巴菲特年紀大了說話不算話?

巴菲特曾說過衍生商品是金融巨大的致命武器，但他最近卻開始玩起選擇權和信用違約交換這些搞垮華爾街的遊戲！雷曼兄弟、 AIG、房利美&房地美 當初快垮時，信用違約交換利率差狂飆 、股票狂跌...仍折磨著投資人，難到老巴還想拿石頭砸自己的腳嗎？

老巴年紀大了，癡呆了，說話不算話了嗎？

其實不然，身為頭號粉絲的芒果，認為老巴並沒有違背自己的信仰！

老巴其實在賣保險！

伯客希哈薩威(Berkshire Hathaway)本身就是一個再保公司 + 收集保險與再保的母公司

它旗下的保險公司有： General Re、GEICO、Berkshire Bond Assurance

保險如何賺錢？

1. 保守的估價風險

2. 適當的分散風險

3. 避免降低保險金與同行惡性競爭

細節下次再與大家分享，我們先討論估價風險層面

保險金就是要超過出險的期望值！

也就是說，保險浮存金就是保險金扣掉未來出險期望值的現值的差。保險有賺錢就代表浮存金是正的，多餘的就是公司的剩餘價值。保險公司要賺錢，就要增加剩餘價值！

公司用浮存金，每年以複利投資， 如果與賠錢期望值相等，代表收支平衡，也就等於浮存金成本

浮存金 x(1+i)^N = 未來賠錢期望值

i=每年浮存金成本

N=從現在到賠錢尚有幾年

保險公司其實是希望以最低的成本向受保人貸款

當日子好的時候，還有可能變成"負的成本"

如果把浮存金成本當成向銀行貸款的利息，當你貸款的利息是負的，是不是等於銀行給你利息呢？保險盈餘高的時候，成本就有可能是負的了

注意：盈餘高不等於是大量賣保險，狂賣低估的保險，根本是自殺行為！

盈餘高其實是保險公司保守賣 + 留住客戶，使他們不跑到其它賤賣的保險公司罷了

回到正題，老巴賣選擇權跟保險有什麼關係？

他賭15~20年後，世界各地的指數不會低於現價，於是賣指數賣權和籃子賣權給避險公司的投資人/投機人。
沒有人可以預測未來，當 S&P 指數在 1400 的時候，他也賣了一堆選擇權，現在看來，他的舉動似乎很蠢，因為他在次級房貸爆發前賣的

在這個金融市場偏向全球化的世界，籃子選擇權是否真的能有效分散風險也是個有趣的問題

以他的角度來看，Black-Scholes 選擇權模型計算短期的選擇權價值是很準的，但計算10~20年，有可能得到很荒謬的價錢

其中很重要的原因是他對股票的波動率異常的敏感，離未來愈遠的波動率，預測愈不可信，因為市場上沒人在交易這種商品，會預測人更少

老巴覺得用保證金/浮動金投資10~20年可以輕易的超過浮動金成本，而那些盲目使用 Black-Scholes 模式的避險公司高估了保證金價格

他在 2008 年的股東信有提到，如果賣 100 年後才截止的選擇權，浮動金成本大約只有 0.7%

"你想用 0.7% 的利息，貸款一百年嗎？"

我必須承認，對於有金融公程背景的我，Black-Scholes 公式就像是聖經的經文一樣， 巴菲特和芒格(Munger) 這兩個老頭，還真是一套！他們可以成為億萬富翁絕對不是偶然！

對於他們來說，商學院教的東西很多都是垃圾 ，大學教授熱愛用簡單的公式來解釋現實， 但他們兩人卻覺得應該要以懷疑的眼光看待任何公式

如何增加 business sense 或者他們所謂的 common sense 才是更重要的課題(他們的 common sense 對我們來說是 uncommon sense)

以下是巴菲特2008年給股東信，關於選擇權的段落：

The Black-Scholes formula has approached the status of holy writ in finance, and we use it when valuing our equity put options for financial statement purposes. Key inputs to the calculation include a contract’s maturity and strike price, as well as the analyst’s expectations for volatility, interest rates and dividends.

If the formula is applied to extended time periods, however, it can produce absurd results. In fairness, Black and Scholes almost certainly understood this point well. But their devoted followers may be ignoring whatever caveats the two men attached when they first unveiled the formula.

It’s often useful in testing a theory to push it to extremes. So let’s postulate that we sell a 100- year $1 billion put option on the S&P 500 at a strike price of 903 (the index’s level on 12/31/08). Using the implied volatility assumption for long-dated contracts that we do, and combining that with appropriate interest and dividend assumptions, we would find the “proper” Black-Scholes premium for this contract to be $2.5 million.

To judge the rationality of that premium, we need to assess whether the S&P will be valued a century from now at less than today. Certainly the dollar will then be worth a small fraction of its present value (at only 2% inflation it will be worth roughly 14¢). So that will be a factor pushing the stated value of the index higher.

Far more important, however, is that one hundred years of retained earnings will hugely increase the value of most of the companies in the index. In the 20th Century, the Dow-Jones Industrial Average increased by about 175-fold, mainly because of this retained-earnings factor.

Considering everything, I believe the probability of a decline in the index over a one-hundred-year period to be far less than 1%. But let’s use that figure and also assume that the most likely decline – should one occur – is 50%. Under these assumptions, the mathematical expectation of loss on our contract would be $5 million ($1 billion X 1% X 50%).

But if we had received our theoretical premium of $2.5 million up front, we would have only had to invest it at 0.7% compounded annually to cover this loss expectancy. Everything earned above that would have been profit. Would you like to borrow money for 100 years at a 0.7% rate?

Let’s look at my example from a worst-case standpoint. Remember that 99% of the time we would pay nothing if my assumptions are correct. But even in the worst case among the remaining 1% of possibilities – that is, one assuming a total loss of $1 billion – our borrowing cost would come to only 6.2%. Clearly, either my assumptions are crazy or the formula is inappropriate.

The ridiculous premium that Black-Scholes dictates in my extreme example is caused by the inclusion of volatility in the formula and by the fact that volatility is determined by how much stocks have moved around in some past period of days, months or years. This metric is simply irrelevant in estimating the probabilityweighted range of values of American business 100 years from now. (Imagine, if you will, getting a quote every day on a farm from a manic-depressive neighbor and then using the volatility calculated from these changing quotes as an important ingredient in an equation that predicts a probability-weighted range of values for the farm

a century from now.)

Though historical volatility is a useful – but far from foolproof – concept in valuing short-term options, its utility diminishes rapidly as the duration of the option lengthens. In my opinion, the valuations that the Black-Scholes formula now place on our long-term put options overstate our liability, though the overstatement will diminish as the contracts approach maturity.

Even so, we will continue to use Black-Scholes when we are estimating our financial-statement

liability for long-term equity puts. The formula represents conventional wisdom and any substitute that I might offer would engender extreme skepticism. That would be perfectly understandable: CEOs who have concocted their own valuations for esoteric financial instruments have seldom erred on the side of conservatism. That club of optimists is one that Charlie and I have no desire to join.

想了解浮存金公式的朋友，請看這裡：

unpaid losses
+ loss adjustment expense
+ unearned premium
+ other policyholder liabilities
- premium balance receivable
- loss recoverable from reinsurance ceded
- deferred policy acquisition costs
- deferred charges on reinsurance
- related deferred income tax
= insurance float