Monday, October 03, 2005

Equity Risk Premium

I've been exchanging emails with a buddy of mine who is still at Chicago getting a PhD in Finance about Barro's recent work on the equity risk premium. Barro actually came and presented his paper at Chicago, and my friend was there to hear what he had to say. Anyway, his note on the topic was very good, and I've reprinted it below.

Background: The "equity risk premium" is the name given to the fact that stocks have outperformed bonds even on a risk adjusted basis for many years now. This means that stocks seem to earn some extra return for reasons no one can really understand. Either the models are wrong, or there has been stable, long term irrationality. Barro argues that low probability catastrophic events are enough to generate an equity risk premium because people can reduce their consumption a little and stay OK but are really sensitive to having their consumption reduced a lot. This extreme preference creates an equity risk premium, since long-tail negative events are really bad.

Barro presented his paper on Tuesday in our finance seminar. Barro is a giant in the field of macroeconomics--it is truly wonderful to be at the University of Chicago and hear so many great speakers.

My take away is that Barro's main point is right--we should consider the possibility of low-probability events. But I still don't think it explains the equity premium. He is still working on his paper--he just discovered Reitz's paper 6 months ago--and right now he uses a very simplistic framework. One parameter in the framework is the level of risk-aversion in a CRRA framework. Most economists believe a risk-aversion coefficient of about 5 is reasonable, and he finds that with a coefficient of 5 you can explain a lot with a 1% chance per year of an "end of the world" type event for financial markets.

To give you an idea about the appropriate coefficient of risk-aversion, let me ask you the following question. One year you will get 60k of consumption. One year you will get 30k of consumption. How much would you pay in 60k-year dollars to get an extra dollar of consumption in the 30k year? For example, maybe you would be willing to pay $2 in 60k-year dollars to get an extra $1 of consumption in the 30k year. If this doesn't work well intuitively, ask how much you would pay to get an extra $100--say enough for a 5-star meal for you and Kat.

Seriously, answer the question before reading further.

Well, the risk-coefficient of 5 means that you would be willing to pay 2^5 dollars in the 60k year for an extra dollar in the 30k year (the 2 is because 60k/30k = 2, the 5 is the coefficient of risk-aversion). That's $32 in the good year for $1 in the bad year. So to get a $100 meal in the 30k year, you would give up $3200 worth of consumption in the 60k year. Well I think that is crazy. I think you might, at most give up $200 in the 60k year to get $100 in the bad year--that is a risk-aversion of 1, not 5. So while Barro/Reitz model is good for most economists, it still doesn't explain things to me. Because I think the only reasonable coefficient of risk-aversion based on intuition is about 1, but that predicts virtually no equity premium.

So in conclusion, I think Barro's insight is important and much better than what most economists argue is driving the equity premium. But the equity premium is still a puzzle to me.
Personally, I don't know how to think how risk averse I am -- I have no idea how much conumption I'd give up in a good year to get more consumption in a bad year.


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