Has Barro solved the equity premium puzzle?
I have been reading the paper on stock market crashes and depressions by Barro and Ursua which among other things appears to solve the equity premium puzzle. The equity premium is called a puzzle because the historical return on stocks (over multi-decadal time frames) has exceeded that on bonds by too wide a margin to be justified by the higher risk of stocks in a standard utility theory framework.
The equity premium was a puzzle because the return on stocks is not too highly correlated with consumption and in a standard utility framework, the relevant risk is actually consumption risk. Crudely speaking, the risk is that you do not have enough money from your investments to support your consumption precisely when incomes are low and therefore the investment money is needed. I say crudely speaking because in the frictionless models of the permanent income hypothesis, consumption is supposed to be a function of wealth (including human capital) and not of income at all. A model of risk premiums which ignores liquidity constraints so brazenly might not be very satisfying to finance people, but that is a different issue altogether.
The solution proposed to this puzzle is essentially that the entire consumption risk of equities is a tail risk. It arises from the high probability that stock market crashes are accompanied (with a variable lag) by an economic depression. One big advantage of depressions over wars and other calamities as the explanation for the equity premium is that depressions make risk free bonds very attractive assets.
Of course, Barro has been saying this for a few years now, but now he has the cross country data to back him up. “Conditional on a stock-market crash [multi-year real returns of -25% or less], the probability of a minor depression (macroeconomic decline of at least 10%) is 30% and of a major depression (at least 25%) is 11%.” Taking this tail risk into account is sufficient to justify the observed equity premium for plausible values of risk aversion.
I think this is definitely a promising line of analysis. Of course, a major econometric problem is that the lag between the stock market crash and the economic depression is not uniform (in some cases, it is even negative due to measurement errors). Barro and Ursua therefore “focus on the 58 cases of paired stock-market crashes and depressions ... and ... calculate the covariance in a flexible way that allows for different timing for each case.”
I am sure that a lot of methodological refinements are needed to understand the phenomenon better, but I like this approach. For Indian readers, it is interesting to note that the sample includes one episode from India (apart from the World War): during 1946-1949, real stock prices fell 49% while real GDP fell 18% during 1947-1950. That makes the current crisis seem quite bearable!
Posted at 3:44 pm IST on Thu, 12 Mar 2009 permanent link
Categories: CAPM, financial history
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