The standard deviation of the rate of return on the market portfolio is 18%. Giv

Question

The standard deviation of the rate of return on the market portfolio is 18%.  Given that a well diversified portfolio has no unsystematic risk (i.e., 100%  of the variation in the portfolio return is explained by the variation in the return of the market portfolio), determine

a. the standard deviation of return on a well diversified portfolio with a beta of .75

b. the standard deviation of return on a well diversified portfolio with a beta of 0

c. the beta of a well diversified portfolio having a standard deviation of 22.5 percent.

Explanation / Answer

a. Standard deviation of well diversified portfolio with beta of 0.75 = market portfolio's standard deviation * beta = 18%*0.75 = 13.5%

b. Standard deviation of well diversified portfolio with beta of 0 = market portfolio's standard deviation * beta = 18%*0 = 0%

c. Beta of well diversified portfolio with with standard deviation of 22.5% = diversified portfolio's standard deviation / market portfolio's standard deviation = 22.5% / 18% = 1.25

Hope this helped ! Let me know in case of any queries.

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