How economists invest

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 in 1971.

Imagine two assets – shares and cash. Merton showed how to split our wealth between them.

First, he said, multiply your CRRA by the annual variance of equity returns. Then divide this into the expected out-performance of cash by equities. The answer is the proportion of your wealth you should hold in shares.

So, let’s say the variance of equity returns is 0.04, corresponding to an annual standard deviation of 20 per cent. And say your CRRA is 2. This gives us 0.08. Assume an equity premium of 0.03 - that is, 3 per cent. Divide this by 0.08 and we have three-eighths. That’s the proportion of your wealth you should put into the stock market.

Do this, and get on with real life. That’s your personal finances sorted out. (I’m assuming you’ve paid your debts).

But are things really this simple? Clearly, equities and cash are not the only assets; there are also housing and (what is often overlooked) human capital to consider. But this is just a mathematical wrinkle.

Nor does it matter whether you’re a long-term or short-term investor, as long as your risk preferences can be described by CRRA. This is because a long-term investor faces the small risk of a big loss, whilst a short-term investor faces a big risk of a small loss. For CRRA-type preferences, the two cancel out.

The complication comes if risk preferences cannot be described by CRRAs. Some people are more averse to unquantifiable risks than quantifiable ones; this is the Ellsberg paradox. And others are sensitive to the small risk of big losses, whilst relaxed about the big risk of small losses; this is loss aversion.

Such preferences do undermine the Merton approach.

Two things, though, are clear.

First, an obvious asset allocation rule cannot easily explain UK pension fund behaviour. These typically have 80 per cent of their assets in equities.

Second, economists’ approach to personal finance is very different from what you read in the newspapers. They are just illiterate hucksters.