2008/10/05
機會率
假設有三位政治專家，預計美國大選結果，第一位說奧巴馬贏的機會是三成，第二位說五成，第三位說九成九。再假設結果，奧巴馬真的勝出。誰測得最準呢? 你可能會說第三位，但我可以說答案有好多個。可以說，他們全部測對，第一位說三成，可能機會率真的是三成，而奧巴馬好彩。機會率也可能較接近五成或九成九，總之，只要2008年美國大選不會重復進行，奧巴馬贏這個事實，沒有告訴我們任何有關機會率的資料。同樣，如果有人告訴你中六合彩的機會是六千萬分之一，你買了，結果中了頭獎，你要多謝那個人否? 應該無需要，因為他沒有誇大機會率誘你買票，他說的是事實，機會是真的六千萬分之一。你中獎是好彩。事後看來，機會才變成百分百，唔買就笨。究竟銀行職員說迷你債券風險低，算不算誤導呢? 我認為不可能用結果去衡量。
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你對機會率的解讀是傳統的頻率學派解讀法。（Frequency probability）另一個學派叫做貝葉斯學派。...um... 本 blog 有一篇寫有關的東西。
http://blog.tiney.com/?p=611
現在的人見到迷債爆煲再將「低風險」改為「高風險」，是很貝葉斯的。我反而想知道，銀行職員在解釋何謂低風險時，有沒有寫明實在是有甚麼風險。（例如發債機構倒閉。）
chainsaw riot,有趣，不過老實講，你的手袋例子，正說明貝葉斯學派的缺點。那位小姐，聽到個「假」字，就睜大眼，你主觀上認為這個資訊增加了「她的袋是假的機會」。但我又可以主觀地認為，她的反應顯示她付的真金白錢買來的真貨，竟然看似假貨，大為震驚。於是，她的反應令我將「她的袋是假的機會」減低。於是呢種所謂主觀的機會率，一點也不科學喎。
而且，用於我的例子，還可能誤導。例如，我中了六合彩，跟據貝葉斯的事後機會率，我會推算我因為今次中頭獎，下次中獎的機會會增加，對，主觀上，我一定會有提升信心的感覺。不過，事實並非如此。
還有，貝葉斯亦無助分析一次性的歷史事件，例如美國大選和金融海嘯，的機會率。因為根據冇可能做sampling。
唔知我有冇理解錯呢?
銀行從業員最起碼都會同你講句投資產品價格可升何跌．．．風險千百幾樣，legal、operational、settlement、credit、market．．．sales肯講、保安肯唔閂門住，個客都應該無耐性聽。
何況，「發債機構倒閉」即使係一個風險，顧客都會問番句「咁機會大唔大呀」，sales實會話「咁又好少可既，呢批銀行都係國際知名既機構呀」。又或者，個客唔駛sales講，都會說服自己「黐線架咩，美國第五大投資銀行，邊會霖丫」。
今天很多公公婆婆(不是佛利民那樣受過教育的人)會去立法會. 你去向他們解釋這些或然率理論吧, 記得拍下過程放上YOUTUBE, 保證有幾十萬點擊率. 如果他們聽了茶怪賜教, 如夢初醒, 放棄追究, 誠最成功的持續進修例子呢.
如果好似你咁講，好易解決，凡事年紀到達到你認為是「公公婆婆」的水平，或「不是佛利民那樣受過教育的人」，一律不准作任何投資。上youtube宣傳的應該是你喎!要持續跟你進修果個應該係我喎!
a couple things
1) mark six.
prob win = 1/60M, you won by luck.
if not by luck, you would have spent 60M x$5 first before you break even.
(in really you only get 25M because of tax, jockey club opex, and charity)
2) you were trying to use the Schroedinger cat analogy but it does not work in this case. there is rigorous maths (conditional probability, etc) saying that since obama 'won', the 3rd guy is more trustworthy.
i.e. one can calculate the 'reliability'(or % he got it right) based on the 3 persons' track record.
3) yes, the bank staff misled you. simply because even he himself does not how much the risk was behind it. he was just playing by the book given to him by the bank manager, who got the same marketing material from lehman.
you are right that results should be dictate right or wrong, it could be luck. but the fact is, he misled you even if you got great return on those lehman "bonds".
you are right that results alone should NOT dictate right or wrong, it could be luck. but the fact is, he misled you even if you got great return on those lehman "bonds"
btw, as i understand it, the "bonds" could be worthless even if Lehman is sound and healthy. the "bonds" were backed up by the MBS/derivatives via Lehman, not by Lehman's assets.
Thanks for your comment, Sin Bun. And thanks for mentioning the Schroedinger cat analogy, which must be very famous. i am just too innocent to have heard about it. Would you please tell me what it is about and how it does relate to my argument? i checked wikipedia, but it was too lengthy...thanks.
thanks for clarifying other points.
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