巴菲特致股东的信（2008年）⑩衍生品

Derivatives

衍生品

Derivatives are dangerous. They have dramatically increased the leverage and risks in our financial system. They have made it almost impossible for investors to understand and analyze our largest commercial banks and investment banks. They allowed Fannie Mae and Freddie Mac to engage in massive misstatements of earnings for years. So indecipherable were Freddie and Fannie that their federal regulator, OFHEO, whose more than 100 employees had no job except the oversight of these two institutions, totally missed their cooking of the books.

衍生产品很危险。它们让我们金融系统中的杠杆率和风险都增加不少。它们让投资者们难以理解和分析我们最大的商业银行和投资银行。它们允许房利美和房地美多年来大规模虚报收益。房地美和房利美是如此令人困惑，以至于它们的联邦监管机构联邦住房企业监管办公室 OFHEO 的 100 多名职员除了监督这两家公司之外什么都不用做，即使如此还完全不得要领，彻底迷失在它们复杂的衍生品账目中。

Indeed, recent events demonstrate that certain big-name CEOs (or former CEOs) at major financial institutions were simply incapable of managing a business with a huge, complex book of derivatives. Include Charlie and me in this hapless group: When Berkshire purchased General Re in 1998, we knew we could not get our minds around its book of 23,218 derivatives contracts, made with 884 counterparties (many of which we had never heard of). So we decided to close up shop. Though we were under no pressure and were operating in benign markets as we exited, it took us five years and more than $400 million in losses to largely complete the task. Upon leaving, our feelings about the business mirrored a line in a country song: “I liked you better before I got to know you so well.”

实际上，最近的一些事件表明，那些大型金融机构的 CEO 或者前 CEO 们，根本没有能力去管理一个如此复杂和庞大的衍生品交易。查理和我也在这个倒霉鬼名单中，当伯克希尔在 1998 年收购通用再保险时，我们知道我们搞不定它同 884 个交易对手达成的 23218 份衍生品合约(其中许多我们从未听说过)。因此我们决定关门大吉。尽管当我们选择退出时没有任何市场压力，但我们花了 5 年时间并损失了 4 亿美元才大致完成这项任务。离别之际，我们对这门生意的感觉正如一句乡村民谣歌词所唱："在我还不了解你之前，我更喜欢你一些。"

Improved “transparency” – a favorite remedy of politicians, commentators and financial regulators for averting future train wrecks – won’t cure the problems that derivatives pose. I know of no reporting mechanism that would come close to describing and measuring the risks in a huge and complex portfolio of derivatives. Auditors can’t audit these contracts, and regulators can’t regulate them. When I read the pages of “disclosure” in 10-Ks of companies that are entangled with these instruments, all I end up knowing is that I don’t know what is going on in their portfolios (and then I reach for some aspirin).

更高的"透明度"——政治家、评论员和金融监管机构最喜欢用这个良方来避免将来出现严重问题——对衍生产品导致的问题也无能为力。据我所知，没有一种报告机制能够接近于描述和衡量庞大复杂的衍生品组合的风险。审计人员无法审计这些合约，监管机构也无法进行监管。当我读到使用这类衍生工具的公司 10-K 年报中"事项披露"部分时，我最后只知道，我对这些公司的投资组合状况一无所知(然后还得吃几片阿司匹林缓解头痛)。

For a case study on regulatory effectiveness, let’s look harder at the Freddie and Fannie example. These giant institutions were created by Congress, which retained control over them, dictating what they could and could not do. To aid its oversight, Congress created OFHEO in 1992, admonishing it to make sure the two behemoths were behaving themselves. With that move, Fannie and Freddie became the most intensely-regulated companies of which I am aware, as measured by manpower assigned to the task.

