The Consumption Risk of the Stock Market
Brookings Papers on Economic Activity, 2 (2001) 279-348.
Abstract
This paper evaluates whether the medium-term risk of the stock market is consistent with its high average rate of return relative to a risk-free investment. The medium-term risk of stocks is measured by the covariance of a market return over a quarter and consumption growth over horizons of one to three years. The medium-term risk of equity in aggregate consumption data is an order of magnitude higher than the contemporaneous risk.(1) This higher level of risk is still insufficient to explain the average premium on equity. The medium-term risk of the stock market for households that hold equity directly is twice as large again and some point estimates are completely consistent with the high average return on equity and reasonable levels of risk aversion. For households that hold equity, the equity premium is rationalized by the consumption risk of the stock market.
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1. If one does not make the assumption of joint lognormality and performs GMM, estimated coefficients of relative risk aversion may or may not decline as one increases the consumption growth horizon. This is driven by the difficult to interpret GMM first-order condition and the sensitivity of GMM (starting values matter for example), rather than, as I worried when I discovered this, the assumption of lognormality. To see this, calculate the robust measure analogous to that in my BPEA article: the covariance of returns and the (nonlinear) stochastic discount factor, as a function of risk aversion. The risk of the stock market increases with horizon; magnitudes change, but my finding does not depend on the approximation that returns and consumption growth are jointly log-normal. See my March 2002 note on this with results.