This paper focuses on the equity premium puzzle, which is one of the most conspicuous puzzles in asset pricing. This was first pinpointed out by Mehra and Prescott (1985). The purpose of this paper is to critically examine and dissertate on this puzzle. By analyzing various approaches undertaken with attempts to solve the puzzle I conclude that this puzzle is eccentric and moreover along imperative situations the adduced declarations decline and I also advance an affirming path for its future analysis.
2 INTRODUCTION
What is an equity premium puzzle? Let us first look on to what is an equity premium. An equity premium is the difference between the returns of stocks and risk-free assets or securities such as bonds or Treasury bills. For example if an investor invests his money say 1,000 dollars each on stocks and Treasury bills in the early nineteenth century. The returns he would get by the end of the century on Treasury bills would be 12,720 dollars and on stocks would be 842,000 dollars which is 66 times that of treasury bills. That is 3.7 percent returns on treasury bills and 10.1 percent returns on stocks (Siegel, J.J. and Thaler, R.H. (1997)). This difference in returns which is outstandingly large is called the equity premium. As stocks are considered more risky than treasury bills, this can be also referred to as equity risk premium.
A basic insight about the tradeoff between return and risk is given by the CAPM (capital asset pricing model), a model with factors having mean-variance propensity based on equilibrium. By the CAPM it can be exemplified that most often a riskiness of an asset is rewarded by a higher return. It can be seen that over the last 110 years the average annual return on stock market was 8.06 percent while that for the short-term debt was only 1.14 percent ( Mehra and Prescott (1985)). This high difference in percent i.e. 6.92 percent is somewhat fascinating since from an analytical point it would mean that the investors receive a higher reward for buying shares than on investing on these risk-free assets. Thus this simply means that stocks are more riskier than bonds. If so then a question arises: Are stocks so risky than bonds to substantiate a 6 percent difference on their rates of returns? This accounts for a puzzle.
The equity premium puzzle was first identified by Mehra and Prescott (1985) and they exhibited that the equity premium puzzle was often correlated with a high level of risk aversion. As this was one of the most popular puzzles in asset pricing, the equity premium puzzle has been comprehensively inspected by many researchers and economists over the last two decenniums. As a consequence there have been various commentaries and approaches pertaining to the equity premium puzzle such as myopic loss aversion (Benartzi and Thaler, 1995), survival bias ( Brown and Goetzmann, 1995) , market segmentation (Mankiw and Zeldes, 1991), disappointment aversion (Ang, Bekaert and Liu, 2005) and habit formation of investors (Campbell and Cochrane, 1999). As the purpose of this paper is to critically analyze and discuss the equity premium puzzle I would be commenting and discussing on some of these approaches henceforth.
The paper is divided into 6 sections in which section 1 gives an abstract of this paper. A brief introduction about the equity premium puzzle is given in section 2. Section 3 reports the historical equity premium with substantial capital markets according to market value in the U.S and in opted countries along with certain observations. Section 4 examines and scrutinizes the literature aspect of the equity premium puzzle. This is done from both empirical as well as from theoretical views. In section 5 the future aspects of the equity premium are discussed. Finally in section 6 the entire paper is summarized by my conclusion.
3 HISTORY OF EQUITY PREMIUM
3.1 PRESUMPTIONS
A question arises whether which calculation arithmetic or geometric, measures the actual average returns in explaining the equity premium. Looking from a logical aspect the geometric measure is more bona fide. For example, if an investment of 5 pounds is made in the first year. And in the second year the value rises to 10 pounds and by the third it falls back to 5 pounds. We can easily say that geometric measure would be 0 percent unlike the arithmetic measure thus showing the average returns in real terms. But according to Mehra and Prescott (1985) they conclude using the arithmetic measure for calculating the average return as according to past data source the stock returns have been fluctuating. And more over in calculating the mean value of an investment the arithmetic measure proves reasonable (Refer appendix 1) which I feel is quite mediocre. So the methodology which I will be looking onto will be in arithmetic terms.