对于监管有效性案例的研究是有必要的，让我们再深入看看房地美和房利美的例子。这两个庞大的机构由国会创立，并且由他们控制，指示他们什么可以做，什么不可以做。为了帮助监管，国会在 1992 年成立了 OFHEO,告诫它要保证这两个巨大的机构行为得当。按照分配到这个任务的人力衡量，这个举措使房利美和房地美成为据我所知监管最严密的公司。

On June 15, 2003, OFHEO (whose annual reports are available on the Internet) sent its 2002 report to Congress – specifically to its four bosses in the Senate and House, among them none other than Messrs. Sarbanes and Oxley. The report’s 127 pages included a self-congratulatory cover-line: “Celebrating 10 Years of Excellence.” The transmittal letter and report were delivered nine days after the CEO and CFO of Freddie had resigned in disgrace and the COO had been fired. No mention of their departures was made in the letter, even while the report concluded, as it always did, that “Both Enterprises were financially sound and well managed.”

2003 年 6 月 15 日，OFHEO 递交 2002 年的报告给国会(其年报可在网上获得)，尤其给参众两院的四个老板，其中包括萨班斯和奥克斯利先生(Messrs.Sarbanes、Oxley)。长达 127 页的报告包括一个自我庆祝的标题："庆祝卓越的 10 年"。房地美的 CEO 和 CFO 在丑闻后辞职以及 COO 被解雇后的九天，转送函和报告被递交。报告的总结跟以往一样："这两家企业的财务状况良好，并且管理得很好"，信中并未提及他们的离开。

In truth, both enterprises had engaged in massive accounting shenanigans for some time. Finally, in 2006, OFHEO issued a 340-page scathing chronicle of the sins of Fannie that, more or less, blamed the fiasco on every party but – you guessed it – Congress and OFHEO.

其实，这两家企业都有一段时间涉及大规模的会计欺骗行为。最后，在 2006 年，OFHEO 发表了长达 340 页的记录，严厉揭露了房利美的罪状，并或多或少地指责了每个团体的失败，当然，你可以猜到，除了国会和 OFHEO。

The Bear Stearns collapse highlights the counterparty problem embedded in derivatives transactions, a time bomb I first discussed in Berkshire’s 2002 report. On April 3, 2008, Tim Geithner, then the able president of the New York Fed, explained the need for a rescue: “The sudden discovery by Bear’s derivative counterparties that important financial positions they had put in place to protect themselves from financial risk were no longer operative would have triggered substantial further dislocation in markets. This would have precipitated a rush by Bear’s counterparties to liquidate the collateral they held against those positions and to attempt to replicate those positions in already very fragile markets.” This is Fedspeak for “We stepped in to avoid a financial chain reaction of unpredictable magnitude.” In my opinion, the Fed was right to do so.

贝尔斯登(Bear Stearns)的破产突显了衍生品交易中对手方问题，这正是我在 2002 年伯克希尔公司的报告中首次提到的定时炸弹。2008 年 4 月 3 日，时任纽约联储主席的 TimGeithner 解释了救援的必要性："贝尔斯登衍生品交易对手突然发现，他们为保护自己免受金融风险的重要金融头寸已经不再有效，这将促使贝尔斯登的交易对手急于清算他们之前持有的抵押品，并且试图在本已脆弱的市场中复制那些投资仓位，这将引发市场的进一步混乱。"美联储发言说："我们介入是未来阻止不可预见的重大金融连锁反应"。我认为，美联储这样做是对的。

A normal stock or bond trade is completed in a few days with one party getting its cash, the other its securities. Counterparty risk therefore quickly disappears, which means credit problems can’t accumulate. This rapid settlement process is key to maintaining the integrity of markets. That, in fact, is a reason for NYSE and NASDAQ shortening the settlement period from five days to three days in 1995.

