In love as in equities, we are regularly fooled by randomness

2011年12月30日 07:18 AM
小心被隨機性欺騙
In love as in equities, we are regularly fooled by randomness
英國《金融時報》專欄作家 約翰•凱



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”.


到了年底，每週發表一篇文章的專欄作家應當回顧這一年，承認自己的文章在哪些地方出過錯誤。我就至少出過一次嚴重的錯誤。我曾寫道，如果男人平均每7秒就想到一次性，那麼男人上一次想到性平均是在3.5秒之前（請見FT中文網2011年9月1日文章《統計數據的誤區》——譯者注）。我本該就此徵詢一下詩人溫迪•可普(Wendy Cope)的意見，因為她曾寫過：“死男人們就像那些可惡的公交車，你一等就得等上將近一年，剛有一輛車靠站，其它幾輛就接二連三地來了。”

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.


她的類比很有幫助。如果公交車到站的時間間隔是固定的，比如7分鐘，那你平均需要等上3.5分鐘。但實際的時間間隔是無法預知的，可普對這一點了解得很清楚：如果同時來了兩輛車，那麼下一輛就得等上很長時間。公交車到站的平均頻率或許仍是每7分鐘一輛，但如果時間間隔變成了要么是0分鐘要么是14分鐘，那麼預期等待時間就變成了7分鐘、而不是3.5分鐘。如果有人現在正站在公交站等車，那麼他們更有可能是要倒霉地去等一輛晚到的公交車，而不是幸運地趕上一輛早到的公交車。

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.


你可能會覺得這件事並沒有那麼重要。但今年夏天，英國商務大臣文斯•凱布爾(Vince Cable)讓我花一整年的時間對股票市場做些思考，結果我發現，股票價值思考所適用的計算，與性思考所適用的計算是相同的。現在買股票的人的平均持股時間是很短的，但股票在其當前持有者手中停留的平均時間卻長得多。高頻交易的交易量遠比被動投資者的交易量大得多，但被動投資者所持股票在已發行股票中佔很大比例。

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 tr​​ading – 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.


排隊在那兒等公交車的，是還沒等到公交車的人。坐在遊艇上的，則是已買到遊艇的人。我們觀察到的現象，永遠都會受研究樣本選擇方式的影響。我們採訪的交易員大多是成功的，因為大多數情況下，仍在從事交易的人正是那些成功者——但過去的成功並不構成未來表現的指引。正如作家納西姆•塔勒布(Nassim Taleb)觀察到的，我們經常被隨機性所欺騙，在那些只由運氣決定的情況中尋找技巧，在實際上毫無規律的數據中尋找規律。

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.


有時候，這種與直覺認識相反的、關於“變動”的數學運算也出現在其它地方。如果寶瑩(Persil)洗滌劑偶爾進行一次特價促銷，那麼從特價恢復為原價時價格上漲的百分比，會高於從原價降為特價時價格下跌的百分比。儘管這個事實看似再正常不過，但它卻足以讓數十萬政府工作人員在上月舉行罷工了。

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.


儘管整個促銷過程結束後價格實際上與原來完全相同，但價格變幅的平均值卻顯示價格出現上漲。當商品處於促銷時，你的購買量甚至購買額很可能會比商品處於原價時要多。畢竟，商家特價促銷的目的就在於此。這些情況給價格指數的編制者造成了麻煩。我們可用多種方法來解決這些麻煩。歐洲新的“消費價格調和指數”(HICP)通常比原先的零售價格指數(RPI)漲幅更小，其主要原因也在於此。英國財政大臣喬治•奧斯本(George Osborne)正打算將編制養老金指數所基的指數從RPI換為HICP，以節省巨額公共開支。

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.


在衡量股市基準和投資組合表現時，也會產生相同的問題。將50%的跌幅和100%的漲幅相平均，得到的結果是上漲了25%。但如果這種情況發生在你的股票上，那你就只是收回初始投資而已。這兩種計算方法得出的結果，都未必與投資者在現實中的感受相符。

I may have made another mistake in my earlier column. Since it appeared, details have been published of a study by researchers at O​​hio 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。



譯者/何黎