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Numerical Examples of Mean, Standard Deviation, and Correlation 1 This handout illustrates how to compute the mean, the standard deviation, the co- variance, and the correlation. For now, we assume that there are only three possible scenarios for next year. There will either be a recession, a boom, or things will con- tinue as normal. Each of these scenarios are equally likely. That is, each happens with probability 1/3. 1. Compare a fund that invests in U.S. stocks to a fund that invests in U.S. bonds. Table I gives the returns on the funds in each of the scenarios. Table I U.S. Stock Fund U.S. Bond Fund Return Deviation Return Deviation Scenario from Mean from Mean Recession -.07 -.18 .17 .10 Normal .12 .01 .07 0 Boom .28 .17 -.03 -.10 Using the results in Table I, the mean return on the stock fund is: ¯ R S = 1 3 ( - . 07) + 1 3 ( . 12) + 1 3 ( . 28) = . 11 The mean return on the bond fund is: ¯ R B = 1 3 ( . 17) + 1 3 ( . 07) + 1 3 ( - . 03) = . 07 Using these numbers, we can compute the deviations from the mean found in the

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