正常的股票债券交易通常在几天内完成，一方获得现金，一方获得证券。交易对方的违约风险很快消失，这意味着信用问题不会积累。这种快速的结算过程是保持市场完整性的关键。事实上，这就是纽约交易市场和纳斯达克交易市场在 1995 年把结算周期从 5 天缩短到 3 天的原因。

Derivatives contracts, in contrast, often go unsettled for years, or even decades, with counterparties building up huge claims against each other. “Paper” assets and liabilities – often hard to quantify – become important parts of financial statements though these items will not be validated for many years. Additionally, a frightening web of mutual dependence develops among huge financial institutions. Receivables and payables by the billions become concentrated in the hands of a few large dealers who are apt to be highly-leveraged in other ways as well. Participants seeking to dodge troubles face the same problem as someone seeking to avoid venereal disease: It’s not just whom you sleep with, but also whom they are sleeping with.

相比之下，衍生品合同往往数年甚至数十年都不结算，交易对手彼此之间积累的巨额的债权。难以量化的"纸面"资产和负债构成为财务报表的重要组成部分，尽管这些款项在多年内都不会得到验证。另外，大型金融机构之间形成了一个可怕的、互相依赖的金融网络。数十亿美元的应收款和应付款都集中在少数几个大型交易商手中，这些交易商在其它方面也往往高度杠杆化。逃避麻烦的参与者其实和躲避性病的人面临相同的问题：重要的不止是你和谁睡，还有他们和谁睡。

Sleeping around, to continue our metaphor, can actually be useful for large derivatives dealers because it assures them government aid if trouble hits. In other words, only companies having problems that can infect the entire neighborhood – I won’t mention names – are certain to become a concern of the state (an outcome, I’m sad to say, that is proper). From this irritating reality comes The First Law of Corporate Survival for ambitious CEOs who pile on leverage and run large and unfathomable derivatives books: Modest incompetence simply won’t do; it’s mindboggling screw-ups that are required.

继续借用我们的比喻，和周围所有人发生关系，其实这对大型的衍生品交易者来说是有用的，因为它保证了如果他们遇到麻烦时，他们会得到政府帮助。换句话说，只有那些可能感染整个系统的问题公司(当然我不会指名道姓)，一定会成为政府的关注对象(我很遗憾地说，这是一个恰当的结果)。这个恼人的事实，缔造了企业生存的第一法例，这一法则适用于那些野心勃勃的 CEO，他们喜欢利用杠杆，经营着大量深不可测的衍生品账簿，一般无能根本不会这样做，他们需要的是令人难以置信无能。

Considering the ruin I’ve pictured, you may wonder why Berkshire is a party to 251 derivatives contracts (other than those used for operational purposes at MidAmerican and the few left over at Gen Re). The answer is simple: I believe each contract we own was mispriced at inception, sometimes dramatically so. I both initiated these positions and monitor them, a set of responsibilities consistent with my belief that the CEO of any large financial organization must be the Chief Risk Officer as well. If we lose money on our derivatives, it will be my fault.

考虑我描述的毁灭性画面，你也许会想知道，为什么伯克希尔公司也是 251 个衍生品合约的一方(除了那些在中美能源和通用再保险剩下的几份出于运营目的的合同)。答案很简单：我相信每份合约的定价在我们拥有时都是不合理的，有时还是非常不合理。我创立和监督这些合约，这一系列的职责也与我的信念一致，即任何大型金融机构的 CEO 也必须同样是首席风险执行官。如果我们在衍生品中有损失，那就是我的错。

Our derivatives dealings require our counterparties to make payments to us when contracts are initiated. Berkshire therefore always holds the money, which leaves us assuming no meaningful counterparty risk. As of yearend, the payments made to us less losses we have paid – our derivatives “float,” so to speak – totaled $8.1 billion. This float is similar to insurance float: If we break even on an underlying transaction, we will have enjoyed the use of free money for a long time. Our expectation, though it is far from a sure thing, is that we will do better than break even and that the substantial investment income we earn on the funds will be frosting on the cake.

