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The equity premium puzzle refers to the phenomenon that observed returns on stocks over the past century are a few percent higher than returns on government bonds. It is a term coined by Rajnish Mehra and Edward C. Prescott in 1985. [ 1 ] [ 2 ] 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 as 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). [ 3 ] 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. [ 4 ]

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.

Contents

Theory [ edit ]

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

where

where β and α are parameters.

where

gives the result. [ 5 ]

They can compute the derivative with respect to the percentage of stocks, and this must be zero.

Data [ edit ]

Much data exists that says that stocks have higher returns. For example, Jeremy Siegel says that stocks in the United States have returned 6.8% per year over a 130-year period.

Proponents of the capital asset pricing model say that this is due to the higher beta of stocks, and that higher-beta stocks should return even more.

Others have criticized that the period used in Siegel’s data is not typical, or the country is not typical.

Possible Explanations [ edit ]

A large number of explanations for the puzzle have been proposed. These include:

• a contention that the equity premium does not exist: that the puzzle is a statistical illusion,
• modifications to the assumed preferences of investors, and
• imperfections in the model of risk aversion.

Kocherlakota (1996), Mehra and Prescott (2003) present a detailed analysis of these explanations in financial markets and conclude that the puzzle is real and remains unexplained. [ 6 ] [ 7 ] Subsequent reviews of the literature have similarly found no agreed resolution.

Denial of equity premium [ edit ]