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    Calculating mean and standard deviation

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    Suppose the security I and security J have the following historical returns:
    Year kI kJ
    2001 20% 40%
    2002 29 36
    2003 -12 -25

    1. What is the (arithmetic) average return on security I?
    2. What is the standard deviation of the return on security I? (Use n-1 for the denominator.)
    3. Suppose you invest 50% of your money in I and the rest in J to form a portfolio P. What is the average return on portfolio P?
    4. What is the standard deviation of the return on portfolio P? (Use n-1 for the denominator.)

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    Solution Preview

    Please refer attached file for better clarity of tables. Some of the formulas may be missing here.

    Solution:

    1. What is the (arithmetic) average return on security I?
    Arithmetic average return on security I=(20%+29%-12%)/3=12.33%

    2. What is the standard deviation of the return on security I? (Use n-1 for the denominator.)
    Mean=arithmetic average ...

    Solution Summary

    Solution describes the steps to calculate mean and standard deviation of historical returns for given stocks and portfolio.

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