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The active versus passive investment argument is not going to be resolved by a contest. But can it be resolved by research? I think so, and here’s my attempt:
On February 1st, Cassandra picks up the Wall Street Journal outside her door and discovers that it is the paper for March 1st, one month in the future. Not trusting that it is the real deal, she simply saves the paper. The next day, February 2nd, a paper dated March 2nd appears. This continues unabated. Come March 1st Cassandra checks the actual stock prices and, sure enough, they all match the prices in the paper she received a month before. The same is true of all the subsequent newspapers. She has a perfect forecasting tool, the dream of all buy-and-hold investors.
Soon Cassandra puts a PC to use and starts ranking stocks based on their average one-month growth rates, using her perfect knowledge. She then partitions her available capital into 21 equal tranches, and each day she uses one of them to purchase the 200 stocks of the Russell 3,000 expected (actually “guaranteed”) to do the best over the next 21 market days (one calendar month). Her partitioning eliminates any start-date bias. The returns she achieves are the best possible for a buy-and-hold strategy over that time frame. After all, it is the result of perfect look-ahead bias. Returns that Cassandra’s “strategy” would have yielded between 2001 and 2008 aren’t surprising: Cassandra would have earned 25.53 times her capital per year.
Cassandra, however, is curious. Although she knows she cannot do better over that period, she recognizes that each day she has additional information. According to information theory, that knowledge has to be worth something.
Cassandra alters her trading. She will now only hold her positions for 15 days instead of 21 days. She does this without knowing in advance what the prices will be 15 days after her purchases, the papers having been long since discarded. When Cassie sells the portfolio on day 15, she will then purchase another 200 stocks based on their next 21-day forecast. Of course, she is investing with sub-perfect knowledge, because she does not know the advance price of those stocks to be sold on day 15.
Intuitively it would seem unlikely that she could tinker her way to a better return than the perfect portfolio. But she can, and she does so repeatedly. Strategy B beats Strategy A, where Strategy B consists of more-frequent forecasting and trading with sub-perfect knowledge, and Strategy A consists of less-frequent activity with perfect knowledge. The 15-day recast produces 39.52 times her capital per annum, about half-again better than the control.
Encouraged by the success of active investment management against a seemingly unbeatable investment, Cassandra shortens up even more. She still forecasts 21 days ahead on the basis of the newspapers, but she only holds for 10 days, or half the forecast period. This yields a whopping 138.53 times her capital per year. Recasting every five days produces 56.62 times her capital annually – less than 10 days, but greater than 15 days or the control period of 21 days.