我们的衍生品交易要求我们的交易对手在合约开始时就向我们付款。因此钱一直在伯克希尔手里，这让我们其实没有任何违约风险。年末，我们收取的资金减去我们付出的损失——称之为我们的衍生品"浮存金"，共计 81亿美元。这些浮存金和保险浮存金类似：如果我们在合约交易中不盈不亏，我们将长期享受免费使用的资金。虽然不确定，但我们的期望会比不盈不亏做得更好，因此，从浮存金中赚得的大量投资收益将是锦上添花。

Only a small percentage of our contracts call for any posting of collateral when the market moves against us. Even under the chaotic conditions existing in last year’s fourth quarter, we had to post less than 1% of our securities portfolio. (When we post collateral, we deposit it with third parties, meanwhile retaining the investment earnings on the deposited securities.) In our 2002 annual report, we warned of the lethal threat that posting requirements create, real-life illustrations of which we witnessed last year at a variety of financial institutions (and, for that matter, at Constellation Energy, which was within hours of bankruptcy when MidAmerican arrived to effect a rescue).

在市场发展对我们不利时，有一小部分合约要求我们放置抵押品。即使在去年第四季度的混乱情况中，我们也只是提供了不到 1%的证券组合作为抵押品(当我们交出抵押品时，我们把它存放在第三方，同时保留所存证券的投资收益)。在 2002 年年度报告中，我们提到了放置抵押品要求引起的致命威胁，去年我们亲眼目睹各种各样金融机构的剧变就是活生生的实例(因为这个问题，当中美能源公司赶到进行救援时，星座能源公司在短短的几个小时内宣告破产)。

Our contracts fall into four major categories. With apologies to those who are not fascinated by financial instruments, I will explain them in excruciating detail.

我们的合约有四大类。对金融工具不感兴趣的人我很抱歉，因为我将很详细的解释它们。

•We have added modestly to the “equity put” portfolio I described in last year’s report. Some of our contracts come due in 15 years, others in 20. We must make a payment to our counterparty at maturity if the reference index to which the put is tied is then below what it was at the inception of the contract. Neither party can elect to settle early; it’s only the price on the final day that counts.

1，我在去年报告中描述的"股票看跌"投资组合适度增加了。我们的一些合约将在 15 年内到期，其他将在 20年内到期。如果与看跌期权合约挂钩的参考指数，低于合约签订时的价格，我们将要在到期时给交易对方支付款项。任何一方都不能选择提前结算，重要的只是最后那一天的价格。

To illustrate, we might sell a $1 billion 15-year put contract on the S&P 500 when that index is at, say, 1300. If the index is at 1170 – down 10% – on the day of maturity, we would pay $100 million. If it is above 1300, we owe nothing. For us to lose $1 billion, the index would have to go to zero. In the meantime, the sale of the put would have delivered us a premium – perhaps $100 million to $150 million – that we would be free to invest as we wish.

举例来说，我们在标普 500 指数在 1300 点时卖出一个价值 10 亿美元、期限为 15 年的指数看跌期权合约。如果指数在到期日下降了 10%到 1170 点，我们将要支付 1 亿美元。如果指数高于 1300 点，我们什么都不欠。如果我们全部损失掉 10 亿美元，指数必须降到 0。与此同时，卖出那份合约将会我们带来一笔收入，大概 1 亿到1.5 亿美元，如果我们想的话，我们可以自由地投资。

Our put contracts total $37.1 billion (at current exchange rates) and are spread among four major indices: the S&P 500 in the U.S., the FTSE 100 in the U.K., the Euro Stoxx 50 in Europe, and the Nikkei 225 in Japan. Our first contract comes due on September 9, 2019 and our last on January 24, 2028. We have received premiums of $4.9 billion, money we have invested. We, meanwhile, have paid nothing, since all expiration dates are far in the future. Nonetheless, we have used Black-Scholes valuation methods to record a yearend liability of $10 billion, an amount that will change on every reporting date. The two financial items – this estimated loss of $10 billion minus the $4.9 billion in premiums we have received – means that we have so far reported a mark-to-market loss of $5.1 billion from these contracts.

