Market Timing and Roulette Wheels

Nobel laureate William F. Sharpe and others have alerted investors to the potential pitfalls of market timing. We also conclude from the study reported here that market timing is generally a difficult game. But the difficulty varies substantially over time-which has some intriguing implications for performance evaluation. Using a new measure of investment performance that we call the “roulette wheel” measure, we analyzed monthly, quarterly, and annual market-timing strategies in the 1926–99 period for six major U.S. asset classes. In the 1995–99 period, buying and holding large-capitalization stocks would have outperformed about 99.8 percent of the more than 1 million possible quarterly switching sequences between large-cap stocks and U.S. T-bills. In 1994, however, if 1,000 portfolio managers had made monthly random choices between large-cap stocks and T-bills, about 591 of them would probably have beaten a buy-and-hold strategy. If 650 of the 1,000 had beaten a buy-and-hold strategy, should all 650 have earned a bonus? Market timers attempt to maximize returns by making good decisions about whether to be in or out of particular asset classes. A market timer might make monthly, quarterly, or annual decisions about whether to be in, for example, stocks or U.S. T-bills. Nobel laureate William Sharpe and others have alerted investors to the potential pitfalls of market timing. We also conclude that market timing is generally a difficult game. But the difficulty varies substantially over time, which has some intriguing implications for performance evaluation.We introduce a new measure of investment performance—the roulette wheel (RW) measure—that is fairly intuitive and simple yet insightful. Picture a simple roulette wheel that consists of either two semicircles, one red and one black, or alternating segments of red and black in equal proportions. Assume that you are going to use this roulette wheel to make monthly decisions about whether to be in stocks or T-bills over the next 12 months. (We use a roulette wheel analogy rather than a coin toss because we also consider choices between more than two assets.) If “investment path” means a sequence of switches in and out of the two assets, the choice between two asset choices in each of 12 months produces 212, or 4,096, possible investment paths. To compute the RW measure for the strategy of buy-and-hold stocks (which is one of the 4,096 possible investment paths), one computes the returns for all 4,096 possible sequences and sorts them by ascending return. If the buy-and-hold strategy ranks 3,786 out of the 4,096 possible returns, this rank is converted (via a simple formula) to a number between 0 and 1. With a rank of 3,786 out of 4,096, the RW measure for this buy-and-hold strategy versus switching is 0.924.The RW measure is constructed in such a way that it averages 0.500 for repeated random choices. If the RW for a historical buy-and-hold strategy is 0.924 (which was true for large-capitalization stocks in 1997, based on monthly switching between large stocks and T-bills), then that strategy was outperforming approximately 92.4 percent of the 4,096 possible investment paths. Therefore, the buy-and-hold strategy performed quite well against alternative paths. In general, we found that buy-and-hold strategies have high RW measures.We report RW values for many combinations of major asset classes, but we will focus on large-cap stocks (with transaction costs not considered) in this digest. In these tests, the buy-and-hold asset in each case was large-cap stocks and the switching choice was between large-cap stocks and T-bills. We found the average RW value (based on 74 years of data from January 1926 through December 1999) for monthly switching over a one-year period to be 0.6622. When the switching choice was made quarterly over five-year periods, the average RW is 0.7539. For annual switches over decades, the average RW is 0.8041. Including transaction costs raises the RW values; a buy-and-hold strategy is even more attractive when switching is costly.The average results for large-cap stocks illustrate the general difficulty of outperforming the simple strategy of buying and holding assets. The averages, however, mask some highly intriguing variability over time. In the 1995–99 period, the buy-and-hold strategy for large-cap stocks was virtually impossible to beat. Based on quarterly switching, the RW is 0.9979 for that period; that is, only 0.2 percent of the 1,048,576 quarterly investment paths would have beaten the buy-and-hold strategy. In some other periods, however, such as 1970–1974, switching strategies would have beaten the buy-and-hold strategy more often.The results have some important implications for performance and reward systems. For example, how much should one reward a manager for beating an index in a period such as 1970–1974, when about 79 percent of randomly chosen quarterly switching paths would have outperformed the index?