[3] The term was coined by Rajnish Mehra and Edward C. Prescott in a study published in 1985 titled "The Equity Premium: A Puzzle".
The authors found that a standard general equilibrium model, calibrated to display key U.S. business cycle fluctuations, generated an equity premium of less than 1% for reasonable risk aversion levels.
[5] Azeredo (2014) shows, however, that increasing the risk aversion level may produce a negative equity premium in an Arrow-Debreu economy constructed to mimic the persistence in U.S. consumption growth observed in the data since 1929.
[6] 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.
This means that for long-term investors, the risk of holding the stock of a smaller than expected can be derived only by looking at the standard deviation of annual earnings.
[8] 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.
In the Mehra and Prescott (1985) economy, the utility function belongs to the constant relative risk aversion class: where
[10] The derivative of the Lagrangian with respect to the percentage of stock held must equal zero to satisfy necessary conditions for optimality under the assumptions of no arbitrage and the law of one price.
These include: 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.
Over time, as well as to determine the factors driving equity premium in various countries / regions may still be active research agenda.
[13] A 2023 paper by Edward McQuarrie argues the equity risk premium may not exist, at least not as is commonly understood, and is furthermore based on data from a too narrow a time period in the late 20th century.
One possible solution to the equity premium puzzle considered by Julliard and Ghosh (2008) is whether it can be explained by the rare events hypothesis, founded by Rietz (1988).
For example, the equity premium persisted during the Great Depression, and this suggests that an even greater catastrophic economic event is required, and it must be one which only affect stocks, not bonds.
[17] Benartzi & Thaler (1995) contend that the equity premium puzzle can be explained by myopic loss aversion and their explanation is based on Kahneman and Tversky's prospect theory.
[18] The two combined creates myopic loss aversion and Benartzi & Thaler concluded that the equity premium puzzle can be explained by this theory.
An example is info-gap decision theory,[20] based on a non-probabilistic treatment of uncertainty, which leads to the adoption of a robust satisficing approach to asset allocation.
The most significant characteristic that is not typically considered is the requirement for equity holders to monitor their activity and have a manager to assist them.
Although, as per the characteristics of equity in explaining the premium, it is only necessary to hypothesise that people looking to invest do not think they can reach the same level of performance of the market.
[24] Palomino described the noise trader model that was thin and had imperfect competition is the market for equities and the lower its equilibrium price dropped the higher the premium over risk-free bonds would rise.
[22] Another explanation related to the observed growing equity premium was argued by McGrattan and Prescott (2001)[25] to be a result of variations over time of taxes and particularly its effect on interest and dividend income.
It is difficult however to give credibility to this analysis due to the difficulties in calibration utilised as well as ambiguity surrounding the existence of any noticeable equity premium before 1945.
After adding these earlier years, the arithmetic average of the British stock premium for the entire 20th century is 6.6%, which is about 21/4% lower than the incorrect data inferred from 1919-1999.
[27] Graham and Harvey have estimated that, for the United States, the expected average premium during the period June 2000 to November 2006 ranged between 4.65 and 2.50.
The authors argue that such an asymmetric volatility effect can be explained by the fact that investors are more concerned with downside risk than upside potential.
The author shows that the slope of the implied volatility smile is a significant predictor of stock returns, even after controlling for traditional risk factors.
The author argues that this relationship between the slope of the implied volatility smile and stock returns can be explained by investors' preference for jump risk.
First, problems of adverse selection and moral hazard may result in the absence of markets in which individuals can insure themselves against systematic risk in labor income and noncorporate profits.
This also brings about questions regarding the need for microeconomic policies that operate by way of higher productivity in the long run by trading off short-term pain in the form of adjustment costs.
[21] Research on the contrary indicates that a large percentage of the general public believe that the stock market is best for investors that are in it for the long haul[39] and may also link to another implication being trends in the equity premium.