### Is the Equity Premium Getting Smaller?

Ronald Reagan said that an economist is someone who, when he sees something work in practice, wonders if it can work in theory. This observation fits no topic in economics more snugly than the equity risk premium (ERP). In 1985, economists Rajnish Mehra and now-Nobel laureate Edward C. Prescott noted that from 1889 to 1978, the equity return in excess of the return on relatively riskless securities was more than 6%. They wondered if this could be true in theory. In their 1985 *Journal of Monetary Economics* paper “The Equity Premium: A Puzzle,” they concluded that no, it could not be true in theory. In fact, they decided, the largest possible premium in theory could be no more than 0.35%, less than a tenth of the observed amount.

Lest the reader think this was a less-than-serious paper on the fringe of economics, think again. A check of the paper on Google scholar finds that it has been cited in other academic works more than 5,000 times. Since Mehra and Prescott’s 1985 paper, the ERP puzzle has been the subject of a plethora of academic studies trying to explain it.

It is understandable that this would be a hot topic. We need an estimate of the expected future return on equity investments — for example, for Monte Carlo simulations. The risk-free long-term rate can be estimated to a good approximation by the 30-year Treasury bond yield and the risk-free short-term rate by Treasury bills. But an estimate of the expected return on equities in excess of that seems to be anybody’s guess. It would be nice to have a sound theory that tells us how to estimate it.

Mehra and Prescott’s 1985 paper prompted the conjecture that the ERP would be much lower in the future. That conjecture was dashed, at least temporarily, by the 15 years after the Mehra-Prescott paper, in which the realized ERP soared much higher than the 6% of their 1889-1978 data set. Nevertheless, the belief stemming from the Mehra-Prescott paper that the expected ERP can’t be as high in the future as it was in the past has lingered.

### Claude Erb’s speculation

The former money manager Claude Erb, who coauthored a paper on gold as a hedge against inflation that was previously reviewed in *Advisor Perspectives*, has added a small amount of fuel to that speculation. In an April 8 presentation titled “The Incredible Shrinking ‘Realized’ Equity Risk Premium,” Erb notes that “the realized ‘equity risk premium’ has been in a downward trend since 1925.” For evidence, he supplies the chart shown below (Figure 1).

### Figure 1. Declining Performance of Stocks Relative to “Safe” Assets

The two straight lines are the best trend-line fits to the realized ERP over short-term T-bills in one case and over intermediate Treasuries in the other. Erb remarks that this is of course very sketchy evidence. The downward trend shown in the two lines is in no way statistically significant – not least because the data include only nine independent 10-year periods (all the other periods represented by the points are overlapping and therefore not independent). Nonetheless, it is interesting information. The trend line in the realized equity premium over Treasury bills declined from almost 9% to less than 5%. Will it continue this downward trend?

However, these numbers are not even close to what Mehra and Prescott said was the theoretical maximum ERP of 0.35%. How did Mehra and Prescott come up with that number?