Secrets Of Success: Long odds do not mean no chance

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The Independent Online

Ploughing through the log-jam of research material on my desk, this item from a research note by an analyst at State Street caught my eye this week. It started by mentioning a horse named Tioga Gold, which until this month had appeared to be "destined for a life of equine obscurity". The eight-year-old gelding had only won one race, a juvenile seller in 2001, and in its previous outing at Pontefract was beaten by more than 100 lengths.

It was hardly surprising, the analyst noted, that Tioga Gold started the one mile, six furlong handicap at Southwell's all-weather track on 2 January at odds of 125-1. But the hopeless horse won the race, going down in history as the longest odds winner on the all-weather circuit in the UK. (The biggest priced winner of all time, it seems, was Equinoctial at 250-1 in a hurdles race at Kelso in November 1990.)

"The trouble is," the note went on, "that impossible events have a habit of happening, especially in allegedly efficient financial markets.

"For example, in the 18 months up to February 2000, growth stocks outperformed value in the US by 125 per cent. It was reported at the time that this represented a 6.8 standard deviation event. Put another way, if you believe the maths, it is something that should happen once every 285 billion years. Unfortunately, we will never get to test the logic of this. The Earth has only existed for 4.5 billion years and will be engulfed by the sun in another 7.5 billion."

Well, I am no expert on the history of the Earth, but the point is clearly a striking one whether or not the figures are precisely right. Similar calculations, the author could have noted, were made about the October 1987 crash, which was another event in theory so rare that you would not expect to see it in hundreds of millions of years. In the case of horse racing, of course, the suspicious mind might conclude that there have been other factors at work to invalidate the historic odds.

In the case of the financial markets, you can try to explain away the October 1987 crash in part by reference to special factors, such as portfolio insurance, the automated and still largely unproven asset allocation tool that prompted a wave of mindless selling by institutions as the market started to fall. But such a plausible, practical explanation can only take you part of the way to an answer.

It is a simple empirical fact, as many academics have demonstrated, that financial markets in practice are far more volatile than either theory or realised outcomes suggest they should be. Common sense might then lead you to conclude that the theory that says extreme market events should be rarer than they are is incorrect (and that, I think, is the right answer).

The crucial assumption that underlies most of modern financial theory is that the returns from financial markets are normally distributed; that is to say that they fit into a standard bell-curve distribution. If any statistical series does follow this pattern, basic probability can then tell you how likely it is that a particular outcome is within one, two or more standard deviations of the average outcome.

In practice, financial markets experience a far greater number of extreme events (more than two standard deviations from the mean) than standard probability assumptions says they should. This ugly fact unfortunately invalidates many of the conclusions that follow from the application of financial theory, not that, in practice, this stops their widespread application in areas such as asset allocation, financial planning and risk measurement.

For investors, there are risks in the fact that valuations move in broad cycles that are more extreme than changes in the fundamentals of earnings, dividends and cash-flow can justify. High p/e ratios and high profit margins do revert to the mean over time; but they rarely revert as quickly or as predictably as they should a year or two ahead, which is the horizon over which most investors measure their performance. In practice, they are heavily influenced by momentum, continuing to buy what has been going up, even when it takes them into potentially higher-risk territory.

Timing the cycles is difficult, so few attempt it. The housing market has become a classic example. UK house prices as a multiple of earnings, according to Jeremy Grantham, are now six standard deviations above their long-term average, which is one of those outcomes, like Tioga Gold's victory at the race course, that should only occur once every Ice Age or so. Another recent survey showed that London house prices are by some margin the most expensive (per square foot) of any other major city in the world. Yet does that stop apparently smart people committing their money in this way? Not at all.

According to calculations by the bond firm Pimco, with interest rates and rental yields where they are, anyone who took out a 100 per cent buy-to-let mortgage at the end of last year is already experiencing negative cash flow; and is 99 per cent certain to lose money over the lifetime of the mortgage - unless they can find a greater fool to sell their property on to at a profit before the reckoning arrives.

As for financial markets, as the State Street analyst noted: "Investors seem ill-prepared for another bolt from the blue. The mood among institutional investors is super sanguine. The risk-seeking behaviour that characterised most of 2006 (bar a short bout of summertime blues) has continued into 2007. Cross-border institutional investor flows into emerging equity markets remain strong, whereas demand for the biggest developed markets, the UK and US, is weak."

This is true. Everyone knows that some sort of reckoning is coming in due course, but will it happen this year, next year or 2010? Perhaps a better question to ask is: what will the trigger be that stops the current bull market run in its tracks? As of yet, I see no obvious answer, which is why my working hypothesis going into 2007 continues to be that complacency will continue to earn rewards for now. But the risks are no less real for being invisible.

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