## Table 137

Standard Deviations of Annual Portfolio Returns

### Slide 13.22

These figures are from Table 1 in M. Statman, "How Many Stocks Make a Diversified Portfolio?" Journal of Financial and Quantitative Analysis 22 (September 1987), pp. 353-64. They were derived from E. J. Elton and M. J. Gruber, "Risk Reduction and Portfolio Size: An Analytic Solution," Journal of Business 50 (October 1977), pp. 415-37.

Ross et al.: Fundamentals I V. Risk and Return I 13. Return, Risk, and the I I © The McGraw-Hill of Corporate Finance, Sixth Security Market Line Companies, 2002

Edition, Alternate Edition

428 PART FIVE Risk and Return typically be a substantial 49 percent per year. If you were to randomly select two stocks and invest half your money in each, your standard deviation would be about 37 percent on average, and so on.

The important thing to notice in Table 13.7 is that the standard deviation declines as the number of securities is increased. By the time we have 100 randomly chosen stocks, the portfolio's standard deviation has declined by about 60 percent, from 49 percent to about 20 percent. With 500 securities, the standard deviation is 19.27 percent, similar to the 20 percent we saw in our previous chapter for the large common stock portfolio. The small difference exists because the portfolio securities and time periods examined are not identical.

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