Equity Risk Premium

9 Pages   |   2,286 Words

Executive Summary:

This paper examines a vital assumption made in the calculation of the level of expected long term premium of return on equity market investments over return on long term fixed income securities.
Over many past decades, capital markets of different countries have displayed an equity risk premium over fixed income securities in the long run. Traditionally, it was viewed that these historic outcomes provide a fair estimate of the expected future equity risk premium in the long run.
This view has presumed over the past few years to an agreement that the future expected risk premium is really fairly lower. This consensus lies on a variety of recent empirical proofs and hypothetical analysis. It lures on both the historical data of market returns, dividends and earnings and other forward looking information gathered by the experts.
On the basis of this exploration, this academic article tries to examine and provide with the reasons provided by various former researchers and economists who have gathered data and run empirical simulations to determine the main reason for equity risk premium. The paper also covers various contradictions, models and implications that were purported by researchers in their published work.

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The equity risk premium denotes to the observed fact that return on stocks has outpaced the returns earned on bonds by a large margin over the period of the last century. The difference between the returns on risky assets and returns on risk free assets is categorized as the equity premium. Many theoretical and empirical reasons have been proposed by various researches, which pose the same question. In this article, both theoretical and empirical works of different researchers have been incorporated to observe the rational investors behavior towards the equity risk premium puzzle.
The data for empirical testing has been gathered over decades have displayed enormous difference between the returns on risky assets i.e. stocks and returns of risk free assets i.e. fixed income securities. The difference can be illustrated by an example. Assuming that a person had a fraction of his money laid aside by the end of 1925. He expected to save that money for his future generation to come. However, his off springs were yet to born. Therefore, as a rational investor he invested $1000 in anticipation of earning great profits through the speculative boom in stocks going on at that time. The reluctance of the investor to risk the money made him invest in risk free treasury bills. His investment remained safe in treasuries bills till the end of 1995. The investment of $1000 had yielded money worth of $12,720. Now, assuming that the investor had decided to invest in a portfolio of risky assets; he would have managed to yield $842,000 for his off spring for the same time period. The difference between the two investment options is shockingly very high and it is called the equity risk premium. Since, the difference is enormously too large to be explained by any regular economic model, so it is called the equity risk premium puzzle (Hammond and Leibowitz, 2011).

The Puzzle:

The common law of finance states that greater the risk, higher will be the returns on any investment. Therefore, the higher returns on stocks than returns on bonds should not come as a surprise. However, too big equity premium risk forms the bases of the puzzle. The two renowned finance gurus were the pioneers to grab the attention of investors towards equity risk premium (Mehra, 1985). They used a typical equilibrium model in which individual investors have independent and separate utility functions and constant comparative degree of risk aversion. In their basic model, coefficient of relative risk aversion which is stated as “A” was the only parameter. The parameter “A” was interpreted if consumption falls by 1 percent, then the marginal value of a dollar of income increases by “A” percent. The value resulted to be between 30 and 40 which was too large to be rational.
The theoretical aspect of “A” states that high value “A” suggests that investors should want even consumption over time because consumption deficits is of more pain than satisfaction provided by the surplus. The underlying explanation provided is that economy tends to flourish in the future, whereas individuals effort to borrow from their bright future to improve their present. However, the desire to borrow from future should result in high interest rates, as well. Instead, the real interest rate has been slight positive in the long run. Thus, equity risk premium puzzle is also called the risk free rate puzzle (Fernandez, Aguirreamalloa and Corres, 2011).
Equity risk premium can be explained under two broad aspects. Firstly, by finding the factors that require adjustment to empirical side of equity risk premium and secondly by discovering related theoretical outline.

Empirical Questions:

Survivorship Bias:

Survivorship bias occurs when the results are based on the calculations of stocks showing positive results while discarding the loss making equities. Equity risk premium can be explained by the investor behavior. Investors are rationally worried about a small chance of an economic catastrophe of any kind. More than 50% of the operational stock exchanges had a major crisis. Hence, the equity risk premium estimated by using US data prostates biased calculations. This has understated the degree of riskiness of stocks by calculations depending on US data. Many objections can be raised for such an explanation.
  1. The time period studied does cover the economic crisis of 1930s, also famous as The Great Depression. During the crisis, stocks lost 80% of their value which was never recovered till World War II (Mehra and Prescott, 1988).
  2. More extended observations of stock markets show that most exchanges rewarded high returns to equity holders. Researchers and analysts have fabricated empirical work to calculate returns for Germany and Japan through World War II. Despite the defeats and huge loss of value, Germany’s annual return was 5.9% and 4.0% for Japan through the years 1926 and 1995.
Therefore, it can be established that if the equity risk premium is calculated as the difference between real returns on stocks and fixed income securities; it was observed to be higher for Japan and Germany than for US for the same time period.

Mean Reversion and Aversion:

The equity risk premium is a puzzle because of the fact that the measured risk linked with return on equity is not big enough to validate the experimental high returns. However, the normal dimension of risk such as the standard deviation may mislead long term risk if annual returns do not follow a random walk. Further elaboration on this implication is inquired. In his article, he observed the volatility and of real returns of equity and fixed income assets over the extended period from years 1802 to1995. His observations concluded to that more deviations from a random walk in stock will result in more complexities of the equity risk premium. If returns are mutually exclusive on a year to year basis, then the standard deviation i.e. risk of annual average will decline with the square root of the horizon. However, it is also depicted that the standard deviation of returns on stocks will actually result in the decline more rapidly than it would have declined if returns were a random walk.  This is supported by the observation that stock returns follow mean reversion i.e. few years in slump will be followed by boom and vice versa (Goedhart, Koller and Williams, 2002).
It is also argued that mean reversion is not a trait of the real returns on the fixed income securities. On the other hand, the standard deviation of average annual real returns to fixed income assets shrink less than the square root of the horizon. This analysis suggests that it is not the risk of stocks which is not big enough to explain the higher rate of return rather fixed income assets have been riskier in real terms.

