The Halloween signal

History suggests so. Ben Jacobsen and Cherry Zhang have studied returns on all national stock markets since they began, and have found that in almost all of them returns are much higher from Halloween to May Day than they are from May Day to Halloween. The UK fits this pattern. Since 1966 the All-Share index has given a total return after inflation of 8.3 per cent on average between Halloween and May Day, but has lost an average of 0.6 per cent from May Days to Halloweens. The fall in the FTSE 100 since May fits this pattern.

What’s more, there’s more chance of big returns in winter and less chance of big losses. Since 1966 we’ve seen 20 gains of 10 per cent or more in the six winter months (November to April) and only three losses of such magnitude. In the six summer months, however, we’ve had 11 gains of more than 10 per cent and 11 losses of more than 10 per cent.

'Buy on Halloween' therefore makes sense if history is any guide*. There’s a good reason for this. Our appetite for risk is seasonal. In the spring we become more optimistic which drives prices up too far: May Day, remember is traditionally a festival of hope and fertility. And as the nights draw in we become anxious and depressed so prices fall too far in the autumn offering good returns for anybody willing to buy then.

You might well have an objection to all this: shouldn’t investors have wised up to all this by now and therefore corrected their behaviour? They should therefore be less inclined now to buy in the spring and less tempted to sell in the autumn.

Evidence for this is, however, mixed. Certainly, it hasn’t happened this year. The Footsie’s strong rise in the spring and fall this month has fitted the seasonal pattern perfectly. Before this year, however, there were signs of fading seasonality: the two summers before this year saw shares rise, and four of the last five winters saw only moderate returns.

This is inconclusive, though: we’d expect such moves in a few points of noisy data even if returns were truly seasonal.

And, in fact, theory is inconclusive, too. Yes, knowing that our appetite for risk is seasonal should curb our urges to buy in the spring and sell in the winter. But there’s the opposite possibility. If we know that attitudes to risk are seasonal, we might buy in the spring in anticipation of others doing so, and sell in the autumn for fear that others will sell. Merely knowing about the seasonal pattern in returns does not therefore guarantee that it will be eliminated.

Let’s, though, take another approach. Let’s assume for the sake of argument that the seasonal pattern has disappeared. Do we have any other reasons to buy or sell now?

Yes. Two lead indicators of future returns tell us to buy. The dividend yield on the All-Share index is above its 30-year average. And figures from the US Treasury show that non-Americans have recently become sellers of US shares. That’s a sign that sentiment is unusually depressed and in the past shares have risen afterwards as sentiment returns to normal.

On the other hand, though, the All-Share index is now below its 10-month moving average. This tells us that momentum is against the market and is a reason to sell.

But we have a problem here. While these indicators are good predictors of annual returns they are not statistically significant at conventional levels as predictors of returns in the six months to May Day or Halloween. This is because at short time horizons the ratio of noise to signal is high.

Whether this means we should ignore them completely is, however, unclear: most investors act on probabilities that are much lower than 95 per cent.

There is, though, one lead indicator of returns that is statistically significant for six-monthly returns: the ratio of the broad money stock in the OECD area to the MSCI’s world index. This ratio is now below its (detrended) average, implying that investors are underweight in cash and overweight in equities. This is a bearish indicator.

But only slightly so. It is less bearish than it was in April because the money stock has grown since then. It points to around a 60 per cent chance of the All-Share index falling over the next six months. If you attach any weight at all to the seasonal pattern, or to the signals sent by the dividend yield and foreign selling of US equities, these would offset this signal.

We have, therefore, a balanced decision. I personally will soon be increasing my equity weighting from around 30 per cent to around 60 per cent, having saved myself a 7 per cent loss by selling in May: I can do so at no cost within my pension fund. Others will of course disagree with this call. Some reasons for doing so are rational, some are not.

*The rule "buy on St Leger day" died in 1987, when the market crashed in October. And it always lacked a scientific basis.