Friday, May 21, 2010

Modelling equities returns

It's a tricky business. We don't actually have all that much information to make statistical judgements about equity performance, and because we know so much about the underlying economics, it's very tempting to cherry-pick your data in order to come up with some sort of "correct" model.

This is important because the return equities generate is of huge importance in long term planning. Many pension funds are invested in equities, for example. The return such a fund earns over forty years or so is very sensitive to the long term rate. In practice, though, assigning a number to this rate has been more art than science:

I recently spoke to an auditor who described the difficulty involved in calculating today's equity premium. If you use recent history in your estimation, you may end up with a zero or negative equity premium. No one wants to use this in their forecasts; otherwise projections look pretty dismal. If you're selling a financial product or strategy that involves equity investment, a zero equity premium will not entice investors.

Some state pension plans have not adjusted their risk premium either since the financial crisis. They expect their equity portfolios to earn them more than 8% per year, a risk premium a bit larger than 5%. The state plans also have no incentive to lower their equity premium. If they do, their projected assets will fall and liabilities will rise. This means their funding ratios will plummet and they will have to start making larger contributions to the plan, which would likely mean higher taxes.

The real problem is modelling the tail risk. If you take annual stock market returns, you have a random variable with quite a convincing bell-like distribution. However, if you fit a particular distribution to them, you get a good fit for a number of distributions in the bulk of observations, but the extreme data values - the ones that are really of interest - do not model well. Getting these wrong mean your knowledge of the risk you are taking is not adequate.

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