Equity premium puzzle

The equity premium puzzle refers to the phenomenon that observed returns on stocks over the past century are much higher than returns on government bonds. It is a term coined by Rajnish Mehra and Edward C. Prescott in 1985, although in 1982 Robert J. Shiller published the first calculation that showed that either a large risk aversion coefficient or counterfactually large consumption variability was required to explain the means and variances of asset returns. Economists expect arbitrage opportunities would reduce the difference in returns on these two investment opportunities to reflect the risk premium investors demand to invest in relatively more risky stocks.

The intuitive notion that stocks are much riskier than bonds is not a sufficient explanation of the observation that the magnitude of the disparity between the two returns, the equity risk premium (ERP), is so great that it implies an implausibly high level of investor risk aversion that is fundamentally incompatible with other branches of economics, particularly macroeconomics and financial economics.

The process of calculating the equity risk premium, and selection of the data used, is highly subjective to the study in question, but is generally accepted to be in the range of 3–7% in the long-run. Dimson et al. calculated a premium of "around 3–3.5% on a geometric mean basis" for global equity markets during 1900–2005 (2006). However, over any one decade, the premium shows great variability—from over 19% in the 1950s to 0.3% in the 1970s.

To quantify the level of risk aversion implied if these figures represented the expected outperformance of equities over bonds, investors would prefer a certain payoff of $51,300 to a 50/50 bet paying either $50,000 or $100,000.

The puzzle has led to an extensive research effort in both macroeconomics and finance. So far a range of useful theoretical tools and numerically plausible explanations have been presented, but no one solution is generally accepted by economists.

Investors are considered to be rational and optimize their utility. A person will maximize:

A commonly used utility function is the power law function:

where β and α are parameters.

Another utility function is:

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