It is perhaps not often that a celebrity’s accident with a penny farthing gives us an opportunity to reflect on some common investment mistakes, but Jeremy Vine banging his head after falling off one gives us just this.
After the accident, he said: “This was the first penny farthing injury the hospital staff could remember seeing, which suggests they are normally extremely safe to ride.” But of course there’s another reason why hospitals don’t see many penny farthing injuries. It’s that hardly anybody rides the contraptions – even in London – and so few people get the chance to injure themselves thereon.
There’s a name for Vine’s mistake: base rate neglect. The base rate probability of riding a penny farthing is extremely low, and it is this that explains why few people end up in hospital having ridden one, rather than the machines’ safety. Penny farthing accidents are rare for the same reason that shark attacks are rare here in Rutland.
Mr Vine is not to be blamed for this error. For one thing, he moves in circles where statistical illiteracy is widespread: a recent survey by the Royal Statistical Society has found that many MPs fail even basic questions about statistics. And for another, base rate neglect is also widespread.
To see how, consider this question: One person in a thousand has a disease. A test to detect it has a false positive rate of 5 per cent. What is the chance that a person found to have a positive result actually has the disease, assuming you know nothing about the person's symptoms?
Even doctors get this question wrong, putting the chance far higher than it actually is, which is 2 per cent. They neglect the base rate probability which is that only one person in a thousand has the disease.
This answer seems counter-intuitive. But imagine a representative sample of 1,000 people are tested. Of the 999 without the disease, 49 (5 per cent) will test positive, along with the one person who actually has the disease. So, given a positive test, your chance of having the disease is one in fifty, or 2 per cent. That’s Bayes theorem.
What’s this got to do with investors? Plenty, because base rate neglect is rife in finance, too.
We see it in takeovers. Investors and company bosses focus upon the likely synergy gains from the merger and neglect the base rate fact which is that, as the University of Virginia’s Robert Bruner has shown, takeovers typically offer “a zero return to buyers.” And so they over estimate the chances that a takeover will succeed.
This has been an expensive error. Royal Bank of Scotland was brought down by its catastrophic acquisition of ABN Amro. That might have been avoided if Fred Goodwin had paid more heed to a 2006 study by Dirk Schmautzer showing that the buyers in cross-border bank takeovers typically lost money.
Base rate neglect happens in another context – new flotations. Newly floated companies look like exciting investments: their owners would not be selling up if they appeared otherwise. But appearances are deceptive. Jay Ritter at the University of Florida and Alan Gregory at the University of Exeter have shown that in both the US and UK newly-floated shares on average underperform the market in their first three years. Aston Martin (AML), Tekmar (TGP) and Network International (NETW) – all of which have fallen since floating in 2018-19 – are more typical than their contemporaries such as Avast (AVST) or Team17 (TM17) which have done well. Paying attention to base rates would save us from losses on such stocks.
The same is true for another class of share: Aim stocks. Base probabilities tell us these are poor investments: in the last 20 years the FTSE Aim index has given a total return of 2.5 per cent a year compared with 6.4 per cent for the All-Share index. Many investors place too little weight upon this fact, however, and too much upon their opinion that such stocks will deliver great growth – thereby also neglecting the fact that corporate growth is largely unpredictable, and our belief in our ability to foresee it owes much to overconfidence.
Base rate neglect also contributes to investors’ reluctance to hold tracker funds. Hendrik Bessembinder at the WP Carey School of Business at the University of Arizona has shown that most shares over their lifetimes underperform not just the market but even cash, and that 1 per cent of companies are responsible for almost all the long-term gains in global stock markets. Base rate probabilities thus tell us that. We’d be better with a tracker fund that guarantees us exposure to the minority of great-performing shares. But we neglect these base probabilities and so over-estimate our chances of beating the market over the long run.
There is, though, a more general example of base rate neglect. “People over-estimate the probability of unlikely events” says the Nobel Laureate Daniel Kahneman. A lot of political and economic punditry does just this, predicting disaster and good times more often than their base probabilities justify.
This isn’t always an expensive error. Quite the opposite. We must insure against the small chance of disaster. But we must also remember that it is just that – a small chance. Base probabilities tell us that modest losses and gains are much more likely than huge ones. Cassandras who predict disaster and boosters who predict great times are both miscalibrating probabilities, and we should discount their utterances accordingly.
Most of us don’t make the mistake of falling off of penny farthings, by having the good sense not to get on them in the first place. But we do often make Vine’s mistake of drawing wrong inferences. Which can be nasty for us – and for him if he gets on a penny farthing again.
