Source: © Stocks, Bonds, Bills, and Inflation 2001 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.

deviation. If we were examining projected future returns, then the procedure would be different. We describe this procedure in the next chapter.

To illustrate how we calculate the historical variance, suppose a particular investment had returns of 10 percent, 12 percent, 3 percent, and -9 percent over the last four years. The average return is (.10 + .12 + .03 - ,09)/4 = 4%. Notice that the return is never actually equal to 4 percent. Instead, the first return deviates from the average by .10 — .04 = .06, the second return deviates from the average by .12 - .04 = .08, and so on. To compute the variance, we square each of these deviations, add them up, and divide the result by the number of returns less 1, or 3 in this case. Most of this information is summarized in the table below.

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(1) - (2)


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