The Consumption Risk of the Stock Market

Abstract

OVER THE PAST century in the United States, the average annual return on the stock market has exceeded that on short-term government bonds by 6 percentage points. The natural economic explanation for the premium on equity is the greater risks associated with investing in the stock market. However, the large premium that we observe cannot be explained by the canonical, consumption-based asset pricing model. Risk is best measured as the extent to which a return alters marginal utility. Since marginal utility is closely related to consumption, and consumption moves little with returns, the measured risk of the stock market is small. (1) One common informal interpretation of this equity premium puzzle is that stocks are a good deal. In this view, the model is taken as a reasonably accurate description of optimal behavior and a poor description of actual behavior. This normative view of the model and the data implies that households should increase their holdings of equity and even borrow to invest in the stock market. (2) Such thinking has also entered important areas of public policy, most notably in proposals to allow funds from the Social Security system--whether the current $1 trillion surplus in the trust fund or the entire $10 trillion in implicit liabilities--to be invested in the stock market rather than entirely in government bonds as is currently done. The positive view of the equity premium puzzle is that we simply do not understand asset prices. Since the puzzle was discovered, economists' efforts to find a model that rationalizes the premium have yielded little success. That is, there is as yet no model of a household investment problem with reasonable levels of risk aversion that explains the variation in returns over time, and the difference in returns between stocks and bonds in particular. This leaves economists largely unable to model investment behavior and largely unable to provide policymakers with guidance for the diversification of the Social Security system. This paper proposes an understanding of the risk-return trade-off between stocks and bonds that departs from the canonical model in two ways. First, I ignore many issues in asset pricing and focus solely on the ultimate risk to consumption of a given portfolio choice. That is, rather than measure the risk to consumption as the contemporaneous response of consumption to returns on the stock market, this paper measures the risk as the medium-term impact of stock market returns on consumption. (3) Second, in addition to studying the medium-term risk of equity as measured by aggregate consumption data, I follow Gregory Mankiw and Stephen Zeldes and ask whether the risk of equity justifies its return for the subset of households that hold equity. (4) The main finding of the paper is that the medium-term risk of equity is much greater than the contemporaneous risk, both for the representative household and for the representative stock. holder. For households that hold equity, the medium-term risk is largely sufficient to justify the high relative return of equity. Measuring the risk of equity as the medium-term impact of a return on consumption has several appealing features. First, this approach maintains the assumption that the primary determinant of utility is the level of consumption. This assumption is intuitive and has proved useful and successful in many other branches of economics. Second, this approach is consistent with the theory of portfolio choice in that the medium-term risk and the contemporaneous risk should be approximately the same according to the canonical model. Most important, the medium-term risk is a better measure of the true risk of the stock market under a wide class of extant models used in the study of household consumption and saving. If consumption responds with a lag to changes in wealth, then the contemporaneous covariance of consumption and wealth understates the risk of equity, and the medium-term risk provides the correct measure. …