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But historical averages can vary widely depending on their starting and ending points. For example, averages that start before the 1929 crash are substantially different from those that start after it, and Mr. Easterling felt that choosing a single date was arbitrary. In response, he created the chart above, which shows annualized returns based on thousands of possible combinations of market entry and exit.

After accounting for dividends, inflation, taxes and fees, $10,000 invested at the end of 1961 would have shrunk to $6,600 by 1981. From the end of 1979 to 1999, $10,000 would have grown to $48,000.

“Market returns are more volatile than most people realize,” Mr. Easterling said, “even over periods as long as 20 years.”