In looking to the future, let us assume for the moment that investors in each country expect the same risk premium as they have received in the past. However, if future volatility were equal to the long-term historical volatility, the expected risk premia would be equal to the historical risk premia. The long-term historical standard deviation is a poor predictor of future volatility, especially since some sources of extreme volatility (such as hyperinflation) are unlikely to recur. We therefore need estimates of expected future risk premia that are conditional on current predictions for market volatility.
In refocusing on the expected future risk premium, however, we must do more than extrapolate from the past.

The question of what equity premium we can expect has, for years, been a source of controversy. In late 1998 Ivo Welch studied the opinions of 226 financial economists who were asked to forecast the thirty-year equity risk premium Most respondents to the Welch survey would have regarded the Ibbotson Associates yearbook as the definitive study of the historical US risk premium. The first bar of the figure shows that the 1926-98 arithmetic risk premium computed from Ibbotson data was 8.8 percent per year. The second bar shows that the key finance textbooks were on average suggesting a premium of 8.5 percent, a little below the Ibbotson figure.

The textbook authors may have based their views on earlier, slightly lower, Ibbotson estimates, or else they were shading the Ibbotson estimates downward. The Welch survey mean is in turn lower than the textbook figure, but since respondents claimed to lower their forecasts when the equity market rises, this difference may be attributed to the market's strong performance in the 1990s. Interestingly, the third and fourth bars of Figure 7 show that the survey respondents also perceived the profession's consensus to be higher than it really was. That is, they thought the mean was around 0.8 percent higher than the 7.1 percent average revealed in the survey.

These survey and textbook figures represent what was being taught at the end of the 1990s in the world's leading business schools and economics departments in the United States and around the world. As such, these estimates were also widely used by investors, finance professionals, corporate executives, regulators, lawyers and consultants. Their influence extended from the classroom to the dealing room, to the boardroom, and to the courtroom.

In August 2001, Welch updated his earlier survey, receiving responses from 510 finance and economics professors . He found that respondents to the follow-up questionnaire had revised downward their estimates of the long-term arithmetic mean risk premium by an average of 1.6 per cent. Over a thirty-year horizon they now estimated an equity premium averaging 5.5 per cent, and over a one-year horizon, an equity premium averaging 3.4 percent (see Figure 7).

The mean premia were the same for those who had previously participated in the earlier survey and those who were taking part for the first time. Although respondents to the earlier survey had indicated that, on average, a bear market would raise their equity premium forecast, Welch (2001) reports that "This is in contrast with the observed findings: it appears as if the recent bear market correlates with lower equity premium forecasts, not higher equity premium forecasts".

Predictions of the long-term equity premium should not be so sensitive to short-term stock market fluctuations, especially in the direction and magnitude revealed by Welch's follow-up survey in 2001. While it is possible that one-year required rates of return fluctuate markedly, it is unlikely that thirty-year expectations can be so volatile. The changing consensus may,however, reflect the new approaches to estimating the premium and /or new facts about long-term stock market performance, such as evidence that other countries have typically had historical premia that were lower than the United States.

The bars in the right-hand figure show the distribution of the responses. The mean forecast was 7.1 per cent; the median was 7.0 per cent, and the range ran from 1 to 15 per cent.
While the bars in the left-hand figureshow the distribution of survey responses, the curved line represents the normal distribution based on the mean over approximately a century and the associated standard error for the US equity risk premium.

Whether Welch's survey mean of 7.1 per cent was appropriate is another matter. A large number of respondents were calibrating their forecasts relative to the longest-run historical benchmark available from Ibbotson, and then shading the historical number downward based on subjective factors, including their judgement of the impact of strong market performance in the late 1990s. By 2001, longer-term estimates of the US arithmetic mean equity premium were gaining popularity.

If Figure 6 is compared with Figure 3, a histogram of historic US premia. it is interesting that the distributions are not normal but skewed, slightly, towards an expectation of lower risk premiums This represents an optimistic outlook.
The long-term historical data would seem to bear this out. However, for short term attitudes, history also shows that wild fluctuations can occur. The use of long-term values is the most reliable procedure.