# Swedroe: The Volatility Of Premiums

September 29, 2014

The size premium was negative in 38 of those years (or 44 percent of them). There were eight years (or 9 percent of them) when the premium was worse than -10 percent, four years (or 5 percent of them) when it was worse than -15 percent, and two years (or 2 percent of them) when it was worse than -20 percent.

The worst year was 1929, when the premium was -32.59 percent, very close to a three-standard-deviation event. The best year was 1967, when the premium was 42.42 percent, in fact a three-standard-deviation event. The gap between the best and worst years was 75.01 percentage points, almost 25 times the size of the premium itself. We had five years when returns were more than two standard deviations from the mean.

The value premium was negative in 33 of those years (or 38 percent of them). There were 10 years (or 11 percent of them) when the premium was worse than -10 percent, five years (or 6 percent of them) when it was worse than -15 percent, and two years (or 2 percent of them) when it was worse than -20 percent.

The worst year was 1999, when the premium was -26.79 percent, a more than two-standard-deviation event. The best year was 2000, when the premium was 37.69 percent, also a more than two-standard-deviation event. The gap between the two was 64.48 percentage points, more than 13 times the size of the premium itself. We had three years when returns were more than two standard deviations from the mean.

Extending The Time Frame

Even if we extend our time frame to five-year periods, we see that there is still risk in the premiums. Using nonoverlapping data, we can put together a total of 17 such five-year intervals.

• There are four periods (or 24 percent of them) when the stock premium was negative. The worst period was 1927-1931, when the stock premium was -46.13 percent.
• There are six periods (or 35 percent of them) when the size premium was negative. The worst period was also 1927-1931, when it was -30.2 percent.
• There are four periods (or 24 percent of them) when the value premium was negative. The worst period was again 1927-1931, when it was -30.49 percent.

If we extend our time frame again, this time to 10 years, we can construct eight nonoverlapping periods. In this instance, there were no periods when either the stock or value premiums were negative, but two periods when the size premiums were negative: 1947-1956, when it was -27 percent, and 1987-1996, when it was -14.9 percent.

Using data from 1963 through 2011, professors Eugene Fama and Ken French found that assuming normal distributions (and stock returns aren’t normally distributed) the probability of a negative stock premium fell from 37.0 percent for a one-year period to 22.8 percent for 5 years, 14.6 percent for 10 years, 4.8 percent for 25 years and 0.9 percent for 50 years. In other words, looking forward, there is almost a 1-in-4 chance that the average premium for a five-year period is negative.

Even at 25 years, there is still almost a 1-in-20 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 only 0.9 percent.

Even if we knew in advance the premium and the volatility (which we obviously cannot), there would still be a 5 percent chance that, over a 25-year period, the riskless one-month Treasury bills would have a higher average annual return than risky stocks. Fama and French found similar results for the size and value premiums, and concluded that this is simply the nature of risk.