Measuring risk: Five numbers, none enough

People say an investment is "risky". But how risky? Finance has invented several measures. None is enough on its own.

The best known: volatility. It is the standard deviation of returns. It measures how far they stray from their average.

Say an investment that returns seven per cent on average, with fifteen per cent volatility.

If returns follow a bell curve, about two years in three end between minus eight and plus twenty-two per cent.

First flaw: volatility counts rises as risk. A good surprise pushes it up as much as a bad one.

Second flaw: it describes ordinary jolts. It says little about rare disasters.

Hence another measure: VaR, value at risk. It answers one question: how much can I lose, ninety-nine times out of a hundred?

Say one hundred thousand euros, fifteen per cent volatility, a bell curve, over one year.

The VaR at ninety-nine per cent is then about thirty-four thousand nine hundred euros. Ninety-nine times out of a hundred, you lose less.

In the app, this chapter is animated and narrated, card by card. Start free trial.

But VaR says nothing about the hundredth time. That day, the loss can be far worse.

That is the role of CVaR: the average loss when you fall into that worst one per cent.

In the same example, it rises to nearly forty thousand euros. And in reality, where extremes are more frequent, often more.

Banks have used these measures since the nineties. They did not stop them being caught out in two thousand eight.

A more concrete measure, which every saver feels: maximum drawdown. The worst fall, from peak to trough.

Your investment rises from one hundred to one hundred and fifty, then falls to ninety. The drawdown is forty per cent, from the peak.

The American S and P five hundred index lost more than fifty-five per cent between two thousand seven and two thousand nine.

And to erase a fifty per cent fall, you then have to gain one hundred per cent. Losses and gains are not symmetrical.

Last measure: semi-variance. You keep only returns below the average. Only the downside counts.

It is closer to what an investor feels. Nobody complains about too strong a rise.

Each measure lights up one angle. Volatility, the agitation. VaR and CVaR, the bad day. Drawdown, the pain lived through.

None tells the risk on its own. And all rest on the past, which does not always warn you.

Before investing, one question is worth every formula: what fall am I ready to live through without selling?