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The following is an excerpt from "Stocks for the Long Run: The Definitive Guide to Financial Market Returns and Long-Term Investment Strategies" by Jeremy Siegel. The excerpt and accompanying Table are from Chapter 19 titled "FUNDS, MANAGERS, AND 'BEATING THE MARKET'"

TABLE 19-2

Probability of Outperforming the Market, Assuming a 14 Percent Expected Return, 16.6 Percent Standard Deviation, and 0.88 correlation coefficient (Based on Data from 1971 to 1996)

Holding Period
1 2 3 5 10 20 30
1% 54.7% 56.6% 58.1% 60.4% 64.6% 70.1% 74.1%
2% 59.3% 63.0% 65.8% 70.1% 77.2% 85.4% 90.1%
3% 63.7% 69.0% 72.9% 78.4% 86.7% 94.2% 97.3%
4% 68.0% 74.5% 79.0% 85.2% 93.0% 98.2% 99.5%
5% 71.9% 79.4% 84.3% 90.3% 96.7% 99.5% 99.9%


It is easy to determine that Magellan's performance during Lynch's years was due to skill in picking stocks. But for more mortal portfolio managers, it is extremely difficult to determine with any degree of confidence that the superior returns of money managers are due to skill or luck. Table 19-2 computes the probability that managers will outperform the market given that they do pick stocks that in a probabilistic sense beat the market, but over short periods of time are subject to normal random movements that mask their higher long-run returns. 11

11. Money managers are assumed to expose their clients to the same risk as the market, and have a correlation coefficient of .88 with market returns, which was typical of equity mutual funds since 1971.

The results are surprising. Even if money managers chose stocks that have an expected return of 1 percent per year better than the market, after ten years there is less than a two-thirds probability that they will exceed the average market return, and after 30 years the probability rises to only 74%. If managers pick stocks that will over the very long term outperform the market by 2 percent per year, after 10 years there is still only a 77% percent chance that they will outperform the market. This means there is almost a one in four chance that they will fall short of the average market performance. In these situations the very long run will most certainly outlive managers' trial periods for determining their real worth.

Detecting a bad manager is an equally difficult task. In fact, a money manager would have to underperform the market by 4 percent a year for almost 15 years before you could be statistically certain (defined to mean being less than 1 chance in 20 of being wrong) that the manger [sic] is actually poor and not just having bad luck. By that time, your assets would have fallen to half of what you would have had by indexing to the market.

Even extreme cases are hard to identify. Surely you would think that a manager who picks stocks that are expected to outperform the market by 5 percent per year, a feat achieved by only one fund other than Magellan since 1970, would easily and quickly stand out. But that is not necessarily so. After one year there is only a 71.9 percent probability that such a manager will outperform the market. And the probability rises to 79.4 percent that the manager will outperform the market after two years.

Assume you gave a young, undiscovered Peter Lynch with a 5 percent per year edge in picking stocks an ultimatum: that he will be fired if he does not at least match the market after two years. There is a one in five chance of firing such a superior analyst, therefore judging him completely incapable of picking winning stocks!

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