Theoretical Explanations:

Many economists have tried to take up on the challenge of equity risk premium and the real rate dilemmas. However, none of economists and researchers had been able to come up with a completely satisfactory solution. One theoretical approach developed was to incorporate the use of the utility function that breaks into the rigid link between the coefficient of comparative risk aversion and elasticity of intertemporal changes. The utility functions for each individual gives a minor explanation for a both a high equity risk premium and a low real rate of interest that exists in the economy (Benartzi and Thaler, 1995).
Other researchers have come up with the explanations that suggest that equity risk premium may be a consequence of total consumption of stockholders and non-stockholders. The result found proclaimed that consumption has turned out to be three times more sensitive to fluctuations due to stock market than the aggregate data. Following the work, other economists have modified the utility function by bringing in different adjustments such as a comparison between current consumption and some benchmarks. In the context of the equity premium, habit formation of investors has the impact of making investors more sensitive to short term decreases in the consumption. This indicates a high degree of risk aversion in the short term to a lower level of risk aversion in the long run. However, habit formation has failed to explain the differences that have occurred in returns between equity and fixed income securities (Siegel and Tharler, 1997).
One of the solutions proposed to solve the equity risk premium problem is to reject that the equity risk premium is any puzzle altogether. It is argued that there is a possibility that investors actually do have a high value associated to the parameter “A”. They discussed that while high levels of risk aversion result in irrational behavior from investors with respect to large changes that occur in consumption. This approach has been criticized because it does not take into account the behavior for small changes in wealth.

Myopic Loss Aversion:

The myopic loss aversion model discusses the assumption that the utility function of consumption is relied on the historic trends of consumption or on the consumption of one’s friends and colleagues. One such approach under similar hypothesis was put forward in one of the famous research work (Benartzi and Thaler, 1995). In their model, all investors were assumed to gain utility by the change in value of their portfolios, which indicates that utility is a function of return and not a function of overall levels of assets. Moreover, the loss aversion is displayed by investors that losses are assumed to be more painful than the satisfaction gained by the profits.
Whenever investors show preference for loss aversion, their behavior towards uncertainty depends analytically on the time span for which the returns are assessed. To evaluate the investments and loss aversion, researchers have worked on the evaluation period that would make investors indifferent between equities and fixed income assets. They estimated this behavior by running various simulation distributions of returns for stocks and bonds over different time periods. In their final conclusion, they figured out that time span that makes equities and other fixed income securities equally attractive to any rational investor are about one year and one month (Benartzi and Thaler, 1995).


After decades of work and empirical testing by many researchers, professors, analysts and economists no certain answer has been postulated. The equity risk premium is a real problem, and it is indeed a complex puzzle to solve within the standard utility-maximizing hypothesis. It has been argued that it seems implausible to settle the high rates of return on equities with very low risk free rate. The bigger problem lies in the investors’ willingness to accept high levels of volatility in returns and at the same time willing to defer the consumption to earn meager 1% per annum. One probable solution is to conglomerate high sensitivity to losses with a cautious propensity to constantly keep check on one’s wealth. In the above discussion, investors are reluctant to accept the variability in return even if in the short term, returns would not affect an individual’s consumption pattern.
The empirical testing and simulations conducted in the past has resulted in the following conclusions:
  • History has just been kind to stock markets.
  • Investors are, in reality, exceptionally risk averse, and they don’t want to risk their investments without any premium in return.
  • All investors are making a common mistake when it comes to the explanation of myopic loss aversion i.e. investors fail to cumulative over time spans.


Benartzi, S. and Thaler, R.H. (1995) 'Myopic Loss Aversion and Equity Premium Puzzle', Quarterly Journal of Economics.
Copeland, T. and Dolgoff, A. (2006) 'Expectations Based Management', Journal of Applied Corporate Finance, vol. 18, no. 2, pp. 82-96.
Fernandez, P., Aguirreamalloa, J. and Corres, L. (2011) 'Market Risk Permium Used in 56 Countries', A Survey with 6,014 Answers, pp. 3-11.
Goedhart, M.H., Koller, T.M. and Williams, Z.D. (2002) 'Perspectives on Corporate Finance and Strategy', MacKinsey on Finance, November, pp. 11-15.
Hammond, P.B. and Leibowitz, M.L. (2011) 'Rethinking the Equity Risk Premium: An Overview and Some New Ideas', pp. 1-15.
Mehra, R. (1985) 'The Equity Premium: Why is it a Puzzle', Forthcoming: Financial Analysts Journal, pp. 2-29.
Mehra, R. and Prescott, E.C. (1988) 'Journal of Monetary Economics', The Equity Risk Premium: A Solution?, vol. 22, February, pp. 133-136.
Siegel, J.J. and Tharler, R.H. (1997) 'Anomalies: The Equity Premium Puzzle', Journal of Ecomonomic Perspectives, vol. 11, no. 1, pp. 191-200.

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