Equity premium puzzle
Stocks have historically out-earned bonds by far more than rational risk aversion can explain.
What it means
The equity premium puzzle is the observation that the historical return on stocks over safe bonds is so large that rationalizing it within standard expected-utility models requires implausibly high risk aversion. First framed as a quantitative anomaly in consumption-based asset pricing, it implies a coefficient of risk aversion orders of magnitude beyond what other evidence supports. The leading behavioral resolution is myopic loss aversion: if investors are loss-averse and evaluate their holdings roughly annually, the frequent appearance of losses makes equities feel risky enough to demand a large premium. The puzzle is significant because it links a macro-financial regularity directly to prospect-theory primitives and mental accounting. It remains a touchstone for debates between rational and behavioral asset pricing.
How big the gap is
The original calculation used long U.S. series from 1889 to 1978, where equities beat safe bills by roughly six percentage points a year. Fed the actual, very smooth history of per-capita consumption growth, the standard model matches that premium only if the coefficient of relative risk aversion sits near 30 to 50, a level at which a person would pay to dodge almost any small gamble. Plausible values lie between one and about ten; there the model yields a premium under half a percentage point. Worse, Weil (1989) showed the fix breeds a second anomaly: the calibration that would justify a high premium implies a risk-free rate far above the roughly one percent observed, the risk-free-rate puzzle. Raising risk aversion just trades one puzzle for another.
The rival explanations
Two camps compete. On the rational side, Rietz (1988) and then Barro (2006) argued that a small annual chance of a catastrophic fall in consumption, from war or depression, can generate the premium at ordinary risk aversion: investors demand compensation for a disaster that mostly did not strike inside the sample. Others rebuild preferences. Campbell and Cochrane's (1999) habit formation makes people fear losses more as consumption nears a slow-moving reference level, and Bansal and Yaron's (2004) long-run-risk model loads on small, persistent shocks to expected growth. Each fits parts of the data; none commands consensus, and several need their own hard-to-observe ingredients. The behavioral camp keeps myopic loss aversion. That one stubborn fact supports so many rival stories is itself part of what makes the puzzle durable.
Evidence for the behavioral account
Myopic loss aversion has an advantage: it makes a prediction testable outside markets. Change how often people see results and their appetite for risk should shift. Gneezy and Potters (1997) had subjects bet repeatedly; those shown the outcome every round bet less than those shown pooled three-round outcomes, exactly as loss aversion plus frequent evaluation predicts, and Benartzi and Thaler backed out a one-year evaluation horizon that reproduces the historical premium. But the effect is fragile. It weakens or vanishes when the gambles differ across rounds, when the horizon is short, or when a task pushes attention onto the pooled distribution (Klos, 2013). The laboratory supports the mechanism without pinning down how much of the premium it can carry.
Is the premium as big as it looks
The puzzle assumes the historical U.S. premium fairly estimates what investors expected. Two doubts weaken that. First, survivorship: the twentieth-century U.S. market was an outlier winner, so a number built from it flatters the past. Using a bias-controlled panel of many countries back to 1900, Dimson, Marsh and Staunton put the worldwide premium over bonds nearer four to five percent, real but a smaller puzzle. Second, a realized premium overstates the expected one when a feared catastrophe, the peso problem, failed to arrive within the sample window, the mirror image of the disaster explanation. Since the 1980s the forward-looking premium implied by valuations has also narrowed. The anomaly is genuine, but smaller and less certain than the headline six-percent figure makes it sound.
Examples
Over the twentieth century U.S. equities returned several percentage points more per year than bonds — a gap a standard model can only match with absurd levels of risk aversion.
An investor checking her pension app every morning sees losses often enough to feel burned and retreats to cash; a colleague who looks once a decade sees almost only gains.
A relative keeps decades of savings in a cash account because 'shares are a gamble' — it is exactly that reluctance that leaves the extra return on the table for everyone else.
A retirement plan that reports balances yearly instead of monthly, and defaults savers into a diversified fund, tends to lift equity holdings by dampening how often a loss is felt.
After a currency and stock-market collapse, an emerging economy's shares long trade cheap and pay a fat premium, as investors price a disaster the smooth averages of surviving markets never record.
First described in Mehra & Prescott (1985); behavioral account, Benartzi & Thaler (1995).
Key references
- Klos, A. (2013). Myopic loss aversion: Potential causes of replication failures. Judgment and Decision Making, 8(5), 617-629. www.cambridge.org/core/journals/judgment-and-decision-making/article/myopic-loss-aversion-potential-causes-of-replication-failures/5DCAF0528D2344B78EC9A0BE83681384
- Dimson, E., Marsh, P., & Staunton, M. (2008). The worldwide equity premium: A smaller puzzle. In R. Mehra (Ed.), Handbook of the Equity Risk Premium (pp. 467-514). Elsevier. ssrn.com/abstract=891620
- Barro, R. J. (2006). Rare disasters and asset markets in the twentieth century. The Quarterly Journal of Economics, 121(3), 823-866. doi.org/10.1162/qjec.121.3.823
- Gneezy, U., & Potters, J. (1997). An experiment on risk taking and evaluation periods. The Quarterly Journal of Economics, 112(2), 631-645. doi.org/10.1162/003355397555217
- Benartzi, S., & Thaler, R. H. (1995). Myopic loss aversion and the equity premium puzzle. The Quarterly Journal of Economics, 110(1), 73-92. doi.org/10.2307/2118511
- Mehra, R., & Prescott, E. C. (1985). The equity premium: A puzzle. Journal of Monetary Economics, 15(2), 145-161. doi.org/10.1016/0304-3932(85)90061-3