor who holds the market portfolio of stocks for the next 50 years will end up with a lower average annual return than an investor who rolls over onemonth Tbills. In sum, no matter how long the investment period, one can never be perfectly certain that the realized average premium will be positive. Such is the nature of risk and return. The stories for the size and value premiums are similar to that for the equity premium.
About Table 2: The Size Premium
From 1963–2011 the size premium averaged 3.69% per year. Yet the volatility of yearbyyear values of the size premium is high, with a standard deviation of 14.16% per year. Table 2 shows that if the true expected size premium is 3.69% per year, the probability that the realized premium will turn out to be negative falls from about 39.7% for a oneyear period to 28% for five years, 20.5% for ten years, and almost 10% for 25 years. In other words, even if we know for certain that small stocks are expected to beat large stocks by 3.69% per year, there is still a oneinten chance that large stocks produce a larger average return in a future 25year period. Even for 50year periods, there is a 3.3% probability that the average size premium will be negative.
Years

1

5

10

15

20

25

50


Size Premium

s(Mean)

14.16

6.33

4.48

3.66

3.17

2.83

2

Prob < 0, E(SMB) = 3.69%

39.70%

28.00%

20.50%

15.70%

12.20%

9.70%

3.30%

About Table 3: The Value Premium
Prospects are a bit rosier for the value premium. The average value return for 1963 – 2011 is 5.29% per year, similar to the average equity premium of 5.95%. The standard deviation of the value premium is large—13.94%—though still less than 17.85% for the equity premium. As a result, if the true expected value premium is 5.29%, the probability that a negative average value premium will be observed in a given period of time is lower that for the equity premium. Still, the probability of a negative value premium for a fiveyear period is almost 20%, falling to 11.5% at 10 years, and 2.95% at 25 years.
Years

1

5

10

15

20

25

50


Value Premium

s(Mean)

13.94

6.24

4.41

3.6

3.12

2.79

1.97

Prob < 0, E(HML) = 5.29%

35.20%

19.80%

11.50%

7.10%

4.50%

2.90%

0.40%

Conclusion
Fama and French have demonstrated that investing in stocks is risky. Even over a long investment lifetime, there is no guarantee that stocks will beat bills, small cap stocks will beat large stocks, or value stocks will beat growth stocks. It should also be noted that their analysis is based on highly diversified portfolios that are probably free of diversifiable volatility. For less diversified portfolios, uncertainty about outcomes is even higher. Fama and French point out this is true for actively managed stock portfolios, which are undiversified almost by definition. And it’s even truer for riskier investments like private equity and hedge funds. In the words of Vanguard founder John Bogle, “Rough as the market seas may be at times, longterm investors must hold stocks because as risky as the market may be, it is still likely to produce better returns than the alternatives. Wise investors won’t try to outsmart the market. They’ll buy index funds for the longterm and diversify."
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