Tuesday, October 26, 2004

A coin flip

Imagine that someone offered you a chance to win a million dollars if you can correctly guess the result of a coin flip. The expected payout would be $500,000 and you could probably sell the chance to some wealthy individual for almost that amount. Buying the chance for $450,000, for instance would be a $50,000 expected return. In other words for a small price (relatively speaking, of course), you could trade a situation with an extreme range of outcomes for a certain outcome.

This is an example of a win-win hedge: you get a large sum of money and the other party gets a discounted chance at a large payout. If the buyer can make this sort of transaction over and over, he'll make a good profit with moderate risk. This is how casinos and insurance companies work more or less.

Suppose you decided to keep the chance and sell a chance to win a million dollars on that same coin flip to someone else. You have an expected return of $500,000 on the first transaction and ($500,000) on the second (plus whatever you sold the chance for). But there are two possible way for these transactions to pay out. It all depends on whether or not you make the same guess as the person you sold a chance to. Here's a chart showing the difference:

You  | Same | Not 
Win  |   0  |  $1,000,000
Loss |   0  | ($1,000,000)

In other words, if the guesses are the same, it's no different than selling your chance. But if they are different, the variation of results is huge. You would risk nothing in the first case and everything on the second. Statistically speaking, you would say that the results if the guesses are the different have a correlation of 1 and -1 when they are the same. If the bets were on two coin flips, the correlation in either case would be 0.

Obviously this is an extreme simplification of what investors are faced with. I own Raytheon stock and work for Raytheon, but there's not a huge amount of correlation between my job security and my company's performance. In some ways the election will matter a lot more, since I depend more on the federal budget than on Raytheon itself.

Real life is more like betting on hundreds of coin flips and we don't always know how they are going to interact. Like an insurance company, you have to spread out the risk and buy it at a discount.

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