Equity premium puzzle

The equity premium puzzle is a term coined in 1985 by economists Rajnish Mehra and Edward C. Prescott. It is based on the observation that in order to reconcile the much higher returns of stocks compared to government bonds in the United States, individuals must have implausibly high risk aversion according to standard economics models. Similar situations prevail in many other industrialized countries. The puzzle has led to an extensive research effort in both macroeconomics and finance. So far a range of useful theoretical tools and several plausible explanations have been presented, but a solution generally accepted by the economics profession remains elusive.

In addition to explanations of the puzzle, some deny that there is an equity premium at all; notably, following the stock market crashes of the late 2000s recession, there has been no global equity premium over the 30-year period 1979–2009, as observed by Bloomberg.

In the United States, some have calculated the observed "equity premium"—the risk premium (in fact the historical outperformance) on equity in stocks vs. government bonds—over the past century was approximately 7% per annum. There is little consensus on the actual calculation, however, and ongoing research and expansion of historical databases has led others to revise and refine it; for example 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 outperformance had great variability—from over 19% in the 1950s to 0.3% in the 1970s. It is this gap that is much larger than would be predicted on the basis of standard models of financial markets and assumptions about risk attitudes. To quantify the level of risk aversion implied if these figures represented the expected outperformance of equities over bonds, investors would have to be indifferent between a bet equally likely to pay $50,000 or $100,000 (an expected value of $75,000) and a certain payoff of $51,209 (Mankiw and Zeldes, 1991).

Possible Explanations

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. Subsequent reviews of the literature have similarly found no agreed resolution.

Denial of equity premium

The most basic explanation is that there is no puzzle to explain: that there is no equity premium.  This can be argued from a number of ways, all of them being different forms of the argument that we don't have enough Statistical Power to distinguish the equity premium from zero:

• Selection bias of the US market in studies. The US market was the most successful stock market in the 20th century. Other countries' markets displayed lower long-run returns (but still with positive equity premiums). Picking the best observation (US) from a sample leads to upwardly biased estimates of the premium.
• Survivorship bias of exchanges: exchanges often go bust (just as governments default), and this risk needs to be included – using only exchanges which have survived for the long-term overstates returns. Exchanges close often enough for this effect to matter  
• Low number of data points: the period 1900–2005 provides only 105 independent years which is not a large number of years statistically.
• Windowing: returns of equities (and relative returns) vary greatly depending on which points are included. Using data starting from the top of the market in 1929 or starting from the bottom of the market in 1932 (leading to estimates of equity premium of 1% lower per year), or ending at the top in 2000 (vs. bottom in 2002) or top in 2007 (vs. bottom in 2009 or beyond) completely change the overall conclusion. However, the premium is still positive in all windows considered here -- the exact amount varies a lot.

A related criticism is that the apparent equity premium is an artifact of observing stock market bubbles in progress.

Note however that most mainstream economists agree that the evidence shows substantial statistical power.

The Equity Premium: A Deeper Puzzle

Azeredo (2007) shows that traditional pre-1930 consumption measures understate the extent of serial correlation in the U.S. annual real growth rate of per capita consumption of non-durables and services ("consumption growth"). Under alternative measures proposed in the study, the serial correlation of consumption growth is found to be positive. This new evidence implies that an important subclass of dynamic general equilibrium models studied by Mehra and Prescott (1985) generates negative equity premium for reasonable risk-aversion levels, thus further exacerbating the equity premium puzzle.

Individual characteristics

Some explanations rely on assumptions about individual behavior and preferences different from those made by Mehra and Prescott. Examples include the prospect theory model of Benartzi and Thaler (1995) based on loss aversion. A problem for this model is the lack of a general model of portfolio choice and asset valuation for prospect theory.

A second class of explanations is based on relaxation of the optimization assumptions of the standard model. The standard model represents consumers as continuously-optimizing dynamically-consistent expected-utility maximizers. These assumptions provide a tight link between attitudes to risk and attitudes to variations in intertemporal consumption which is crucial in deriving the equity premium puzzle. Solutions of this kind work by weakening the assumption of continuous optimization, for example by supposing that consumers adopt satisficing rules rather than optimizing. An example is info-gap decision theory (Ben-Haim, 2006), based on a non-probabilistic treatment of uncertainty, which leads to the adoption of a robust satisficing approach to asset allocation.

