Hypothesis Testing in Alternative Investments
Suppose that a manager runs a fund called The Trick Fund. The fund manager claims the ability to consistently outperform the S&P 500 Index but refuses to divulge the details of the strategy. It turns out that for each $100 of value in the fund, the manager initially holds $100 in a portfolio that mimics the S&P 500, and then on the first of each month, the fund manager writes a $0.50 call option on the S&P 500 that is far out-of-the-money and expires in a few days. If the fund manager has bad luck and the S&P 500 rises dramatically during the first week so that the call option rises to $2.50—or is about to be exercised—the fund manager purchases the call at a loss (covering the option position). The fund manager purchases the call option back using money obtained from writing large quantities of new out-of-the-money call options for the second week at combined prices of $2.50. If the second group of options rises in value to $12.50, the fund manager repeats the process by selling even more call options for the third week to generate proceeds of $12.50 that are used to cover the second option positions. The strategy continues into the fourth week, such that if the third set of short options rises to $62.50, a fourth set of out-of-the-money options is sold for $62.50. By the end of the fourth week, either the fourth set of options is worthless, or the fund is ruined.
If at any point during the month one of the set of options ...