Warren Buffett famously stated in his 2002 letter to shareholders “Charlie and I are of one mind in how we feel about derivatives and the trading activities that go with them: We view them as time bombs, both for the parties that deal in them and the economic system.”

The growth over the last 15 years in the derivatives market has been startling, with most retail investors now indulging in directional bets (calls and puts) before earnings as well as volatility selling strategies. Selling volatility was what led to the downfall of LTCM in 1998 and requires knowing two key variables, the price of the underlying asset and the future expected volatility of the asset until expiration (implied volatility). Implied volatility is a more important variable in my opinion for pricing options. (A general heuristic is the lower the IV, the cheaper the option; most assets' price and volatility have a negative correlation.)

I will not get into much detail here about the BSM or option pricing, but knowing the limitations of the BSM are important. The major limitation being the length to expiration date (the further the expiration, the less valid the BS formula).

Black-Scholes Formula

Buffett wrote the following to his partners regarding the BSM (part of multiple excerpts regarding derivatives over the years).

“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 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.)

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.Â

Berkshire Derivative Book

As Buffett noted, the derivative liabilities are both overstated and advantageous to exploit provided the expected probability of loss is outweighed by the future value of the premiums received. Berkshire (BRK.A, Financial)(BRK.B, Financial) is no foreigner to black ink from derivatives and made over $1.4 billion in 2012 fourth quarter, from a derivative book with a notional value of approximately $37 billion.

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The difference between Buffett and retail investors is Buffett understands the contracts that he has exposure to, how they were/are mis-priced, the counter party risk associated with the issue and the time value of the premiums received. He essentially uses the method of selling index puts as a cheap way to finance investments. It is also fair to say that not all retail investors are able to negotiate the terms of the contract Buffett has recived regarding their derivative book.

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“We have long invested in derivatives contracts that Charlie and I think are mispriced, just as we try to invest in mispriced stocks and bonds. Indeed, we first reported to you that we held such contracts in early 1998. The dangers that derivatives pose for both participants and society – dangers of which we’ve long warned, and that can be dynamite – arise when these contracts lead to leverage and/or counterparty risk that is extreme. At Berkshire nothing like that has occurred – nor will it. It’s my job to keep Berkshire far away from such problems. Charlie and I believe that a CEO must not delegate risk control. It’s simply too important. At Berkshire, I both initiate and monitor every derivatives contract on our books, with the exception of operations-related contracts at a few of our subsidiaries, such as MidAmerican, and the minor runoff contracts at General Re. If Berkshire ever gets in trouble, it will be my fault. It will not be because of misjudgments made by a Risk Committee or Chief Risk Officer.”

“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.”

OTC Derivatives Growth

It is possible for derivatives to be a positive sum exchange provided parties involved have an opposite interest, one wanting to unload risk while the other is willing to take it on, an example being grain producers and grain users. A grain grower wants to hedge against the uncertainty associated with future prices falling (effecting  future cash flows). The wheat producer will sell a forward contract legally binding the company to sell/deliver the wheat at a specific price, up until a specific time, if exercised. The buyer of the contract, the grain user, will hedge against rising prices (the opposite of what the producer wants) allowing them the option to purchase a certain quantity of wheat, at a certain price, until a specified date. Both parties win as “risk” is diminished/transferred. Unfortunately the booming growth in the derivatives market cannot be attributed to positive sum exchanges, but rather, negative-sum speculation (after commission, fees and taxes) driven by interest rate swaps, followed by CDSs and an expansion/introduction of individual equity options, weekly options and mini-options (which have not been a hit).

General Re Derivatives Book

The lack of liquidity of these non-transparent contracts is only apparent when crisis strikes or as a liquidation of derivatives takes place, as Berkshire learned with General Re.Â

“Long ago, Mark Twain said: “A man who tries to carry a cat home by its tail will learn a lesson that can be learned in no other way.” If Twain were around now, he might try winding up a derivatives business. After a few days, he would opt for cats.

We lost $104 million pre-tax last year in our continuing attempt to exit Gen Re’s derivative operation. Our aggregate losses since we began this endeavor total $404 million.

Originally we had 23,218 contracts outstanding [made with 884 counter parties]. By the start of 2005 we were down to 2,890. You might expect that our losses would have been stemmed by this point, but the blood has kept flowing. Reducing our inventory to 741 contracts last year cost us the $104 million mentioned above.

Remember that the rationale for establishing this unit in 1990 was Gen Re’s wish to meet the needs of insurance clients. Yet one of the contracts we liquidated in 2005 had a term of 100 years! It’s difficult to imagine what “need” such a contract could fulfill except, perhaps, the need of a compensation- conscious trader to have a long-dated contract on his books. Long contracts, or alternatively those with multiple variables, are the most difficult to mark to market (the standard procedure used in accounting for derivatives) and provide the most opportunity for “imagination” when traders are estimating their value. Small wonder that traders promote them.

