Equity premium puzzle
Encyclopedia
The equity premium puzzle is a term coined in 1985 by economists Rajnish Mehra
Rajnish Mehra
Rajnish Mehra is an Indian American economist. He currently holds the E. N. Basha Chair at Arizona State University and is a research associate of the NBER...

 and Edward C. Prescott
Edward C. Prescott
Edward Christian Prescott is an American economist. He received the Nobel Memorial Prize in Economics in 2004, sharing the award with Finn E. Kydland, "for their contributions to dynamic macroeconomics: the time consistency of economic policy and the driving forces behind business cycles"...

. It is based on the observation that in order to reconcile the much higher returns of stock
Stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...

s compared to government bond
Government bond
A government bond is a bond issued by a national government denominated in the country's own currency. Bonds are debt investments whereby an investor loans a certain amount of money, for a certain amount of time, with a certain interest rate, to a company or country...

s in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

, 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
Research
Research can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...

 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
Late 2000s recession
The late-2000s recession, sometimes referred to as the Great Recession or Lesser Depression or Long Recession, is a severe ongoing global economic problem that began in December 2007 and took a particularly sharp downward turn in September 2008. The Great Recession has affected the entire world...

, 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
Risk premium
A risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the known return on a risk-free asset, in order to induce an individual to hold the risky asset rather than the risk-free asset...

 (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:
  • Empirically, over the past 40 years (1969–2009), there has been no significant equity premium in (US) stocks.
  • Selection bias
    Selection bias
    Selection bias is a statistical bias in which there is an error in choosing the individuals or groups to take part in a scientific study. It is sometimes referred to as the selection effect. The term "selection bias" most often refers to the distortion of a statistical analysis, resulting from the...

     of the US market in studies. The US market was the most successful stock market in the 20th century. Other countries' markets displayed substantially lower long-run returns. Picking the best observation (US) from a sample leads to upwardly biased estimates of the premium.
  • Survivorship bias
    Survivorship bias
    Survivorship bias is the logical error of concentrating on the people or things that "survived" some process and inadvertently overlooking those that didn't because of their lack of visibility. This can lead to false conclusions in several different ways...

     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.
  • Low number of data points: the period 1900–2005 provides only 3.5 independent 30-year windows, which is a very low number from which to conclude out-performance (over 30-year periods).
  • 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 (89% lower), 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.

A related criticism is that the apparent equity premium is an artifact of observing stock market bubble
Stock market bubble
A stock market bubble is a type of economic bubble taking place in stock markets when market participants drive stock prices above their value in relation to some system of stock valuation....

s in progress.

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
Prospect theory
Prospect theory is a theory that describes decisions between alternatives that involve risk i.e. where the probabilities of outcomes are known. The model is descriptive: it tries to model real-life choices, rather than optimal decisions.-Model:...

 model of Benartzi and Thaler (1995) based on loss aversion
Loss aversion
In economics and decision theory, loss aversion refers to people's tendency to strongly prefer avoiding losses to acquiring gains. Some studies suggest that losses are twice as powerful, psychologically, as gains....

. A problem for this model is the lack of a general model of portfolio choice and asset valuation for prospect theory
Prospect theory
Prospect theory is a theory that describes decisions between alternatives that involve risk i.e. where the probabilities of outcomes are known. The model is descriptive: it tries to model real-life choices, rather than optimal decisions.-Model:...

.

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
Intertemporal consumption
Economic theories of intertemporal consumption seek to explain people's preferences in relation to consumption and saving over the course of their life...

 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
Satisficing
Satisficing, a portmanteau "combining satisfy with suffice", is a decision-making strategy that attempts to meet criteria for adequacy, rather than to identify an optimal solution...

 rules rather than optimizing. An example is info-gap decision theory
Info-gap decision theory
Info-gap decision theory is a non-probabilistic decision theory that seeks to optimize robustness to failure – or opportuneness for windfall – under severe uncertainty, in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a given estimate of the...

(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
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....

 and dividend
Dividend
Dividends are payments made by a corporation to its shareholder members. It is the portion of corporate profits paid out to stockholders. When a corporation earns a profit or surplus, that money can be put to two uses: it can either be re-invested in the business , or it can be distributed to...

 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
Market failure
Market failure is a concept within economic theory wherein the allocation of goods and services by a free market is not efficient. That is, there exists another conceivable outcome where a market participant may be made better-off without making someone else worse-off...

 have been considered as explanations of the equity premium. First, problems of adverse selection
Adverse selection
Adverse selection, anti-selection, or negative selection is a term used in economics, insurance, statistics, and risk management. It refers to a market process in which "bad" results occur when buyers and sellers have asymmetric information : the "bad" products or services are more likely to be...

 and moral hazard
Moral hazard
In economic theory, moral hazard refers to a situation in which a party makes a decision about how much risk to take, while another party bears the costs if things go badly, and the party insulated from risk behaves differently from how it would if it were fully exposed to the risk.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
Implied volatility
In financial mathematics, the implied volatility of an option contract is the volatility of the price of the underlying security that is implied by the market price of the option based on an option pricing model. In other words, it is the volatility that, when used in a particular pricing model,...

 (in this case VIX
VIX
VIX is the ticker symbol for the Chicago Board Options Exchange Market Volatility Index, a popular measure of the implied volatility of S&P 500 index options. Often referred to as the fear index or the fear gauge, it represents one measure of the market's expectation of stock market volatility over...

, 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
John Quiggin
John Quiggin is an Australian economist and professor at the University of Queensland. Quiggin studied at the Australian National University, obtaining bachelor's degrees in Arts and Economics in 1978 and 1980 respectively, and completing a master's degree in Economics in 1984. Quiggin was awarded...

 (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
    Ellsberg paradox
    The Ellsberg paradox is a paradox in decision theory and experimental economics in which people's choices violate the expected utility hypothesis.An alternate viewpoint is that expected utility theory does not properly describe actual human choices...

  • Loss aversion
    Loss aversion
    In economics and decision theory, loss aversion refers to people's tendency to strongly prefer avoiding losses to acquiring gains. Some studies suggest that losses are twice as powerful, psychologically, as gains....

  • Risk aversion
    Risk aversion
    Risk aversion is a concept in psychology, economics, and finance, based on the behavior of humans while exposed to uncertainty....

  • List of cognitive biases
  • Economic puzzle
    Economic puzzle
    A puzzle in macroeconomics is a situation where the outcome of theory is inconsistent with observed macroeconomic data.An example might be the Equity premium puzzle which relates to the fact that over the last two hundred years, the risk premium of stocks over bonds has been around 5.5 %, much...

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