Not normal

My table shows the point. It shows the distribution of weekly returns on various assets since the start of 1988; I'm using weekly returns because these give us lots of data and thus a more powerful test than monthly or annual data.

The table shows that returns of two standard deviations or more are indeed more likely than the normal distribution implies. That's well known. But it also tells us that small losses are less likely than they would be if they were distributed as a bell curve. Take, for example, the All-Share index. Since 1988 it has had average weekly returns of 0.23 per cent with a standard deviation of 2.2 percentage points. A one standard deviation loss is therefore a drop of 1.97 per cent. A normal distribution tells us we should have seen 221 weeks since 1988 in which the market lost this amount or more. But in fact, we've seen only 182. That's 17.7 per cent less - or, if you prefer, a frequency of 13.1 per cent rather than 15.9 per cent. This implies that losses of between one and two standard deviations are 24 per cent less common than the bell curve implies.

Whether this is a lot or a little is, I suspect, a matter of taste. All theories are wrong by the toughest standards but right by looser ones.

Much the same is true if we look at big stocks or small ones, and even if we look at other assets such as gilts or gold.

Now, probabilities must equal 100 per cent. If moderate losses are less likely than a bell curve implies, then something else must be more likely. That something is not just big losses. Nor is it decent sized gains; rises of more than half a standard deviation are also less likely than a bell curve predicts.

Instead, what's more likely is price stability. A normal distribution tells us that we should have seen 534 weeks in which All-Share returns were within half a standard deviation of average. In fact, we've seen 625 - 17 per cent more. And again, much the same is true for other assets.

This gives us a picture. Asset returns are more stable than a bell curve implies, except for brief spells when they are more volatile. This might be why, traditionally, former army officers were hired as equity salesmen - because stock markets, like the military, consist of long periods of boredom, interrupted by spells of panic.

This is consistent with volatility clustering. Much of the time, volatility is low because traders disagree - for every optimist there's a pessimist - and so prices don't need to move much for a seller to find a buyer. Occasionally, however, disagreement becomes agreement. When it does, sellers can't so easily find buyers and so prices must fall a lot. In this way, the market oscillates between small moves and big ones, with fewer middling ones.

Does this matter for investors? Not necessarily. For some investors, the good news that moderate losses are less likely than a bell curve implies is offset by the bad news that big losses are more likely.

However, for two types of investor it does matter. One type is the loss averse - those who are more than averagely worried by big losses. In monetary terms, a 1 per cent chance of a 5 per cent weekly loss is the same as a 10 per cent chance of a 0.5 per cent loss. In psychological terms, however, the former might be more uncomfortable. For this type of investor, the fact that returns aren't normally distributed makes shares less attractive.

Secondly, decent-sized gains are also less likely than a bell curve implies; one standard deviation rises in the All-Share index have occurred only 11.5 per cent of the time, against a normal distribution's prediction of 15.9 per cent. This implies that equities - or at least a diversified portfolio of them - are less attractive to anyone wanting quick returns than a bell curve implies. In this sense, equities are a get-rich-slow investment.