To see why, consider a different case. Imagine you were to buy high-beta stocks such as banks and miners and that the general market then rose. The chances are that you would outperform the market. But nobody would think this evidence against efficient markets. The efficient market hypothesis (EMH) is entirely consistent with people making great returns, if they take extra risk. As Burton Malkiel, one of the great advocates of the EMH said, "financial markets are efficient because they don't allow investors to earn above-average risk-adjusted returns".
And buying on Halloween is just like buying high-beta shares. Shares are lowly priced in the autumn because the longer nights make people depressed and jittery. The investor who buys shares then earns profits by taking risks that others want to avoid - just as the buyer of high-beta stocks does.
The EMH is consistent with returns varying over time, just as it is consistent with returns varying across shares, as long as such variations are due to variations in risk.
Half of the 'buy on Halloween, sell on May Day' rule is, therefore, consistent with the EMH.
But what about the fact that equities in the summer months underperform cash, on average? Surely this violates the efficient market hypothesis that riskier assets much earn higher expected returns than safe ones.
Not necessarily. If investors enjoy taking risks, then returns on risky assets can rationally be below those on safe ones. If you like gambling, it's not irrational to go to a casino or bookies - which offer negative expected returns - because you are paying to get a buzz. Likewise, if you enjoy gambling on shares, negative returns are the price you pay for the entertainment.
All this, though, raises a question. While risk aversion in the winter might explain some of the additional returns investors get then, does it explain all of them? Likewise, does risk-loving behaviour in the spring explain all of the summer's poor returns?
This question matters because there's an alternative hypothesis here.
It's obvious that our spirits improve in the spring and worsen in the autumn. But is this because we become tolerant of risk in the spring - in which case poor equity returns in summers are consistent with the EMH? Or is it because we become overly optimistic in the spring, in which case bad summer returns are inconsistent with the rational markets hypothesis at least?
It's difficult to say. Although there is a sharp theoretical difference between optimism and risk appetite, the two are often practically and psychologically intermingled.
There is, however, one piece of evidence that risk appetite really is unusually high in the spring. It's simply that pretty much all the big gambling events traditionally take place then: the Cheltenham Festival, the Grand National, Derby, Royal Ascot. This suggests that our appetite for risk, and not just our optimism, is greatest in the spring. It's quite possible, then, that bad returns in the summer are consistent with the EMH.
This, though, still leaves open the issue of whether all the winter's good returns are a reward for taking risk, or rather a reward for exploiting other investors' excessive pessimism. Sadly, there is, to my knowledge, no robust evidence on this.
It is, then, at least possible that seasonal investing is consistent with markets being efficient.
I don't say all this to defend the EMH; the claim that markets are, or are not efficient, strikes me as grandiose big-think. It's just that, if you want evidence against it, then you'd be better off looking at the long-run performance of momentum or defensive stocks rather than the seasonality of the market.
