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November 17, 2004
Risk Aversion-- Gollier Table to Check Your Own Level
What percentage of your wealth would you give up to
eliminate a risk of losing 10% of your wealth? Less than
10%, of course, but how much less? The table below, from
Table 2.1 of Christian Gollier's The Economics of Risk
and Time, says what your "relative risk aversion"
coefficient is if you have constant relative risk aversion
utility.
Relative risk aversion 10% risk 30% risk
.5 .3% 2.3%
1 .5% 4.6%
4 2% 16%
10 4.4% 24.4%
40 8.4% 28.7%
If you would give up 2% of your wealth to avoid a 50-50
risk of losing or gaining 10%, then you have a coefficient
of relative risk aversion of 4. That's about where I am, I
think, for the 10% risk. That implies, though, that I would
give up 16% of my wealth to avoid a 30% gamble, which I'm
less sure about.
One of the hard things in doing this kind of
introspection is that it matters how we define "wealth". It
matters whether it is lifetime wealth (including the value
of my human capital-- the wages I can earn) or just the
amount of wealth I have in hand right now. If I lost 30% of
my non-human capital this year, that would not be nearly so
serious as if I lost 30% of the value of my future wages.
The cleanest theoretical model is to think of lifetime
wealth, and we all make our investment decisions based on
that. But, knowing, for example, that we can fall back on
our wages, and that we can modify our investment policy in
case of disaster, we can look very risk-loving with respect
to our investments.
Posted by erasmuse at November 17, 2004 01:34 PM
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Eric Rasmusen provides a neat way of calculating your coefficient of relative risk aversion (CRRA). You need to know this because it might solve the only investment decision you have to take in your lifetime, as Robert Merton showed back [Read More]
Tracked on November 20, 2004 05:15 AM