Prof. Jayanth R. Varma’s Financial Markets Blog

A blog on financial markets and their regulation

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!

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