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# Calculating mean and standard deviation

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.)

#### 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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