How to Stay Solvent Longer Than the Market Can Stay Irrational
By Bryan Caplan
How often have you heard the quip, “The market can stay irrational longer than you can stay solvent”? The idea: Even if the market is ridiculously overvalued, you won’t make money by shorting it. You’ll probably go bankrupt instead of laughing all the way to the bank.
But isn’t the obvious solution to this problem simply to repeatedly sell a smaller amount short?
Suppose for example that you’ve got $100,000 in assets. You know with virtual certainty that the market will eventually fall from its present level of 100 down to its fundamental value of 50. The catch: You don’t know when it will fall. Every year, the market has a 50% of going up 20%, and a 50% chance of plummeting down to 50. So if you sell $100,000 short with contracts that resolve after a year, you’ll lose your shirt if the market goes up five years in a row.
However, you could easily just sell $10,000 short each year. In year one, you lose $2,000 if the market goes up to 120, and make $5000 if the market falls back to 50. In year two, you lose $2,000 if the market goes up to 144, and gain $5833 if it falls back to 50. In year three, you lose $2000 if the market goes up another 20%, and gain $6528 if it falls back to 50. Every year you can expect to make money, and unless you’re wrong 50 times in a row, you stay solvent.
Did I cook the numbers to make this work? I don’t think so. The strategy won’t work if the ex ante payoff from short-selling is negative. If the market has a 50% chance of doubling and a 50% chance of falling to its fundamental level, you quickly go broke. But under realistic assumptions, what’s wrong with my strategy?