It pays to sell in May

It's just because it's that time of year

Yes. The old advice to "sell in May and go away" really does work. Since 1965, the All-Share index has given an average total return between 31 October and 30 April of a whopping 14.4 per cent. Between 30 April and 31 October, it has returned just 1.8 per cent.

Let's put this another way. If you had been a seasonal investor - switching from cash to shares every 31 October, and from shares to cash every 30 April - £100 in April 1965 would have grown to £63,323. And, yes, you can do this easily. Most personal pension plans allow you to switch freely between cash and shares.

By contrast, £100 left in the market continuously would have grown to just under £17,800. And £100 left in cash would have grown to £2,750. Indeed, a 'reverse seasonal' strategy - holding shares in the summer and cash in the winter - would have grown your £100 to a mere £774. That's less than cash.

This is truly remarkable. It means we must rethink the most basic idea in investing: that there is a trade-off between risk and reward. This trade-off predicts that equities must offer higher returns than cash, because they are riskier. But, for half the year, they don't. All the equity premium in the past 40 years has come only in the winter months.

And not just the past 40 years. Ben Jacobsen, an economist at Erasmus University in Rotterdam, has found that the 'sell in May' rule has worked for UK shares ever since 1694.

But why does the rule work so well?

People used to think that it was because stockbrokers took the summer off, preferring Ascot and Henley to the Square Mile, with the result that there was no-one around to ramp up shares.

Now, we know differently. There are two competing explanations.

One says that the winter is a risky time for the economy. Since 1965, real GDP has fallen by an average of 4.9 per cent in the first quarter of each year, having risen strongly in the previous quarter. Yi Wen, an economist at Cornell University, in New York, says that these seasonal fluctuations can have long-lasting effects. He estimates that they can account for half of all business-cycle fluctuations. If winter creates economic risks, returns on shares should be high in winter months to compensate for these extra dangers.

Mark Kamstra, an economist at Simon Fraser University, in Canada, has an alternative explanation: It's all about the winter blues.

As the nights get longer in September and October, we naturally start to feel more anxious and depressed. As a result, we are loath to take risks and buy shares. So the market falls: September, in particular, is traditionally a terrible month for the All-Share, with an average return since 1965 of -0.9 per cent. This causes shares to become cheap by the end of October, with the result that subsequent returns are good.

This process gets a further kick in March and April, when the lighter evenings cheer us up, and encourage us to take risks and buy shares. April is usually a good time for the All-Share, with average returns of 3.1 per cent in the month. From such high levels, though, subsequent returns are poor. Hence, the lacklustre summer returns.

which of these explanations is right?

Here, things get a little tricky. There's an obvious flaw in the economic risk argument. To see it, consider Australia. Its economy is even more seasonal than the UK's, with bigger falls in output in the first quarter, and bigger rises in the fourth quarter.

You would, therefore, expect its stock market to show a similar seasonal pattern to the UK's. But it doesn't. Since 1973, the UK market has outperformed Australia's by an average of 4.7 per cent between 31 October and 30 April. But it has underperformed Australia's by 3 per cent between 30 April and 31 October.

This is inconsistent with the seasonality of economic fluctuations. But it's perfectly consistent with the winter blues theory. In the land of Kylie, the winter blues depress returns in October-April, but raise them the rest of the time - exactly the opposite pattern to our own.

However, there's also a problem with the winter blues theory.

If daylight hours merely affected our appetite for market risk, you would expect its effects to be subsumed within valuations. Our rising appetite for market risk in March and April would depress the dividend yield, and this would lead to low returns. Controlling for the dividend yield, however, there should be no effect of the seasons upon returns.

But this is not the case. Seasonality and the dividend yield both predict returns, so that the seasonal effect is separate from the dividend yield effect. A simple equation shows this. Taking six-monthly returns on the All-Share since 1965 (for the periods ending 30 April and 31 October), we can predict returns with the equation:

Returns = 6.88 x dividend yield + 10.71 x winter dummy - 27.89.

The winter dummy has the value of one for the six-month period ending 30 April, but otherwise it is zero.

There are four important things to consider about this equation:

* It shows that seasonality is a powerful influence on returns, even aside from valuations. Controlling for the dividend yield, the mere fact of winter adds 10.71 per cent to All-Share returns between 31 October and 30 April.

* It explains a huge proportion of the variation in six-monthly returns, so that 38.3 per cent of this variation - almost two-fifths - can be attributed to yield and seasonality alone. Given that the so-called 'experts' often ignore these and talk about other things, this is remarkable.

* There is no sign of the equation breaking down and the seasonal effect weakening. In the past three years, its forecast errors have been no bigger than in the past. And its prediction for returns in the six months to 30 April was exactly spot-on, at 7.1 per cent.

* The equation suggests that you shouldn't stay in the market now because it seems cheap. It's pointing to a negative return of 4.4 per cent in the next six months.

If history's any guide then, it's time to sell

But what should we sell? Our chart suggests some obvious candidates. It shows that so-called 'cyclical' sectors - such as construction, engineering, electronics and IT hardware - have an big seasonal pattern.

For example, since 1987, construction stocks have fallen by an average of 8.6 per cent in summer, but risen by 15.4 per cent in winter. Engineering stocks have fallen by 5.9 per cent in summer, but risen 11.9 per cent in winter. Only a few sectors - tobacco, pharmaceuticals and utilities - have beaten cash during the summer. These tend to be so-called 'defensives'.

Herein, though, lies a puzzle. Tobacco stocks have been among the market's best performers in the past three years. And history suggests that good performance over three years often leads to bad performance in the next three. Doesn't this mean that we should ignore the seasonal message, and sell tobacco stocks? Not necessarily. Mean reversion in returns doesn't seem to happen during the summer.

To test this, I ran a simple experiment. I asked what would have happened if, on 30 April each year, you had bought the five best and five worst-performing sectors over the previous three years, and held them for six months?

The table shows the results. It shows that, on average, there has been little difference in the two portfolios. The five best-performing sectors in the previous three years gave an average return of a paltry 1.2 per cent during the summer. The five worst performers did even worse, giving a gain of just 0.8 per cent.

And there is no clear tendency for past losers to gain ground over the summer. As often as not, mean reversion just fails. So now is not the time to buy past losers in the hope of a bargain.

There's probably a simple reason for this: momentum. The reason why good long-run returns lead to bad ones is that some investors jump on the bandwagon, forcing prices up beyond the 'fundamental level', with the result that they eventually fall. However, there is no reason why the bandwagon must stop after exactly three years - the same things that cause a share to become 'overvalued' can keep it overvalued for a while.

Consequently, it's possible for returns in the six months after a good three-year period to remain good. It's only in longer periods - a year or more - that the bandwagon goes into reverse and mean-reversion works.

The bottom line here is clear. Investors should prepare for the market to underperform cash, with so-called cyclicals likely to do especially badly. And whatever you buy or sell, don't think that mean reversion or momentum are any help for predicting returns over the next few months.

This table shows total returns on the All-Share index for each month since 1966. Returns in January and April, in particular, are significantly better than average.Returns in June and September are worse.Also significant are the number of months in which the market falls. If there were no seasonality, you would expect to see around 15 falls for each month.However, November, December, January and April have seen fewer falls than this. The summer months, except for August, have generally seen more falls.