我们的看跌合约总共价值 371 亿美元(按照当时汇率计算)，分布在四大指数中：美国标普 500 指数，英国的富时 100 指数，欧盟 50 指数和日本的日经 225 指数。我们第一份合约在 2019 年 9 月 9 日到期，最后一份在2028 年 1 月 24 日到期。我们已经获得了 49 亿美元的保险费，这些钱我们已经用来投资了。同时，我们不用支付任何东西，因为所有的到期日都在很遥远的未来。尽管如此，我们采用了 BlackScholes 计价方法去记录年末的100 亿美元债务，这个数字在每个报告日都会变动。用预计损失 100 亿美元减去收取的 49 亿保险费，意味着到目前为止，以市值计算，我们的合约带来了 51 亿美元的损失。

We endorse mark-to-market accounting. I will explain later, however, why I believe the Black-Scholes formula, even though it is the standard for establishing the dollar liability for options, produces strange results when the long-term variety are being valued.

我们支持用市值计价的会计方法。稍后我会解释为什么我觉得 BlackScholes 公式在长期品种被估价时会生成奇怪的结果，即使它是期权计价的标准。

One point about our contracts that is sometimes not understood: For us to lose the full $37.1 billion we have at risk, all stocks in all four indices would have to go to zero on their various termination dates. If, however – as an example – all indices fell 25% from their value at the inception of each contract, and foreign-exchange rates remained as they are today, we would owe about $9 billion, payable between 2019 and 2028. Between the inception of the contract and those dates, we would have held the $4.9 billion premium and earned investment income on it.

我们的合约中有一点有时候不被理解：如果我们要损失掉所有的 371 亿美元，所有四个指数中的所有股票都必须在到期日跌到零。比如，如果所有指数都比合约生成时下降 25%，汇率保持今天的水平不变，我们在 2019到 2028 年将会产生 90 亿元的应付款。在合约生成和到期日间，我们将持有 49 亿元的保费并赚取投资收益。

•The second category we described in last year’s report concerns derivatives requiring us to pay when credit losses occur at companies that are included in various high-yield indices. Our standard contract covers a five-year period and involves 100 companies. We modestly expanded our position last year in this category. But, of course, the contracts on the books at the end of 2007 moved one year closer to their maturity. Overall, our contracts now have an average life of 21⁄3 years, with the first expiration due to occur on September 20, 2009 and the last on December 20, 2013.

2，在去年报告中提到的第二类衍生品，要求我们当各类高收益指数中的公司发生信用损失时，我们要支付损失。我们的标准合约覆盖 5 年期，涉及 100 家公司。我们去年适当增加了这类衍生品的投资。当然，2007 年末账面上的合约离到期日又近了一年。总之，我们的合约平均寿命约是 2.3 年，第一个到期日是 2009 年 9 月 20日，最后一个是 2013 年 12 月 20 日。

By yearend we had received premiums of $3.4 billion on these contracts and paid losses of $542 million. Using mark-to-market principles, we also set up a liability for future losses that at yearend totaled $3.0 billion. Thus we had to that point recorded a loss of about $100 million, derived from our $3.5 billion total in paid and estimated future losses minus the $3.4 billion of premiums we received. In our quarterly reports, however, the amount of gain or loss has swung wildly from a profit of $327 million in the second quarter of 2008 to a loss of $693 million in the fourth quarter of 2008.

年末我们从这些合约收到了 34 亿美元的保费，并且支付了 5.42 亿美元的损失。按以市值计算的原则，我们建立了未来损失的负债，年末一共是 30 亿美元。支付和预计损失一共 35 亿美元，减去收到的 34 亿美元保费，因此我们一共记录的损失是 1 亿美元。然而，在我们的季度报表中，收益和损失变化很大，从 2008 年第二季度的 3.27 亿美元利润到 2008 年第四季度的 6.98 美元损失。

Surprisingly, we made payments on these contracts of only $97 million last year, far below the estimate I used when I decided to enter into them. This year, however, losses have accelerated sharply with the mushrooming of large bankruptcies. In last year’s letter, I told you I expected these contracts to show a profit at expiration. Now, with the recession deepening at a rapid rate, the possibility of an eventual loss has increased. Whatever the result, I will keep you posted.

