Risk-Adjusted Return, and Why the Denominator Decides the Answer

The idea, which is correct

Two funds returned the same amount over the same period. One did it smoothly and one lurched. They are not equally good, and comparing them on return alone treats them as though they were.

That is the whole motivation for risk-adjusted return, and it is right. Any ranking by return alone rewards whoever took the most risk in a period that happened to reward risk-taking, which is a selection rule with an obvious flaw.

The implementation is where the difficulty starts.

How a ratio is built

Almost every risk-adjusted measure has the same shape: take the return, subtract what you could have had without taking risk, and divide by a measure of risk.

The numerator is uncontroversial. Earning a certain amount matters only relative to what a deposit would have paid, because the deposit was available without doing anything.

The denominator is where all the disagreement lives. Different measures put different things there, and each choice embeds a different opinion about what risk is:

• The spread of returns around their own average, which counts good surprises as risk.
• The spread of only the disappointing returns, which does not.
• The worst fall in the period, which is a single observation rather than a spread.
• How much the holding moved when the market moved, which ignores risks the market did not cause.

Those are the four measures set out in the risk numbers on a fact sheet, and each produces a different ranking of the same funds.

Why the choice usually decides the winner

Here is the consequence people miss. A fund whose good years are spectacular and whose bad years are ordinary will be penalised by any measure that counts upside movement as risk, and rewarded by any measure that does not. Nothing about the fund differs between the two calculations. The ranking flips because the definition of the denominator flipped.

This is not a subtle effect at the margin. When two risk-adjusted rankings of the same funds disagree, the disagreement is usually about the measure rather than about the funds — and the person showing you a ranking chose the measure.

The natural test follows. If a fund is presented as superior on a risk-adjusted basis, ask whether it is superior on the others as well. A fund that leads on every measure has told you something. A fund that leads on one is telling you about that one.

Four more things a ratio cannot do

It depends on the period. Like every statistic computed from a price history, it describes the window it was computed over, and a window that excludes a crash flatters everything in it.

It says nothing about whether the risk taken was necessary. Two funds can reach the same ratio with wildly different amounts of risk — one with a modest return and very little movement, another with a large return and a great deal. The ratio treats them as equivalent. Whether you can live through the second is a separate question the ratio does not ask.

It cannot be compared across categories. A ratio computed for an equity fund and one computed for a short-duration debt fund are not on the same scale, because the risks in the denominators are different in kind rather than in degree.

And it does not know you. Risk-adjusted return is a property of the holding. Whether the risk suits you depends on when you need the money and what else you own, which is the argument in risk against volatility.

How to use one sensibly

Use it to compare within a category, over a common window, as a sanity check — a fund whose return looks excellent but whose risk-adjusted figure is unremarkable earned that return by taking more risk, and now you know.

Use it to notice inconsistency. If a fund's ranking moves sharply depending on the measure, it has an unusual shape of returns, and finding out why is more informative than the ratio.

Do not use it to choose. A ratio computed on past returns inherits every problem past returns have, including that it is a description of a period that ended — which is why past performance is not enough to choose a fund.

What to take away

The principle is sound: a return should be judged against the risk taken to get it. The measure is weaker than the principle, because "the risk taken" has several defensible definitions that produce different answers.

So when you are shown a risk-adjusted figure, the question is not whether it is high. It is what went in the denominator, over what period, and whether the same conclusion survives a different choice. If nobody can tell you which measure was used, you have been shown a ranking rather than an argument.