2011年4月4日星期一

情迷黑天鵝

勿以為談的是 Natalie Portman 飾演芭蕾舞蹈員的得獎電影《黑天鵝》;要說的其實是 Nassim Nicholas Taleb 的名著《黑天鵝》﹝The BLACK SWAN: The Impact of the Highly Improbable﹞。

很多人都讀過《黑天鵝》這本書,亦知道所謂的「黑天鵝」指什麼;但有幾多人留意到 Taleb 這本享負盛名之作,是向 Benoît Mandelbrot 致意的呢?書首乾乾淨淨的一頁白,印著:

To Benoît Mandelbrot,
a Greek among Romans


諗過理科的都不會對這個名字感到陌生吧! Benoît Mandelbrot ,世人尊稱他為分形幾何學之父, 對於其生平事跡,維基百科講得十分詳盡,在此不贅。唯一想指出的,是他發現金融市場中的價格變化並不依循常態分佈﹝ normal distribution ﹞,而是遵從 Lévy stable distributions ,價格的上落亦非隨機﹝ random ﹞,而是 fractional Brownian motion in multi-fractal time 。

可是他的理論備受冷落,眼見金融學日益興盛,但內容盡是建基於不盡不實的假設之上,架牀疊屋地用數學推導出來的「垃圾」,而推出這堆「垃圾」的學者居然一個又一個地獲頒諾貝爾經濟學獎,他的心情可想而知。

在 2007 年《黑天鵝》初版推出之際,金融海嘯尚未發生, Taleb 在書中已指出世人普遍以一堆猶如「垃圾」的金融理論來衡量風險,遲早出事。這本書風靡全球,除因為其涉及面既廣且深﹝不單限於經濟與金融,而及至哲學﹞,且有先見之明之外,作者對象牙塔學者不留情面的批評,言詞尖酸之程度,可謂一絕:

'The Nobel Committee could have tested the Sharpe and Markowitz models - they work like quack remedies sold on the Internet - but nobody in Stockholm seems to have thought of it. Nor did the committee come to us practitioners to ask us our opinions; instead it relied on an academic vetting process that, in some disciplines, can be corrupt all the way to the marrow. After that award I made a prediction: "In a world in which these two get the Nobel, anything can happen. Anyone can become president."'
    ── 節錄自《黑天鵝》第 17 章

《黑天鵝》這本書的意義在於警世,亦替 Benoît Mandelbrot 抱了個不平:

'In sum, four decades ago, Mandelbrot gave pearls to economists and résumé-building philistines, which they rejected because the ideas were too good for them. It was, as the saying goes, margaritas ante porcos, pearls before swine.'
    ── 節錄自《黑天鵝》第 16 章

可知古時偉大的數學家﹝尤指幾何學家﹞皆出於希臘;而羅馬人基本上是輕蔑數學的,縱然算術及概率理論﹝用於賭博?﹞是源自羅馬。Taleb 稱 Benoît Mandelbrot 為 'a Greek among Romans' 實在可圈可點。

'Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.'
    ── Benoît Mandelbrot (1924-2010)

參考資料
The BLACK SWAN: The Impact of the highly improbable, Nassim Nicholas Taleb
The (Mis)behavior of markets: A fractal view of risk, ruin & reward, Benoît Mandelbrot & Richard Hudson
How Fractals Can Explain What's Wrong with Wall Street, Benoît Mandelbrot, Feb 1999, Scientific American
The Drunkard's Walk: How randomness rules our lives, Leonard Mlodinow