令人惊讶是，去年，去年我们为这些合约只支付了 9700 万美元，远远低于比我们签订合约时的估计数。然而今年随着大规模破产的激增，损失将会大大增加。在去年的信中，我告诉你我期望这些合约在到期时会产生利润。现在，随着经济衰退加速，最终损失的可能性增大。无论结果如何，我都会随时告诉你。

•In 2008 we began to write “credit default swaps” on individual companies. This is simply credit insurance, similar to what we write in BHAC, except that here we bear the credit risk of corporations rather than of tax-exempt issuers.

3，2008 年，我们开始对私人公司出售"信用违约掉期"业务。这只是一种信用保险，和我们在 BHAC 出售的类似，只不过我们在这里承保的是公司的信用风险，而不是免税债券发行人的信用风险。

If, say, the XYZ company goes bankrupt, and we have written a $100 million contract, we are obligated to pay an amount that reflects the shrinkage in value of a comparable amount of XYZ’s debt. (If, for example, the company’s bonds are selling for 30 after default, we would owe $70 million.) For the typical contract, we receive quarterly payments for five years, after which our insurance expires.

比如，如果 XYZ 公司破产了，而我们签订了一张价值 1 亿美元的合约，我们有义务支付 XYZ 债务的缩水部分(例如，如果公司的债券在违约后价值 3 千万，我们就欠 7 千万美元)。典型的合约是，我们 5 年里每季度收到对方支付的保费，直到我们的保险到期。

At yearend we had written $4 billion of contracts covering 42 corporations, for which we receive annual premiums of $93 million. This is the only derivatives business we write that has any counterparty risk; the party that buys the contract from us must be good for the quarterly premiums it will owe us over the five years. We are unlikely to expand this business to any extent because most buyers of this protection now insist that the seller post collateral, and we will not enter into such an arrangement.

年末，我们一共出售了 40 亿美元的合约，涉及 42 个公司，每年保费约 9300 万美元。这是我们承保的唯一具有违约风险的衍生品合约。合约的买方必须在未来 5 年内有能力按季度支付保费。我们将不会扩大这项业务，因为这种保险大多数买方现在坚持要求卖方提供抵押品，而我们不会参与这样的交易。

•At the request of our customers, we write a few tax-exempt bond insurance contracts that are similar to those written at BHAC, but that are structured as derivatives. The only meaningful difference between the two contracts is that mark-to-market accounting is required for derivatives whereas standard accrual accounting is required at BHAC.

4，在客户的要求下，我们承保了一些免税债券保险合约，与 BHAC 承保的类似，但结构是衍生品。两份合约唯一真正的不同是，衍生品要求是以市值计价，而 BHAC 要求用标准权责发生制会计规则。

But this difference can produce some strange results. The bonds covered – in effect, insured – by these derivatives are largely general obligations of states, and we feel good about them. At yearend, however, mark-to-market accounting required us to record a loss of $631 million on these derivatives contracts. Had we instead insured the same bonds at the same price in BHAC, and used the accrual accounting required at insurance companies, we would have recorded a small profit for the year. The two methods by which we insure the bonds will eventually produce the same accounting result. In the short term, however, the variance in reported profits can be substantial.

但这些差异会产生奇怪的结果。实际上，这些衍生品保险的债券多数是国家的义务，我们对此感觉良好。但是在年末，以市值计价的会计原则要求我们记录 6.31 亿美元的衍生品合约损失。如果我们在 BHAC 以同样的价格为这些债券承保，运用保险公司要求的会计规则，我们今年将会产生少量利润。我们承保债券的这两种方法最终会产生一样的会计结果。但是短期内，报告的利润差异会很大。

We have told you before that our derivative contracts, subject as they are to mark-to-market accounting, will produce wild swings in the earnings we report. The ups and downs neither cheer nor bother Charlie and me. Indeed, the “downs” can be helpful in that they give us an opportunity to expand a position on favorable terms. I hope this explanation of our dealings will lead you to think similarly.

