2011年12月30日 07:18 AM
In love as in equities, we are regularly fooled by randomness
As the year ends, the author of a weekly column should look back and acknowledge the things he got wrong. I made at least one serious mistake. I wrote that if men think about sex on average every seven seconds, the average man last thought about sex three and a half seconds ago. I should have consulted the poet Wendy Cope, who wrote that: “Bloody men are like bloody buses – / You wait for about a year / And as soon as one approaches your stop / Two or three others appear”.
Her analogy is helpful. If a bus arrives at fixed intervals of seven minutes, you will wait an average of three and a half minutes. But, as Ms Cope knows all too well, the interval is unpredictable: two buses come at once and then there is a lengthy wait for the next one. The average frequency of the bus may still be seven minutes. But if the intervals are alternately zero and 14 minutes the expected wait is now seven minutes, not three and a half. If someone is standing at a bus stop, it is more likely that they are victim of a bus which is late than the beneficiary of one that is early.
You may think this does not matter very much. But this summer the UK business secretary Vince Cable asked me to devote an entire year to thinking about equity markets. I discovered that the arithmetic of thinking about share values is the same as the arithmetic of thinking about sex. The average length of time for which buyers hold shares today is very short. But the average length of time for which shares have been held by their current owner is much longer. There are many more high frequency trades than passive investors, but passive investors hold a high proportion of outstanding shares.
The people queuing for a bus are the people whose bus has not arrived, and the people on yachts are those whose boat came in. What we see will always be influenced by the ways in which the sample studied is selected. The traders we interview are mostly successful because mostly it is the successful who are still trading – and this past success may be no guide to future performance. As the essayist Nassim Taleb has observed, we are regularly fooled by randomness, identifying skill where there was only luck, finding patterns in data when none really exist.
The sometimes counter-intuitive mathematics of variation crops up in many different places. If Persil is sometimes on special offer, the percentage increase when it goes back to its usual price will be larger than the percentage price reduction when it goes on special. If that seems an unremarkable fact, it was enough to send several hundred thousand government employees on strike a month ago.
The average of price changes shows an increase even though the price has remained the same. And perhaps you buy more, perhaps even spend more, when the item is on offer than when it is at full price. After all, that is why they put it on special. These issues pose problems for compilers of price indices, and there are different methods of handling them. That is the principal reason why the new European harmonised index of consumer prices generally increases by less than the old retail prices index. The UK chancellor George Osborne is planning to make large savings in public expenditure by shifting pension indexation from one basis to the other.
The same problem arises in measuring benchmarks and portfolio performance in equity markets. If you average a 50 per cent fall and a 100 per cent increase, you show a 25 per cent gain. But if that happened to your shares, you would – just – have recouped your initial investment. Neither method of calculation is necessarily a guarantee to the experience of real investors.
I may have made another mistake in my earlier column. Since it appeared, details have been published of a study by researchers at Ohio State University. They surveyed college students – who, one might expect, think about sex more often than the average of the population. The subjects were asked to make a note each time the topic entered their heads. Men thought about sex, on average, 19 times a day (the figure for women was only 10). Does this mean that we should correct “every seven seconds” to “on average, once every waking hour”? Only if men think about sex at absolutely regular intervals. And neither love nor equity markets are so predictable.
在先前的專欄文章中，我可能還出過另一個錯誤。那篇文章發表後，俄亥俄州立大學(Ohio State University)的研究人員發布了一項調查的詳細結果。人們可能認為大學生想到性的頻率比一般人高，於是研究人員就對大學生進行了調查。他們要求調查對象每次想到性時，就在記錄中記上一筆。結果顯示，男生平均每天有19次想到性（女生則只有10次）。這是不是意味著，應該把“每7秒”修改成“醒著的時候平均每小時想到一次”？不見得，除非男人想到性的時間間隔是絕對固定的。而且，無論是預測愛情還是預測股市，都沒那麼容易。
「華人戴明學院」是戴明哲學的學習共同體 ，致力於淵博型智識系統的研究、推廣和運用。 The purpose of this blog is to advance the ideas and ideals of W. Edwards Deming.
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