Question

The market portfolio has an expected return of 11.0 percent and a standard deviation of 21.0 percent. The risk-free rate is 4.0 percent.

  

a.	What is the expected return on a well-diversified portfolio with a standard deviation of 8.0 percent? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

  

Expected return

%

  

b.	What is the standard deviation of a well-diversified portfolio with an expected return of 19.0 percent? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

  

Standard deviation

%

Answer 1

R_m = 11%

R_f = 4%

a.

For well diversified portfolio,

Correlation Coefficient = 1

Beta_p = 0.08/0.21 = 0.38

Using CAPM model,

Expected return of Portfolio = R_f + Beta(R_m - R_f)

Expected Return of Portfolio = 0.04 + 0.38(0.11 - 0.04)

Expected Return of Portfolio = 6.66%

b.

Expected Return = 0.19

Using CAPM model,

Expected return of Portfolio = R_f + Beta(R_m - R_f)

Beta = (0.19 - 0.04)/(0.11 - 0.04) = 2.14

For well diversified portfolio,

Correlation Coefficient = 1

Beta = Standard Deviation of Portfolio/Standard Deviation of market

Standard Deviation of Portfolio = 2.14 * 0.21

Standard Deviation of Portfolio = 44.94%