Minds over markets?

Whilst on my way home tonight I saw this advert for managed funds (at Stratford station in London, UK). Note that the last line of the small print does say that investments can fall as well as rise, but the large print has a fairly clear message.

I have no idea how well or badly this particular group has performed over a long period. However, in the market as a whole it is not possible to predict which managed funds will beat the market. Just by chance, some funds do beat the market index in any given year but most funds don't. And beating the market in one year does not predict success in the next year.

In his book "A mathematician plays the market", John Allen Paulos asks us to consider two stock pickers, Tom and Harry. Both are actually performing at chance level, but nonetheless Tom outperforms Harry over the course of the year. And this is exactly what we would expect from a chance process. You can see this for yourself through a simple coin tossing exercise. Toss a coin 101 times and keep a running tally of how many heads and how many tails there have been. At any given point in the sequence of coin tosses either Heads or Tails will be in "the lead" or there will have been even numbers of both. Most people seem to think that the lead will be continually changing, but actually such sequences typically produce very few changes of lead. It's not uncommon for one side of the coin, say Tails, to go into the lead on the very first coin toss and stay in the lead for the remainder of the trials. In fact, as far as a precise number of lead changes is concerned, the most likely number of such changes is zero. This counter-intuitive result was shown to be true by the mathematician William Feller in the 1950s. A popular account is given by John Haigh in "Taking chances: Winning with probability" (see also "A random walk down Wall Street", by Burton Malkiel). Of course, over increasing numbers of such sequences we'd expect the overall proportion of Heads and Tails to converge towards 50%, but in any given sequence the overall proportion is rarely exactly 50% and - as just mentioned - there are typically very few changes of lead.

So our stock pickers Tom and Harry are rather like our coins. In any given year, just by chance, one is most likely to have outperformed the other and is also very likely to have done so consistently across the year. People may well form the conclusion that Tom is a better stock picker, particularly as Tom will now place lots of advertisements flagging up his success.