"A fool learns from his mistakes. A wise man learns from history." - Chinese Proverb

Sports writers are fond of saying that a player that has performed well recently is "in form" or having a "hot streak". Many feel that a player can enter into a period of significantly better than average performance, and with their newly found drive and power will be unstoppable.

Coaches send out players to take advantage of their hot streak. Some nights athletes just seem to have their whole game together and perform exceptionally well. These are the players you want to field on any particular night.

The cold hard gaze of the statistician says otherwise. While it may seem that sometimes a player gives an extraordinary performance, a more reliable guide is his or her longer term performance. From the point of view of a statistician most "hot streaks" are made of luck. Rarely will a mediocre player give a superior performance - recent performance aside - that will justify him playing to the exclusion of a much better player.

Although players and their fans may think they are in some kind of superhuman groove, analysis of subsequent performance is just as likely to show the streak ending as carrying on. Mediocre players that turn in an above average performance are more likely to give a mediocre performance at their next attempt than another above average one.

In the stock market there are very few exceptional companies. The vast majority are to a large extent just average. This is not an insult, because generally in a highly competitive market companies are quite well run and standards are high. But by the same token in such special company it is difficult to maintain a performance that is significantly better than average.

In equities the way to measure company performance is return on equity. This is the statistic that measures how high a return a company can achieve on its shareholder's money. A company that gives a high return on equity is able to deploy capital more effectively than its rivals.

In commerce competitive advantages are hard to maintain. When a company achieves a high return on equity other companies soon notice and will copy the strategies in production and marketing that have lead to the eminence of this company. Others will enter the market in direct competition with their own similar products and against such a barrage it is very difficult to maintain a large advantage.

Similarly companies that perform very badly will either recover or go bust. Going completely under is quite rare as sooner or later a company that is mismanaged will become the target of corporate scavengers and the company will be taken over for liquidation or a turn around.

Statisticians call this two-way reversal of fortunes "regressing to the mean". It means that performance that is dramatically higher or lower than average is difficult to sustain and that in a subsequent period performance will be reversed.

Many studies have demonstrated regression to the mean in stocks. The typical finding is that if you track the fortunes of companies in the top quintile of performance over the next decade or more they will fall through the pack and settle at a level little better than average.

Conversely companies right down at the bottom can experience a similar reversal of fortune and make their way from the bottom to the middle over the same period.

It is difficult to forecast who the greatest winners and losers will be in the next ten years but if one thing is certain it is that they will not be the companies that presently occupy these positions.

Only a rare company can continue to grow at above average rates for an extended period of time, yet even great companies will eventually reach a stage where they outgrow their markets.

Ben Graham, who one might call the inventor of value analysis, in his influential book Securities Analysis summed up regression to the mean in the stock market as follows:

The truth of our corporate venture is quite otherwise [than investors think]. Extremely few companies have been able to show a high rate of uninterrupted growth for long periods of time. Remarkably few also of the large companies suffer ultimate extinction. For most, this history is one of vicissitudes, of ups and downs, with changes in their relative standing.

Regression to the mean is a powerful effect and is encountered everywhere in the man made world as well as nature.

When a pair of exceptionally tall parents have children it is quite rare for their offspring to be taller than they are. It is in fact more usual for the children of exceptionally tall parents to be of lesser stature, reflecting the fluke height of the parents.

If you know that the long term average temperature in a particular place is 25 degrees Celsius, but the thermometer records four consecutive days of 35 degree weather, rather than assuming that the average temperature of the area is now permanently higher, it would be safer to assume that some time in the future you will start to measure much cooler temperatures.

In fact if you know that the temperature in this area has historically ranged between 15 and 45 degrees, you might expect that there will be some very cold days that follow, that will continue the tendency for the weather in the area to average 25 degrees.

What regression to the mean implies is that you should never trust above average - or below average performance. You should never project trends to assume that high performance will be sustained. It is also just as dangerous to assume that when something is right down the bottom of the heap that it will stay there.

What it means in nature is that life does not trend toward the production of freaks. If the children of abnormally tall parents usually came out even taller, or the converse for short parents, then after a few generations the world would be full of giants and dwarfs. The same general idea applies to investment, in a competitive marketplace there is no tendency toward all economic power being concentrated on only a few giga corporations, last time I checked there were still thousands of companies on the Australian Stock Exchange, the rest didn't just fail while half a dozen got all the spoils.

If the long term average return of the stock market is 10% per annum, which it approximately is, it is extremely dangerous to assume that 30% returns of a bull market can be sustained indefinitely. In fact it is more likely that several years of 30% performance will be followed by flat or negative returns such that the market in the long term does not get away from its 10% average.

Similarly it is dangerous to predict that a specific sector or asset class will continue to outperform many other sectors that have historically done just as well. One strategy that is frequently used to take advantage of this is contrarian asset allocation, which I will discuss shortly.

In brief, the method assumes that since property trusts, Australian shares and international shares offer very roughly similar long term performance, it pays to concentrate on buying the out of favour asset class. It works on regression to the mean because with this insight you know that the one that just posted the best returns probably won't do as well in a future period as the one that is ready to bounce.

Regression to the mean does not imply that the immediate short term future will reflect the principle of regression to the mean, but it does assert that in a large sample and over the longer term extraordinary returns will be not sustained.

Regression to the mean is not an infallible short term forecaster of prices because if the price of a stock does move in a truly random walk then there is no way at all to predict the very next movement. A stock's next move is, as statisticians would say, an independent event. An independent event is one that depends on its own probability, not affected by what has come before.

On the aggregate though, if a company is not going to take over the world, or crash and burn, something is going to happen that will slow its growth or rescue it.

The same effect is exploitable in timing decisions for choosing a managed fund. If you know that in the long term competition between funds is going to lead to very similar returns from the universe of fund managers, selection of funds according to short term underperformance may lead to superior performance at a future date.

An example that I will expand on later is the sort of return offered by funds with a different style bias. In practice fund managers tend to turn in very similar long term results as a result of their phobia of "tracking error", they take active steps such as diversification and limits on "overweight" and "underweight" positions that virtually guarantee long term performance in line with (or lower than) market averages.

If you believe that two funds are likely to achieve a similar long term performance relative to a benchmark index, it is usually less risky and more profitable to purchase the fund that just posted a -30% annual return in place of the other fund that just had a bumper year. If the 10% historical mean return is going to reassert itself then in all probability in a subsequent period the two funds will soon reverse their relative positions. Morningstar produced some interesting data that demonstrates regression to the mean very well. In a paper released April 1 1994, Morningstar averaged the performance of a variety of different Mutual funds in various sectors:
Fund type 5 Years to March 1989 5 years to March 1994
International Stocks 20.6% 9.4%
Income 14.3% 11.2%
Growth + Income 14.2% 11.9%
Growth 13.3% 13.9%
Small Company 10.3% 15.9%
Aggressive Growth 8.9% 16.1%
Average 13.6% 13.1%