The Big Short


In his book, "The Big Short", Michael Lewis wrote that In July of 2002, Capital One's stock fell 60 percent to about $30 a share in two days after management disclosed that they were in a dispute with government regulators as to how much capital they needed to reserve against subprime losses. The 'market' suspected that regulators had discovered fraud and were about to punish Capital One.

Two young entrepreneurs, Jamie Mai and Charlie Ledley, who had formed a money management firm with $110,000 in assets and that operated out of a shed in the back of a friend's house, studied the situation, interviewed some people, and concluded that maybe the people at Capital One were crooks, but probably were not.  This led them to an unusual approach to financial markets (in a way, somewhat similar to what we our experiment will focus on) that made them rich. They noticed that, in the six months following the news of Capital One's troubles with the Federal Reserve and the Office of Thrift Supervision, Capital One's stock traded in a narrow band around $30 a share.  Charlie and Jamie reasoned that either the company was a fraud, in which case the stock was probably worth zero, or the company was as honest as it appeared, in which case the stock was worth around $60 a share.

Since they felt there was a reasonable probability that the company would be cleared, they considered purchasing the stock.  But instead of buying the stock, they did what Joel Greenblatt had written about in his book You Can Be a Stock Market Genius" -- they bought a derivative security called a LEAP (for Long-term Equity AnticiPation Security), which gave the buyer the option to buy the stock at a fixed price for a certain amount of time.  The price of the LEAP with the option to buy Capital One's shares for $40 at any time in the next two and a half years cost a bit more than $3.  Wondering why the option cost so little, they found that the model used by Wall Street to price LEAPs, the Black-Scholes option pricing model, made some strange assumptions -- it assumed a normal distribution for future stock prices, meaning that prices around $30 were more likely than prices around $35 which were more likely than prices around $45 and so on.  That didn't make sense to them since they reasoned that if the company were vindicated, the price would move up a lot -- near $60 and if they were convicted, it would move close to zero.

Jamie and Charlie bought 8,000 LEAPs for about $26,000.  When Capital One was vindicated by its regulators, its stock price shot up and their $26,000 option position was worth $526,000.  Jamie and Charlie continued to look for situations where probabilities of extreme changes were not in line with option prices.  Four and a half years after, having starting with $110,000, they netted more than $80 million.

That didn't mean that they didn't lose some money along the way.  In fact, their losses, by design, were part of the plan.  They had more losers than winners, but their losses, the cost of the options, had been trivial compared to their gains.  Ben Hocket, who had spent nine years trading derivatives for Deutsche Bank in Tokyo before meeting Jamie, his neighbor and eventually joining both Jamie and Charlie, shared Charlie and Jamie's view that people, and markets, tended to underestimate the probability of extreme change.  He explained "Financial options were systematically mispriced.  The market often underestimated the likelihood of extreme moves in prices.  The options market also tended to presuppose that the distant future would look more like the present that it usually did."  He also explained "The longer-term the option, the sillier the results generated by the Black-Scholes option pricing model, and the greater the opportunity for people who didn't use it."


Jamie and Charlie were successful because they capitalized on opportunities where the price of options, as established by the commonly accepted Black-Scholes model, were very low compared to the potential gain that could reasonably be 'expected'.   Their expectations were not based on a computation using an assumed probability distribution, but a more crude reasoning that, for example, paying $3 for an option that had somewhere around a 50% chance of being worth a lot more. ...

According to Michael Lewis in The Big Short, both Jamie and Charlie "sensed that people, and by extension markets, had difficult attaching the appropriate probabilities to highly improbable events. Both had trouble generating conviction of their own but no trouble at all reacting to what they viewed as the false conviction of others.  Each time they came upon a tantalizing long shot, one of them set to work on making the case for it.  They entered markets only because they thought something dramatic might be about to happen in them, on which they could make a small bet with long odds that might pay off in a big way".   Was this investing or gambling?  Although Jamie and Charlie did not actually compute the expected values of the purchases by multiplying the probability of possible outcomes by the returns of those outcomes, they did so intuitively by observing that with a probability of about .5 they could get a very large gain which equated to an expected value much greater than the cost of buying the options.

Rather than 'guessing' at probabilities, as Jamie and Charlie did, we will, in this experiment, derive probabilities from the Wisdom of Crowds using the Analytic Hierarchy Process.