3.2 SURVEY METHODOLOGY
The survey methodology is done to see if there are any variations and to check the returns both from stocks and risk free securities over the past 2 decades. From Mehra and Prescott (2003) we can divide the history of equity premium into three sub periods namely 1802-1871, 1871-1926 and 1926-present.
1802-1871 = The stock return data for this period was quite deceptive. The data was based on stock indexes which composed of bank, insurance and railroad stocks and their returns ignored the dividends. And as there were no risk free securities during this period the equity premium remained zero.
1871-1926 = The stock return data for this period was clear cut as they included the dividends as well which enabled in the calculation of total stock returns. As the treasury bills were introduced in the late 1920's, the short term commercial paper was used mainly in assessing the returns for risk-free securities. This means an equity premium for this period is quite discontented
1926-present = " This period is the "Golden Age" in regards to accurate ï¬nancial data" (Mehra and Prescott (2003)) This period records authentic stock return data and since the treasury bills also came into existence by this period a calculation of an equity premium is very suffice.
3.3 EVALUATION OF THE EQUITY PREMIUM
Table 1 gives an insight of the U.S equity premium based on different data sets. It can be seen that the return on stocks has always been substantially higher than risk-free securities.
From table 2 it is clear that not only in U.S but also in UK, Japan, Germany and France the return on stocks were higher than the treasury bills resulting in an adequate equity premium.
In table 3 it can been seen how a 1dollar investment made on stocks and treasury bills gives returns where in the stocks returns are obviously higher than treasury bills both in real as well as in nominal terms.
"This long-term perspective underscores the remarkable wealth building potential of the equity premium. It should come as no surprise therefore, that the equity premium is of central importance in portfolio allocation decisions, estimates of the cost of capital and is front and center in the current debate about the advantages of investing Social Security funds in the stock market" (Mehra and Prescott (2003)
This aspect can be agreed only when checking the equity premium from periods after the 1920's since before this period the stock data seems to be inconsistent and biased and moreover proper risk free securities were also not introduced. Thus looking onto table 4 it can be said a proper equity premium recorded for U.S is from 1934-2000.
Table 1, 2, 3 and 4 from (Mehra and Prescott (2003)
3.4 OVERALL CHANGES IN THE EQUITY PREMIUM
Apart from an existence of an equity premium it is interesting to note that there have been overall fluctuations in the equity premium. These changes can be seen in figures 1 and 2.
In figure 1 it can been seen that the fluctuations even resulted the equity premium to go below 0. These fluctuations are reasoned to be because of time perspectives. In figure 3 and 4 the equity premium is compared with the market value or the national income. By observing both these figure an inverse relationship can be seen between these two factors. That is when the market value or national income is high the equity premium is low and vice-versa.
Figures 1, 2 , 3 and 4 from (Mehra and Prescott (2003)
The reason behind this is "Since After Tax Corporate Proï¬ts as a share of National Income are fairly constant over time, this translates into the observation that the realized equity premium was low subsequent to periods when the Price/Earnings ratio is high and vice versa. This is the basis for the returns predictability literature in Finance [Campbell and Shiller (1988) and Fama and French (1988)]" (Mehra and Prescott (2003). The other reason for this can also be because of changes in the consumption pattern of the nation. Because when the price or earnings ratio is high the consumption of individuals increases leading to low investment on stock thus resulting in low equity premium.
Thus looking on to history review of equity premium it can be said that there exist an equity premium and the stock returns have been always higher than risk free assets. But is this mainly because stocks are considered to be more risky? Now let's review the literature aspect of equity premium puzzle.
4 LITERATURE ANALYSIS
The equity premium puzzle was first identified in 1985 by Mehra and Prescott. By analyzing the U.S data from 1889-1978 they concluded that the average real annual yield on stock market were 7 percent and that for risk-free securities were less than 1 percent. They further exhibited that there was no relation between the equity risk premium with the standard rational models. After them there have been many other literature works to intellectualize this puzzle.