A business in which huge amounts of compensation flow from assumed numbers is obviously fraught with danger. When two traders execute a transaction that has several, sometimes esoteric, variables and a far-off settlement date, their respective firms must subsequently value these contracts whenever they calculate their earnings. A given contract may be valued at one price by Firm A and at another by Firm B. You can bet that the valuation differences – and I’m personally familiar with several that were huge – tend to be tilted in a direction favoring higher earnings at each firm. It’s a strange world in which two parties can carry out a paper transaction that each can promptly report as profitable.

I dwell on our experience in derivatives each year for two reasons. One is personal and unpleasant. The hard fact is that I have cost you a lot of money by not moving immediately to close down Gen Re’s trading operation. Both Charlie and I knew at the time of the Gen Re purchase that it was a problem and told its management that we wanted to exit the business. It was my responsibility to make sure that happened. Rather than address the situation head on, however, I wasted several years while we attempted to sell the operation. That was a doomed endeavor because no realistic solution could have extricated us from the maze of liabilities that was going to exist for decades. Our obligations were particularly worrisome because their potential to explode could not be measured. Moreover, if severe trouble occurred, we knew it was likely to correlate with problems elsewhere in financial markets.

So I failed in my attempt to exit painlessly, and in the meantime more trades were put on the books. Fault me for dithering. (Charlie calls it thumb-sucking.) When a problem exists, whether in personnel or in business operations, the time to act is now.

The second reason I regularly describe our problems in this area lies in the hope that our experiences may prove instructive for managers, auditors and regulators. In a sense, we are a canary in this business coal mine and should sing a song of warning as we expire. The number and value of derivative contracts outstanding in the world continues to mushroom and is now a multiple of what existed in 1998, the last time that financial chaos erupted. [Wrote in 2008]

Our experience should be particularly sobering because we were a better-than-average candidate to exit gracefully. Gen Re was a relatively minor operator in the derivatives field. It has had the good fortune to unwind its supposedly liquid positions in a benign market, all the while free of financial or other pressures that might have forced it to conduct the liquidation in a less-than-efficient manner. Our accounting in the past was conventional and actually thought to be conservative. Additionally, we know of no bad behavior by anyone involved.

It could be a different story for others in the future. Imagine, if you will, one or more firms (troubles often spread) with positions that are many multiples of ours attempting to liquidate in chaotic markets and under extreme, and well-publicized, pressures. This is a scenario to which much attention should be given now rather than after the fact. The time to have considered – and improved – the reliability of New Orleans’ levees was before Katrina.

When we finally wind up Gen Re Securities, my feelings about its departure will be akin to those expressed in a country song, “My wife ran away with my best friend, and I sure miss him a lot.

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).

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. “

Macro Risk of Derivatives, Accounting Gimmicks and Counter-Party Risk

One of the prerequisites of an investment is knowing what you do not know and cannot control, acknowledging the times when you do not understand the portfolio of the company and deciding to stop there. How can an expected probability of gain or loss be calculated if a strong grasp of the portfolio composition cannot be understood? The counterparty risk is entangled between all the major financial institutions of the world, levered to astronomical sizes and still growing! What can be done to curb this growth? Why is it happening? Unfortunately there is not much that can be done, as envy (not so much greed) is a key driver of our capitalistic society, and changes are unlikely to occur until a catastrophic event occurs.

The Glass-Steagall Act was not implemented until 1933, after the speculative frenzy that caused the great depression had occurred. The growth of derivatives is likely happening and will continue to happen due to the incentives behind the accounting of these derivatives and high (non-transparent) fees associated with initiating/maintaining the trades (that the investment banks and consultants push). Retail investors (speculators) are seduced by the get-quick-rich scheme and envy of others.

“The valuation problem is far from academic: In recent years, some huge-scale frauds and near-frauds have been facilitated by derivatives trades. In the energy and electric utility sectors, for example, companies used derivatives and trading activities to report great “earnings” – until the roof fell in when they actually tried to convert the derivatives-related receivables on their balance sheets into cash. “Mark-to-market” then turned out to be truly “mark-to-myth.”

I can assure you that the marking errors in the derivatives business have not been symmetrical. Almost invariably, they have favored either the trader who was eyeing a multi-million dollar bonus or the CEO who wanted to report impressive “earnings” (or both). The bonuses were paid, and the CEO profited from his options. Only much later did shareholders learn that the reported earnings were a sham.

