The ratios that judge them

Two funds. The first made eight per cent, the second twelve. Which is better? It is a trick question.

The risk taken to get there is missing. That is what ratios are for: dividing the gain by the risk.

The most famous is the Sharpe ratio, proposed by the economist William Sharpe in nineteen sixty-six.

You take the return, subtract what a risk-free investment would have given, and divide by volatility.

Say a risk-free rate of two per cent. Fund A makes eight, with a volatility of ten. Six divided by ten: zero point six.

Fund B makes twelve, with a volatility of twenty-five. Ten divided by twenty-five: zero point four.

Fund B gained more. But each unit of risk earned less there. By Sharpe, A is better.

One criticism: volatility also punishes rises. Yet nobody complains about a sharp rise.

Hence the Sortino ratio. Same calculation, but only the volatility of falls counts.

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If fund A's falls only weigh six points, say, its Sortino is six divided by six: one.

A fund that rises in leaps but falls little is treated better by Sortino than by Sharpe.

The Treynor ratio divides the gain not by volatility, but by beta. Market risk alone.

Say a beta of zero point eight for A, and one point two five for B.

A: six divided by zero point eight, seven point five. B: ten divided by one point two five, eight. This time, B comes out ahead.

Who is right? If the fund is your entire wealth, Sharpe. If it is only one piece of a diversified whole, Treynor makes sense.

That leaves funds that follow an index and want to do a bit better. For them, one measure: tracking error.

It is the gap with the index followed, measured like a volatility. The bigger it is, the further the fund strays from its benchmark.

A well-run index fund has a tiny tracking error. An active manager takes some on purpose.

The information ratio judges this distance: the lead over the index, divided by the tracking error.

Say a fund beats its index by one and a half points a year, with a tracking error of three. Information ratio: zero point five.

Each point of distance taken from the index earned half a point of lead. That is the talent you pay the manager for.

Careful: all these ratios look at the past. A good score over three years promises nothing for the next three.

And they assume risk is well measured. A fund selling insurance against crashes can show a superb Sharpe, until the crash.

Remember the shared idea: a gain is never judged alone. Always divided by the risk it took.