I have read about Warren Buffett engaging in derivatives but I did not know exactly what he did.

Today, I learned that he was selling naked options! (Pardon my tardiness as this happened in 2008.)

Isn’t selling naked options risky where your loss is unlimited? Didn’t Warren Buffett warn the dangers of derivatives?

He disclosed his options position in his 2008 letter to shareholders and gave an explanation for what he has done. Besides options selling, he also went into writing Credit Default Swaps (CDS) but we are just focusing on options here. I have extracted the part of the letter that talks about selling options:

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“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 counter-party 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.”

Put options on equities are usually more expensive than call options – stocks comes down faster than they go up. Hence, it made sense for Buffett to sell puts and collect more premiums.

He chose long term options with 15 to 20 years expiry because they are mispriced. Options are priced according to the Black-Scholes formula and Buffett discussed about the shortcomings in the same letter:

“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 everyday 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.”

#### The Key to Warren Buffett’s Wealth

Yes, Warren Buffett is darn good at picking stocks. But he wouldn’t be as rich as he is today just by picking stocks. He needed another key element, which is the access to large amount of capital at a cheap cost.

In his early days, his source of capital came from clients’ money. But the real break into his wealth came from the control of insurance companies. The insurance premiums collected served as investment capital for Warren Buffett. But these premiums come at a cost – he needs to pay out the sum assured to the clients if the pre-agreed conditions happened to the latter. The underwriters have to get the risk calculation right and make sure the collective premiums are sufficient to cover the amount owed to a small group of clients.

By selling options, Warren Buffett is doing something similar to collecting insurance premiums. He is ‘borrowing money’ in advance and at a cheap cost to invest for a higher rate of return. He calculated that his maximum loss in options selling is 6.2% per annum (indices go to zero). In fact, he expects his real ‘borrowing cost’ to be 0.7% per annum (indices drop 50%), but with a 1% chance of happening. Being an exceptional investor, he could achieve 20% returns per year. Selling options becomes a no brainer way for him to raise cash to invest.

Buffett’s mantra: borrow as much money, and as cheaply, as possible, and invest it. Shrewd and well played.

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