Estimating Variations in the Equity Risk Premium: A New Approach

For years, researchers have used historical returns as proxies for estimating equity risk premiums. This approach is problematic, however, because the resulting estimates don’t vary from one year to the next, even though equity market returns can be wildly divergent from year to year.

Katsunari Yamaguchi, CFA, president of Ibbotson Associates, Japan, has developed a new method that addresses variations in the equity risk premium over time. Yamaguchi explains his process in a recent Take 15 interview with Larry Cao, CFA.

“The historical return series is the only available data we can see, but the equity risk premium, as a concept, is a forward-looking concept,” Yamaguchi says. “We cannot see it directly in the historical data, so we have to estimate by some means and — especially when it comes to variation of the equity risk premium over time — it’s hard to do that.”

Yamaguchi’s approach relies on monthly data to generate a better estimate. “I use the monthly return series and try to decompose it into a mean and deviation from mean, and I keep track of the deviation from mean return,” he says.

“If you imagine a perpetual bond, the yield and price are inverse relations, and equity is considered a kind of perpetual bond,” he says. “So a similar phenomenon may happen, when yield changes, price changes in an inverse way.”

Yamaguchi has used this method to analyze historical data from both the United States and Japan from 1952 to 2013, and found that over the first 30 years, equity risk premiums in both countries remained lower than the historical average, but rose higher than the historical average over the second 30 years.

“The problem with equities is that we can only observe the price change,” he says. “So from observed price change . . . I am trying to estimate the implied risk premium change behind the return data.”

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