Warren Buffett on 'dangerous' derivatives
Derivatives
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.
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.”
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).
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.
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.”
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.
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.
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.
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.
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.
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.
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.
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).
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.
• 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.
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.
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.
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.
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.
• 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.
By year end 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.
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.
• 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. 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.
At year end 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.
• 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.
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 year end, 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.
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.
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.
Extracted from http://www.berkshirehathaway.com/letters/2008ltr.pdf
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.
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.”
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).
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.
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.”
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.
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.
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.
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.
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.
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.
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.
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).
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.
• 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.
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.
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.
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.
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.
• 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.
By year end 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.
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.
• 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. 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.
At year end 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.
• 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.
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 year end, 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.
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.
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.
Extracted from http://www.berkshirehathaway.com/letters/2008ltr.pdf
posted by Silabilm at 2:21 PM
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