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Guns Don’t Kill People

March 18, 2008

Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back”.
John Maynard Keynes

Is the Black-Scholes option pricing model responsible for the current credit crisis? The writer Michael Lewis (whose writing I generally admire) answers “yes” in “Inside Wall Street’s Black Hole” in the March 2008 issue of Portfolio magazine. He pins the blame on papers written 35 years ago by “academic scribblers.” He doesn’t blame Alan Greenspan, borrowers, lenders, ratings agencies; or investment banks. He blames professors. I don’t think this is one of Lewis’s finer efforts, but since he is highly regarded and widely read, it seems worthwhile to consider what he has to say.

Lewis makes two sets of claims. First, he says that the Black-Scholes model is based on faulty assumptions, gives erroneous and misleading prices, and implies that hedging is possible when it isn’t. Second, (echoing Nicholas Nessim Taleb, who is quoted extensively in the article) he says that the Black-Scholes model creates an environment of false certainty: “The academics, in lecturing the birds, have made flying more difficult. …the model has a pernicious effect: By leading investors to think they understand complicated financial risk when they actually do not, and by mispricing that risk, Black-Scholes encourages them to take more chances than they rationally should.” I’ll address these two points in reverse order.

Lewis claims that the rhetoric of finance has damaged financial markets, lending an air of certainty to inherently uncertain calculations, and leading bankers to act irresponsibly. I think he’s got it exactly backwards: The fact that too few people understand option theory has contributed to the credit crisis. Both borrowers and lenders, for example, seem to have believed that real estate prices would keep going up. This reliance on the good outcome is the exact opposite of what finance has to teach us, and it also flies in the face of the market data available at the time.

The Chicago Mercantile Exchange started trading housing futures contracts in May 2006. These contracts allow investors to bet on the future value of the S&P Case-Shiller index, which measures city-specific housing prices. The CME housing contracts have been very thinly traded, but futures prices clearly indicated, beginning in the summer of 2006, that housing prices were expected to decline. On May 22, 2006, investors valued the August 2006 contract at 293.8 and the May 2007 contract at 311.2, an annualized increase of 7.9%. By contrast, on July 14, 2006, investors valued the August 2006 contract at 276.2 and the May 2007 contract at 259.4, an annualized decline of 8.1%.

Figure 1: Annualized decline in the Miami Case-Shiller index implicit in CME housing futures

Figure 1: Annualized decline in the Miami Case-Shiller index implicit in CME housing futures

The adjacent graph shows the implied annual change in the index for those dates when multiple prices were available. After June 2006, there was never an indication in the housing futures market that investors expected housing prices in Miami to rise. The data from Boston, Los Angeles, and other cities is similar. This was a very thin market, but investors could and did trade these contracts and the resulting prices were available to everyone. (The actual Case-Shiller index for Miami declined from 278.68 in May 2006 to 231.71 in December 2007. This was a 17% decline.)

If mortgage lenders had looked at the housing futures data, it would have been natural to consider the behavior of home buyers in a declining market. Look at what happened in 2007: According to The New York Times, the median down payment for first time home buyers that year was 2%, and 29% of all homebuyers put no money down. These are remarkable numbers. In the face of declining real estate prices, lenders were making no-money-down loans to almost 30% of borrowers.

Suppose that you had put 2% down on a house that stretched your financial limits. What would you do if the real estate market softened? You would see prices starting to fall and your neighbors unable to sell their homes. With no investment in your own house (you would probably have already lost your initial 2%), you might behave rationally: You would walk away from both your house and your mortgage payment. This would be particularly easy if you lived in a state where mortgages are non-recourse (the lender can’t come after your other assets). Walking away is what financial economists refer to as exercising an option: You give up the minimal equity interest in your house in return for eliminating your mortgage obligation.

An analyst who paid the slightest attention to the CME housing futures market would have been forced to consider the possibility that housing prices could fall substantially, and it would have been a short step to thinking about widespread mortgage defaults. Of course, housing prices could have either risen or fallen. But the point of option pricing is that it forces you to think hard about the distribution of possible outcomes. A large decline in prices would have been part of that distribution.

The questions are obvious: Did mortgage companies understand and try to value the options they were handing out to homeowners? Did homeowners understand the value of the interest rate adjustment options that would eventually work against them? Did the banks dealing in mortgage-backed securities seriously consider the possibility of large declines in housing prices and the consequent widespread mortgage defaults? Did the ratings agencies try to drill down through the structures and examine in detail the mortgages underlying the debt that they were rating AAA? I doubt that the answer to all of these questions is yes.

Lewis also claims that Black-Scholes option pricing simply doesn’t work, because prices sometimes move too fast for hedging to be possible. Lewis is correct, but this is well known. One of the first people to make this point was the academic scribbler Robert Merton, when in 1976 he developed an option pricing model for the case in which stock prices jump and exact hedging is not possible. Merton was clear that that this was not just an academic exercise: “Empirical studies make a prima facie case for the existence of such jumps,” he said. Merton did make one important and unrealistic assumption when he assumed that stocks do not all jump at once. Asset prices sometimes do jump all at once, and the academic literature is clear that a) the pricing model has to be modified to account for this and b) the resulting risk from selling the option cannot be perfectly hedged. This point is stated quite clearly in at least one derivatives text, (p. 437): “It is precisely when large market moves occur that [Black-Scholes] hedging breaks down. Just like an insurance company, a market-maker requires capital as a cushion against losses.”

Option pricing is a tool that can be used well or poorly, and it is an aid to careful analysis, not a replacement. We have a long way to go before the story of this financial crisis is written, but the Black-Scholes model will not be high on the list of culprits.

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