之前我已经告诉你，运用市值计价会计原则的衍生品合约，在报表中利润变化会很大。这种波动都不会使我和查理欢呼或者烦恼。事实上，"下降"可以非常有助于我们以有利的条款扩大我们的机会。希望我们对交易的解释也让你有同样的想法。

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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.

Black-Scholes 期权定价模型在金融界有着接近神圣的地位，我们用它在报表中定价我们的股票卖出期权。计算需要的关键数据包括合约的期限、行权价格、和分析者对波动性、利率和股息的预测。

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.

如果在较长的时间期限内运用这个公式，将会产生荒谬的结果。说实话，Black 和 Scholes 一定对这一点很明白。但他们的忠实的追随者可能忽略了两位先生第一次公布这个公式时附加的任何警告。

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.

用一个极端的情形测试一个理论通常非常有用。因此，假设我们出售了一张期限为 100 年，价值 10 亿的标普 500 指数看跌期权，执行价格为 903(2008 年 12 月 31 日的水平)。使用我们长期合约的隐含波动率假设，加上合适的利率和分红假设，我们发现，这份合约正确的 Black-Scholes 价格为 250 万美元。

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.

要评判这个价格的合理性，我们必须估计标普指数一个世纪后会不会比今天低。当然，美元到时候会贬值(按2%通货膨胀率算，到时候 1 美元价值大概 14 美分)。因此，这将是一个推动指数上升的因素。然而更重要的是，100 年的保留收益将会大大的增加指数中大多数公司的价值。在 20 世纪，道琼斯平均工业指数上升了大概 175倍(年化 5.3%)，主要是因为留存收益这一因素。

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%).

考虑到所有因素，我相信指数在 100 年后下跌的可能性少于 1%。但让我们就用这个数字，并且假设如果真的发生，最有可能的是下跌 50%。在这个假设下，我们的合约计算出来的预计损失是 500 万美元(10 亿 * 1% *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?

但如果我们提前预收了 250 万美元的理论保费，我们只需要以每年 0.7%的复合收益率投资，就可以弥补这个预期损失，超出 0.7%的部分都是利润。那么你愿意以 0.7%的利率贷款 100 年吗？

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.

让我们用最坏的角度来看我这个例子。记住，如果我们的假设是对的，有 99%的概率我们不用支付任何东西。但即使在最坏的那 1%的可能性里，假设损失 10 亿美元，我们的贷款成本也只是 6.2%。显然，要么我这两个假设都是荒唐的，要么这个公式是不正确的。

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 probability-weighted 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.)

在我这个极端的例子中，Black-Scholes 公式计算出来的荒谬的结果，是因为在公式中包括了波动性，而波动性又是由在过去的日，月，年终有多少股票在波动的结果决定的。在预计 100 年后美国商业价值的概率加权范围时，这一指标无关紧要。(想象一下，如果你愿意，每天从一个患有狂郁症的邻居哪里得到一个农场的报价，然后用这些价格计算出来的波动率，作为这个公司里重要因素来预测农场在 100 年后的价值可能范围)。

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.

虽然历史的波动率是一个评定短期期权的有用概念，但却不够完善，随着期权期限的延长，它的有效性就会迅速降低。在我看来，Black-Scholes 公式用在我们的长期看跌期权时，其计算高估了我们的负债，尽管这种高估会随着合约到期而逐渐减少。

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.

即使这样，在财务报告中，我们会继续使用 Black-Scholes 公式去估算我们的长期股票看跌期权。这个公式代表了传统的智慧，任何我可能提出的替代品都会引起极端的质疑。这个很好理解：方面，那些使用深奥的金融工具编造自己估值的 CEO，很少站到保守主义一边。我和查理都没有欲望加入乐观主义的行列。