4.1 TRADITIONAL ECONOMIC ASPECT OF EQUITY PREMIUM PUZZLE
Utility function = This was an approach developed by Epstein and Zin(1989). It is assumed from Mehra and Prescott model that the coefficient of relative risk aversion is the inverse of elasticity of intertemporal substitution. But the utility function tends to alter this relation and tries to solve the puzzle. The outcome of this function was not satisfactory .This might be because breaking such a relationship would possibly result in hampering the consumption pattern of the economy which is unconventional.
Consumption differences= By using 17 years of data from the Panel Study of Income Dynamics Mankiw and Zeldes(1991) proved that there existed an aggregate consumption difference between the stockholders and non-stockholders. And it was pointed that in U.S only one-quarter of families owned stock. It was believed that this difference would explain the puzzle. But in current scenario even non-stockholders take active part in investments thus making this approach stagnantly discontent.
Mean reversion and aversion = According to( Siegel(1992b)) Siegel, J.J. and Thaler, R.H. (1997) the stock returns displayed a mean reversion characteristics with an actual standard deviation of 2.76 percent for a 20 years period. In contrast the risk free assets displayed a mean aversion characteristics with actual standard deviation of 2.86 percent for the same time period. This difference in percent concluded that the risk free assets were more risky than stocks for long term investors thus expanding the puzzle. But this conclusion is not elusive since the economic holocausts mainly inflation during this period have been ignored.
Habit persistence = This was an approach developed by Constantinides(1990) . According to him an equity premium puzzle can be resolved in rational expectation models by a phenomenon called habit persistence where time separability preferences are relaxed and adjacent complementarily in consumption are allowed. Because of time non-separability of consumption and positive subsistence rate of consumption investors require a high premium with given degree of risk aversion as they become easily harmed by the short term consumption fluctuation. Along with Campbell and Cochrane(1999) this model was modified in which the consumption growth process and slow-moving external habit of the utility function was independently and identically distributed. This model enabled in explaining the extensive arrays of dynamic asset pricing phenomenon but not the puzzle.
Survival bias = According to Brown, Goetzmann and Ross (1995) the estimates of equity risk premium was high since the data available for empirical analysis suffered a survival bias. This bias basically meant missing data during a calamity i.e. the stocks which had low earnings were either abolished or vanished and the stocks which survived were recorded. This would mean that there would be a discontinuous data series if the crises are for longer periods. Even though this approach was ample it still couldn't explain the puzzle effectively.
4.2 BEHAVIOURAL ECONOMIC ASPECT OF EQUITY PREMIUM PUZZLE
Myopic loss aversion = This approach was proposed by Benatzi and Thaler(1995). This approach is a combination of loss aversion with repeated evaluations. Loss aversion is based on the prospect theory of Kahneman and Tversky(1979) which explains that individual investors are more likely to be sensitive towards losses than gains thus making them to demand a higher premium to be awarded from larger return variability. Whereas repeated evaluations refers to investors interest in checking their return on the invested stocks frequently thus influencing their decision-making. With this approach many tests were undertaken to solve the puzzle. But all resulted in the individual investors to be short sighted and myopic loss averse. When this approach was extended to institutional investors such as pension funds and endowments they resulted in being more myopic loss averse than the individual investors and this was due to firm problems. This approach seems to be valid as investors nowadays want quick heavy returns with minimum risks.
Disappointment aversion = The fundamental Disappointment aversion structure of Gul(1991) were the basis for Ang, Bekaert and Liu(2005).Accordint to them "Gul's preferences are a one-parameter extension of the expected utility framework and have the characteristic that good outcomes, i.e. , outcomes above the certainty equivalent, are down weighted relative to bad outcomes." They also explained that as the expectations are less likely to be met even if the related stocks have a large premium , the investors generally do not invest on them .Instead the investors invest on those stocks which have higher possibility of fulfilling their expectation even if it is expected to provide lower returns. In current scenario this approach cannot be rationalized since investors are myopic averse, they would like to earn returns quickly so would naturally go for stocks which assures heavy returns.
