An Option Model for Value Investors

The Black-Scholes model does an admirable job at valuing short-term options. If an option expires in a few weeks, the current price of the underlying stock and its recent volatility have a good deal of influence on the outcome of the option investment. A simple Black-Scholes calculation has a lot of flaws (none of which I’ll go over), but in my opinion it does alright on the short-term options. However, the further away the expiration date, the worse it gets.

Value investors know that the historic volatility of a stock has nothing to do with its long-term value, and therefore should never be used when making a purchase. However, when purchasing equities, value investors have the luxury of waiting however long they need until price eventually reaches fair value.

If a stock is worth $30, that doesn’t mean a call option with a strike of $20 is worth $10. The option value must also depend on the duration of the option: the further out the expiration, the greater the underlying valuation should affect the option price (and the less volatility should matter). A lot of value investors purchase LEAPs, or options a year or more out, for this very reason.

The Graham-Olson Option Valuation Model

In honor of Benjamin Graham, I put forth the following equation as the value of a call option: Continue reading “An Option Model for Value Investors”

Berkshire Part 2: Selling Puts

Buffett has pulled it off again. He’s made a creative, favorable bet that may pay off handsomely for long-term Berkshire shareholders.

Over the past year, Berkshire Hathaway sold put options on the S&P 500 and three foreign indices. Expiration of these puts range from 12 to 20 years out, and Berkshire collected $4.5 billion in premiums. Unlike regular puts, these are exercisable only at their expiration dates. On those dates, Berkshire makes a payment only if the index has lost money over the period of the option.

Selling these puts is essentially saying: In 15 years, I promise to buy the S&P 500 from you at a price of $1,468 (closing 2007), if it trades below that price. In exchange, you give me $4.5 billion right away.

Buffett doesn’t disclose the size of the actual options. The $4.5 billion in premiums tells you they are big, but apparently not big enough relative to Berkshire to cause any problems.

The counterparties (the people who made the agreement and paid the premium) are most likely large financial institutions who are hedging their long-term bets in favor of the market. So it may turn out to be a dumb bet for them, but they’re essentially purchasing insurance on what they have or will have in the market.

For Berkshire to lose money, a few things have to happen. To keep it simple, let’s just talk about the S&P 500, because we don’t know which foreign indices were used.

  1. First, over the next 12 to 20 years, the market would have to have a negative cumulative return.
  2. Second, that negative return would have to be large enough to overcome the premiums received.

How large? Once again, we don’t know the size of the options. But the premiums, which were $4.5 billion at the time they were written, will have compounded for more than 15 years by the time of expiration. If Buffett (or future Berkshire managers) can achieve 15% annual returns, the premium cash will have grown to over $36 billion. So the aggregate losses on the put options—the size of the options times the amount of negative returns—would have to exceed $36 billion for any profits to be erased.

Because of their long-term length, it mitigates the risk of a short-term Black Swan-type event affecting the options. A “Black Monday” one day anomaly would have little effect, other than a temporary quarterly adjustment. Something could still happen (i.e. a long depression, or a nuclear war, God forbid) that would cause losses. But this bet seems pretty favorable as long as the world economy does alright in the long run. Chalk one up for the Oracle of Omaha.