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What volatility means (and doesn't)

Created:
5 February 2008
Written by:
Chris Dillow

It won't have escaped your attention that market volatility has risen recently. But what does this mean? There are two common errors to avoid here.

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Error one: "High risk means high rewards, so higher volatility points to the market rising."

This is often true. But not always. Rewind to 2000. An investor back then might have known that, in the previous five years, there had been a positive correlation between volatility (as measured by the VIX index) and subsequent All-Share returns - high volatility in autumn 1998, for example, proved to be a great buying opportunity. So, seeing volatility above average, he might have bought shares.

And he'd have lost, as the market slumped.

The reason for this is simple. The trade-off between volatility and returns has a nasty habit of changing suddenly. Our chart illustrates this point. It shows that, over five-year periods, volatility and returns are often negatively correlated; this is consistent with there being a positive correlation within these periods. For example, high volatility in the 1970s, 1988-92 and 1999-2003 was associated with poor returns, while low volatility in the mid-80s and 90s was associated with better returns.

There's a pattern here. When the economy is weak, or when investors expect it to be, volatility is high and returns are low. But when the economy does all right, volatility is low and returns are high.

This raises the possibility that higher volatility is not a buying signal, but rather is a sign that we've shifted to a period of low returns and higher volatility.

So, while there are reasons to be optimistic about the market, higher volatility isn't necessarily one of them.

Error two: "High volatility makes it more important to be a long-term investor, so you can ride out short-term turbulence."

This misunderstands the maths. Let's take the simplest case, in which returns during one period are uncorrelated with those of the next period. In this case, the volatility of returns rises with the square root of time. So, if annual volatility is 20 per cent, two-year volatility is 28.3 per cent (20 times √2), and so on.

Now, let's assume real returns average 5 per cent a year. In this case, the probability of a loss in a year is a 5/20 standard deviation event - a 40 per cent chance. The probability of a loss over five years is a 27.6/44.7 standard deviation event - a 27 per cent chance. And the probability of a loss over 10 years is a 62.9/63.2 standard deviation event - a 16 per cent probability.

The chances of a loss over the long-term are therefore lower. But they are much nastier outcomes. If you lose money over 12 months, you've lots of time to recoup your money. But if you lose over a 10-year period, you might well have to abandon hopes of retiring early.

So, which do you prefer - the big chance of a small problem, or the smaller chance of a big problem? It's not obvious. Which means the case for having longer-term investing horizons is not at all clear.

There is, however, an objection here. I've assumed returns are serially uncorrelated, so that a fall in one month is as likely to be followed by a fall as by a rise the next month. But maybe this is wrong. There's some evidence that returns have been mean-reverting, with bad times leading to good and vice versa. If this continues to be the case, then long-term investing is safer.

But is this any more true when volatility is high than when it is low? Perhaps not. In the mid-70s, when volatility was very high, monthly returns were positively correlated - good months led (more than 50:50) to good and bad to bad. And in the mid-80s, when volatility was low, monthly returns were slightly negatively correlated. So perhaps it's unwise to hope that mean-reversion can protect us from high volatility.

All this raises the question. If high volatility doesn't portend higher returns or mean that long-term investing is a good idea, what does it mean?

It means that we can't tell what the market's true return is.

We know that the All-Share has returned 3.6 per cent a year after inflation over the last 10 years. But it's possible that this was thanks to luck rather than to the fact that equities are a really good investment. Perhaps shares' true average returns are lousy, and we just had some good luck in the past 10 years.

To tell which it is, we need to know the standard error of returns. And this is easily calculated. We simply divide annual volatility - 13.6 per cent in the last 10 years - by the square root of the number of years we're interested in. In this case, it's 10, so the standard error is 13.6/3.16 = 4.3.

We can now estimate the range in which the All-Share's true return lies. There's a two-thirds chance it's within one standard error of 3.6 per cent - that is, in the range minus 0.7 to plus 7.7.

So, if we had only the evidence of the last 10 years, we couldn't be at all confident that equities have a positive return. And the higher is volatility, the less confident we can be, for a given observed return.

Exactly the same holds for fund managers. Higher volatility means it's hard to distinguish between luck and skill.

To see the point, consider M&G's Recovery fund. Over the past five years, it's beaten the All-Share by an average of 3.7 percentage points a year. It's tracking error during this time has been just under 6 per cent a year. This means - using the same logic as above - that the standard error of its annualised returns is 2.7 per cent.

Given this, we can estimate the chances that M&G could have delivered outperformance of 3.7 percentage points a year by luck alone. It's a 3.7/2.7 standard error event - just under 9 per cent.

However, tracking error usually rises as market volatility rises. If this were to double - all else being equal - then there'd be a one-in-four chance of a fund outperforming by 3.7 percentage points a year merely by luck.

Higher volatility, then, makes it much harder to judge fund managers.

And why have I picked on M&G Recovery? Simple. It's the fund that's just inside the top 10 per cent of all companies funds for the past five years. If volatility makes it hard to tell if even a top decile fund has skill rather than luck, then it makes life very murky indeed.

And that's the point. High volatility doesn't mean investors should do anything. But it does mean we can know much less.

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