Ambiguity aversion = This is another approach undertaken by Olsen and Troughton(2000) to solve the puzzle. Investors are generally ambiguity averse when they have less knowledge of the profit dispersions. In order to collect the data Olsen and Troughton(2000) used questionnaire from professional investment managers and resulted in finding that these mangers were themselves ambiguity averse. As a result the investors required larger returns as compensation for having an ambiguity averse on stock market. In order to test whether the ambiguity aversion was reflected by equity premium an empirical study was conducted by Erbas and Mirakhor(2007). In their study for the degree of ambiguity in the sample countries they used World Bank institutional quality indexes and other proxies. They came to positive conclusions that indeed the equity premium exhibited ambiguity aversion. Since investors at present are more ambiguous , thus this approach seems to be more ample and appeasing and can be likely to clarify the equity premium puzzle.
5 FUTURE ASPECTS OF EQUITY PREMIUM PUZZLE
For sum association of scholars and experts there is no equity premium at present and thus no puzzle. But this can be concluded only by studying the equity premium from two aspects and that is from ex-post and ex-ante aspect. The ex-post aspect is quite clear as the history review clearly states that there existed an equity premium wherein the return of stocks were considerably higher than risk free assets Mehra and Prescott(1985)(2003) .The ex-ante aspect refers to looking from the future point of view. As the stocks have been identified to be mean reverting it can be predicted that initially the ex-ante premium would be low but after certain adjustments it may tend to rise. So expected equity premium can be quite small. Moreover the future of the equity premium also depends on the various horizons. If an investor wants to invest then he would look onto the planning horizon to take decisions.
It is also interesting to note that the previous observations of the equity premium were made on the lines of long investment horizons. So it resulted in overall fluctuations in the equity premium which is seen from the figures mentioned earlier. Thus the past equity premium were stochastic in nature. The stock watchers and other investors who are engaged in short-term investments must have proper planning horizon to succeed.
Thus the future of equity premium can be contradistinctive. Based on past evaluations the only conclusion which can be said is, in short term period there might be low or no equity premium but in the long run there would be a substantial equity premium and the returns of the stock would always be higher than that of the risk free assets.
6 CONCLUSIONS
In this paper I have critically reviewed and discussed the equity premium puzzle. I have come to the following conclusions. Looking at the history review of the equity premium I can say that this puzzle is overall a robust phenomenon in most parts of the world. Looking at the data from 1926-present this puzzle can be seen as an eccentric puzzle.
On analyzing the literature of this puzzle, even though many approaches have been developed most of these fail along imperative situations since the adduced declarations in these approaches decline. The future aspect of this puzzle seems to be promising only on long term evaluations as in short term basis there would either be low or no equity premium.
REFERENCES
Ang, A., Bekaert, G. and Liu, J. (2005), "Why Stocks May Disappoint". Journal of Financial Economics, Vol.76, No.3, pp.471-508
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Brown, S. Goetzmann, W. and Ross, S. (1995), "Survival". Journal of Finance, Vol. 50, No. 2
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Erbas, S. N. and Mirakhor, A, (2007) "The Equity Premium Puzzle, Ambiguity Aversion, and Institutional Quality: Implications for Islamic Finance". Journal of Islamic Economics, Banking and Finance, Vol. 6, No.
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Mankiw, N. Gregory, and Zeldes, Stephen P. (1991), "The Consumption of Stockholders and Nonstockholders", Journal of Financial Economics, Vol.29, pp.97-112
Mehra, R. and E.C. Prescott, 2003, "The Equity Premium in Retrospect" Handbook of the Economics of Finance. Edited by G.M. Constantinides, M. Harris, and R. Stulz. Amsterdam, Netherlands: North-Holland., 888-933
Olsen, Robert A. and Troughton, George H. (2000), "Are Risk Premium Anomalies Caused by Ambiguity", Financial Analysts Journal, Vol. 56, No. 2, pp24-31
Siegel, J.J. and Thaler, R.H. (1997) Anomalies: The Equity Premium Puzzle, The Journal of Economic Perspectives, Vol. 11 (1), 191-200.
The Equity Premium: Why Is It a Puzzle? Author(s): Rajnish Mehra Reviewed work(s): Source: Financial Analysts Journal, Vol. 59, No. 1 (Jan. - Feb., 2003), pp. 54-69
