Question

The market portfolio has an expected return of 12.3 percent and a standard deviation of 22.3 percent. The risk-free rate is 5.3 percent. a. What is the expected return on a well-diversified portfolio with a standard deviation of 9.3 percent? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the standard deviation of a well-diversified portfolio with an expected return of 20.3 percent? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16) Expected return Standard deviation

Answer 1

a. Standard deviation of well diversified portfolio = 9.3%, Standard deviation of market = 22.3%

For a well diversified portfolio,

Beta = Standard deviation of well diversified portfolio / Standard deviation of market = 9.3% / 22.3% = 0.4170

Now according to Capital Asset Pricing model

Expected return on well diversified portfolio = Risk free rate + Beta(Expected return on market - Risk free rate) = 5.3% + 0.4170(12.3% - 5.3%) = 5.3% + 0.4170 x 7% = 5.3% + 2.9190% = 8.2190% = 8.22% (rounded to two decimal places)

Expected return on well diversified portfolio = 8.22%

b. Expected return of well diversified portfolio = 20.3%

According to Capital Asset pricing model

Expected return of well diversified portfolio = Risk free rate + Beta(Expected return on market - Risk free rate)

20.3% = 5.3% + Beta(12.3% - 5.3%)

15% = Beta(7%)

Beta = 15% / 7% = 2.1428

Standard deviation of well diversified portfolio = Beta x Standard deviation of market = 2.1428 x 22.3% = 47.7844% = 47.78%

Hence Standard deviation of well diversified portfolio = 47.78%