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OPINION

On elusive theories

On elusive theories
November 8, 2016
On elusive theories

Consider the theory behind 'buy on Halloween'. It is that investors become more risk-averse as the nights get longer in the autumn and this causes shares to become underpriced, while the better weather in the spring brightens our mood and encourages us to buy shares, pushing their prices up.

The problem is that this doesn't imply that investors snap out of their gloom on 1 November. It's consistent with shares bottoming out in mid-October, or late November or any number of dates. All the theory says is that share prices at some time in the spring will be higher than at some time in the autumn - more so than for other comparable periods. This is vague. 'Buy on Halloween: sell on May Day' is just one of many possible ways of giving it precise substance and therefore testing it. Halloween and May Day aren't necessarily the best times to buy and sell. They're just obvious dates we can use to test the theory.

What we have here is an example of the Duhem-Quine problem. This says that hypotheses can never be tested in isolation but only in conjunction with other hypotheses. In our case, we can test the 'buy on Halloween: sell on May Day' hypothesis. Historically, it has worked. But it is a test of (at least) two hypotheses: that risk aversion increases in autumn and falls in the spring; and that Halloween and May Day are good times to buy and sell. But one hypothesis can be true without the other.

This problem is widespread. Take another hypothesis - that momentum investing works. But how do we measure momentum: by returns in the last 12 months, or six, or three, or what? And how many stocks should a momentum portfolio contain: 10, 20, 50, 100? Again, the theory has many possible specifications. Luckily, the work of US academics Sheridan Titman and Narasimhan Jegadeesh suggests that several specifications work, which increases our confidence in the momentum effect.

In fact, this problem afflicts all stock-picking. The claim 'this share is cheap' can only be tested alongside other hypotheses. One of these is that you have the trading skill to buy and sell at good prices: this is an especial issue for institutional investors trying to trade big sums in an effort to exploit small mispricings.

Another hypothesis is that the share doesn't carry especial risk. This is a big problem because it is fiendishly hard to identify all possible risks and the returns that they justify. Liquidity risk, cyclical risk and benchmark risk, to take just three examples, are hard to measure. And even the most apparently obvious measure of market risk - beta - is in fact controversial: economists and investors use different measures of it.

This problem matters. It means that even if you enjoy decent gains on a share you can only very rarely be sure it is because you were clever enough to spot a genuine mispricing rather than because you took a risk and got lucky.

This is one reason why there is still a debate about whether stock markets are efficient or not.

The Duhem-Quine problem implies that we might never know the truth about some theories. Worse still, it implies that bad ideas don't always get killed off. Of course, it is not just in investing that this is true.