Although the stock market's real rate of return has apparently been remarkably steady over long periods, the rate has been subject to considerable variation from year to year. To measure the volatility of these returns, we use the standard deviation of annual returns. Table 1.2 presents the year-to-year volatility of returns in each of the three major periods of stock market history and since 1982. It also presents the all-time high and low annual returns in each period. From 1802 to 1870, returns varied from the 7 percent average by a standard deviation of 16.9 percent; in other words, real returns fell within a range of -9.9 percent to +23.9 percent about two-thirds of the time. From 1871 to 1925, the standard deviation of returns was 16.8 percent, almost unchanged from the first period. In the modern era, 1926 to the present, the standard deviation of returns has risen to 20.4 percent. As Table 1.2 indicates, annual stock returns can, of course, fall beyond the ranges described by their standard deviations. The stock market's all-time high, reached in 1862, was a real return of 66.6 percent. The all-time low, recorded in 1931, was a real return of -38.6 percent. Plainly, the tidy patterns that are evident in a sweeping history of the stock market's real returns tell little about the return an investor can expect to earn in any given year.
Nonetheless, these wide variations tend to decline sharply over time. Figure 1.3 shows
that the one-year standard deviation of 18.1 percent drops by more than half, to 7.5 percent, over just five years. It is cut nearly in half again, to 4.4 percent, over 10 years. Though most of the sting of volatility has been eliminated after a decade, it continues to decline as the period lengthens, until it reaches just 1.0 percent over an investment lifetime of 50 years, with an upper range of return of 7.7 percent and a lower range of 5.7 percent. The longer the time horizon, the less the variability in average annual returns. Investors should not underestimate their time horizons. An investor who begins contributing to a retirement plan at age 25, and then, in retirement draws on the accumulated capital until age 75 and beyond, would have an investment lifetime of 50 years of more. Our colleges, universities, and many other durable institutions have essentially unlimited time horizons.