Equity characteristics

A second class of explanations focuses on characteristics of equity not captured by standard capital market models, but nonetheless consistent with rational optimization by investors in smoothly functioning markets. Writers including Bansal and Coleman (1996), Palomino (1996) and Holmstrom and Tirole (1998) focus on the demand for liquidity.

Tax distortions

McGrattan and Prescott (2001) argue that the observed equity premium in the United States since 1945 may be explained by changes in the tax treatment of interest and dividend income. As Mehra (2003) notes, there are some difficulties in the calibration used in this analysis and the existence of a substantial equity premium before 1945 is left unexplained.

Market failure explanations

Two broad classes of market failure have been considered as explanations of the equity premium. 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. Second, transactions costs or liquidity constraints may prevent individuals from smoothing consumption over time.

Implied volatility

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. They found a modest correlation of 0.62 between the 10-year equity premium and a measure of implied volatility (in this case VIX, the Chicago Board Options Exchange Volatility Index).

Other explanations

Arguably more likely explanations are:

• Over the period, the observed outperformance of equities was substantially in excess of market expectations at the beginning of the relevant periods. This is not altogether surprising in view of the variability referred to above.
• Part of the reason for investment in fixed interest bonds was that many of the liabilities of insurance companies and pension funds requiring to be matched were expressed as guarantees of fixed currency amounts.

Implications

The magnitude of the equity premium has implications for resource allocation, social welfare, and economic policy. Grant and Quiggin (2005) derive the following implications of the existence of a large equity premium:

• Macroeconomic variability associated with recessions is expensive.
• Risk to corporate profits robs the stock market of most of its value.
• Corporate executives are under irresistible pressure to make short-sighted decisions.
• Policies—disinflation, costly reform that promises long-term gains at the expense of short-term pain, are much less attractive if their benefits are risky.
• Social insurance programs might well benefit from investing their resources in risky portfolios in order to mobilize additional risk-bearing capacity.
• There is a strong case for public investment in long-term projects and corporations, and for policies to reduce the cost of risky capital.
• Transaction taxes could be either for good or for ill.

See also

• Ellsberg paradox
• Loss aversion
• Risk aversion
• List of cognitive biases
• Economic puzzle

References

• Mehra, Rajnish; Edward C. Prescott (1985). "The Equity Premium: A Puzzle" (PDF). Journal of Monetary Economics 15 (2): 145–161. doi:10.1016/0304-3932(85)90061-3. http://www.academicwebpages.com/preview/mehra/pdf/The%20Equity%20Premium%20A%20Puzzle.pdf. 
• Kocherlakota, Narayana R. (March 1996). "The Equity Premium: It's Still a Puzzle" (PDF). Journal of Economic Literature 34 (1): 42–71. http://www.econ.ucdavis.edu/faculty/kdsalyer/LECTURES/Ecn200e/Kocherla.pdf. 
• Mehra, Rajnish; Edward C. Prescott (2003). "The Equity Premium Puzzle in Retrospect". In G.M. Constantinides, M. Harris and R. Stulz. Handbook of the Economics of Finance. Amsterdam: North Holland. pp. 889–938. ISBN 978-0-444-51363-2. http://www.academicwebpages.com/preview/mehra/pdf/epp_retrospect.pdf. 
• Benartzi, Shlomo; Richard H. Thaler (February 1995). "Myopic Loss Aversion and the Equity Premium Puzzle". The Quarterly Journal of Economics (The MIT Press) 110 (1): 73–92. doi:10.2307/2118511. JSTOR 2118511. http://ideas.repec.org/a/tpr/qjecon/v110y1995i1p73-92.html.  (subscription required to download paper)
• Yakov Ben-Haim, Info-Gap Decision Theory: Decisions Under Severe Uncertainty, Academic Press, 2nd edition, Sep. 2006. ISBN 0-12-373552-1.
• Dimson, Elroy, Paul Marsh, and Mike Staunton. (2006) "The Worldwide Equity Premium: A Smaller Puzzle". London Business School.
• Azeredo, F. (2007), "The Equity Premium: A Deeper Puzzle", University of California at Santa Barbara, Economics Working Paper Series, [1]
• Haug, J. et al. (2011), "Risk Aversion in the Large and in the Small", Working Paper, University of Zurich, Switzerland. [2]

• Mostafa Hahsemi ERP System 2012.Afzarhesab Organization [3]