Another commonality of reinsurance and derivatives is that both generate reported earnings that are often wildly overstated. That’s true because today’s earnings are in a significant way based on estimates whose inaccuracy may not be exposed for many years. Unless derivatives contracts are collateralized or guaranteed, their ultimate value also depends on the creditworthiness of the counterparties to them. In the meantime, though, before a contract is settled, the counterparties record profits and losses – often huge in amount – in their current earnings statements without so much as a penny changing hands. The range of derivatives contracts is limited only by the imagination of man (or sometimes, so it seems, madmen). At Enron, for example, newsprint and broadband derivatives, due to be settled many years in the future, were put on the books. Or say you want to write a contract speculating on the number of twins to be born in Nebraska in 2020. No problem – at a price, you will easily find an obliging counterparty. 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.Â

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.

The derivatives genie is now well out of the bottle, and these instruments will almost certainly multiply in variety and number until some event makes their toxicity clear. Knowledge of how dangerous they are has already permeated the electricity and gas businesses, in which the eruption of major troubles caused the use of derivatives to diminish dramatically. Elsewhere, however, the derivatives business continues to expand unchecked. Central banks and governments have so far found no effective way to control, or even monitor, the risks posed by these contracts.”

I hope that it does not takeanother macro liquidity crisis, this time with a tapped FED balance sheet, to have policy/regulation changes implemented. If it were to occur again in the near future the only real market participant with a clean balance sheet able to step in would be the IMF. Many businesses would fail as liquidity ceases due to the counter party risk associated with posting collateral, credit downgrades and meeting other current liabilities; it would likely end in a very severe recession globally.

“Derivatives also create a daisy-chain risk that is akin to the risk run by insurers or reinsurers that lay off much of their business with others. In both cases, huge receivables from many counterparties tend to build up over time. (At Gen Re Securities, we still have $6.5 billion of receivables, though we’ve been in a liquidation mode for nearly a year.) A participant may see himself as prudent, believing his large credit exposures to be diversified and therefore not dangerous. Under certain circumstances, though, an exogenous event that causes the receivable from Company A to go bad will also affect those from Companies B through Z. History teaches us that a crisis often causes problems to correlate in a manner undreamed of in more tranquil times.

In banking, the recognition of a “linkage” problem was one of the reasons for the formation of the Federal Reserve System. Before the Fed was established, the failure of weak banks would sometimes put sudden and unanticipated liquidity demands on previously-strong banks, causing them to fail in turn. The Fed now insulates the strong from the troubles of the weak. But there is no central bank assigned to the job of preventing the dominoes toppling in insurance or derivatives. In these industries, firms that are fundamentally solid can become troubled simply because of the travails of other firms further down the chain. When a “chain reaction” threat exists within an industry, it pays to minimize links of any kind. That’s how we conduct our reinsurance business, and it’s one reason we are exiting derivatives.

Many people argue that derivatives reduce systemic problems, in that participants who can’t bear certain risks are able to transfer them to stronger hands. These people believe that derivatives act to stabilize the economy, facilitate trade, and eliminate bumps for individual participants. And, on a micro level, what they say is often true. Indeed, at Berkshire, I sometimes engage in large-scale derivatives transactions in order to facilitate certain investment strategies. [as noted with previous personal wheat example]

Charlie and I believe, however, that the macro picture is dangerous and getting more so. Large amounts of risk, particularly credit risk, have become concentrated in the hands of relatively few derivatives dealers, who in addition trade extensively with one other. The troubles of one could quickly infect the others. On top of that, these dealers are owed huge amounts by non-dealer counterparties. Some of these counterparties, as I’ve mentioned, are linked in ways that could cause them to contemporaneously run into a problem because of a single event (such as the implosion of the telecom industry or the precipitous decline in the value of merchant power projects). Linkage, when it suddenly surfaces, can trigger serious systemic problems.”

The lack of game theory knowledge in today’s capitalistic society is startling, and many of the major players must simply be ignorant/naïve of counter party risk, systemic risk, knowing what you don’t know and a ratchet-down effect of forced selling/posting collateral. I elect to believe that these players do understand the consequences of their actions but are blind due to the thrill of the pursuit (outsized bonuses they receive) and as a majority have what Nassim Taleb calls “negative skin in the game.” These risk takers are playing a game of heads they win a lot, tails they still win a lot, which is clear by the size of severance packages given to the culprits. When regulators are in the pockets of lobbyists (large banks), under-funded relative to what they are supposedly monitoring, settlements occur (from shareholders' pockets) every time a firm makes its way to court. The whole financial system is on its head and we have learned nothing from just five short years ago. I am not calling a top, bubble or over-priced security but am addressing the systematic risks that are present in the derivatives market.

“In God We Trust; All Others Pay Cash.”

2002 Berkshire Letter
2008 Berkshire Letter
2009 Berkshire Letter

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