The following article was condensed from “Some Lessons from 250,000 Years of Stock Returns” by Truman A. Clark of Dimensional Fund Advisors.

“My stocks are down 30 percent. What are the chances they will come back soon?” “Man, I wish I had been out of stocks for the past three years. How often are stocks likely to beat cash over periods of three years or longer?” Investment professionals often are asked such questions. These are questions about probabilities. At present, about 76 years of reliable returns data are available from the Center for Research in Security Prices (CRSP) database. Routine sampling with these data provides satisfactory estimates of probabilities for holding periods of three years or less. But for longer holding periods, 76 years of data examined in chronological order do not provide enough independent observations to obtain dependable estimates. Bootstrap simulations solve this problem.

What is Bootstrapping?

Bootstrapping is a Monte Carlo procedure for using limited data to create large samples of independent holding-period returns. In this study, the source data are the July 1926 through December 2002 monthly returns of seven stock indexes and one-month Treasury bills. To construct a simulated history, each of the 918 months is assigned an equal probability of selection. One month is chosen at random (e.g., June 1992), and the returns of the indexes and bills in that month are recorded. A second month (e.g., August 1947) is selected randomly, and the returns for that month are recorded.

This process is repeated until a simulated holding period of the desired length (e.g., 12 months for a one-year holding period or 300 months for a 25 year holding period) is created. All drawings are done “with replacement” so that a given month can be selected more than once in any sample holding period. This procedure was repeated to create 10,000 simulated histories of one-year through 25-year holding period returns. By construction, these returns are independent, and they yield reliable estimates of long-term probabilities.

Probabilities of Recovery from an Initial 30 Percent Loss

“What are the chances my stocks will recover from a 30 percent loss?” The answer to this question depends on the type of stocks and how long they will be held. Table 1 reports the estimated probabilities of recovery from an initial 30 percent loss for seven stock indexes over various time horizons. The probabilities of recovery in one year are not high. They are less than ten percent for large growth and the S&P 500. For large value, small growth, the CRSP 6-101, small value and the CRSP 9-10, the probabilities of recovery in one year are 14 percent or more. As the time horizon is extended, chances of full recovery become better and better. Over three years, the probabilities of recovery exceed 40 percent for all indexes. At 25 years, all probabilities exceed 90 percent.

Also in This Issue:

Portfolio Rebalancing: Keep Your Hands on the Wheel
The High-Yield Dow Investment Strategy
Recent Market Statistics
The Dow-Jones Industrials Ranked by Yield
Asset Class Investment Vehicles