Friday, May 29, 2009

Gambler's Ruin

I found an interesting instance of the Gambler's Ruin problem the other day.

A simple version of the Gambler's Ruin:

Assume a gambler finds the only fair casino in the world. At a normal game of chance at a casino, the return is less than one dollar per dollar for each bet. This means that over time a gambler is statistically guaranteed to lose money.

At this casino, however, he finds a game of chance where the return is one dollar per dollar. Given a fair game of this sort, if he plays long enough he is still statistically likely to lose more than he wins. Why?

In a game of chance with an even return, like this one, what matters in the long run is who has more money! Since the casino almost certainly has far more money than he does, statistically he will run out first.

Check this out if you don't believe me: Gambler's Ruin (Wikipedia)

Index funds are a way to invest your money automatically across a lot of different companies. An index fund could, for instance, attempt to match the performance of the S&P 500 by investing in the stocks listed in the S&P 500. There are actually funds that will attempt to double or triple the return of some index in this way. To make it work, the fund managers basically borrow money to invest extra. It would be the same as having $100,000 and borrowing $200,000 to invest a total of $300,000.

When I heard about this some time last year, I thought people must be crazy to gamble like that. When I mentioned it to one of my coworkers though, he said "Oh, you should obviously do it, since the stock market always goes up over time, thus mathematically it will work out in the long run."

It certainly would probably work out in the long run, assuming the stock market keeps going up generally, but only if one has infinite capital! Otherwise, any time the index the fund is tracking falls by 1/3, you lose everything. The Dow itself has fallen further than that lately.

The entire economy right now is suffering because of people who told themselves that investments always appreciate and borrowed enormous sums of money, hoping to get rich quick.

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