Question

Suppose the standard deviation of the market return is 20%. The risk-free rate is 3%. What...

Suppose the standard deviation of the market return is 20%. The risk-free rate is 3%. What is the standard deviation of returns on a well-diversified portfolio with a beta of 0.9?

a. 22.22%

b. 19.80%

c. 16.20%

d. 18.00%

e. 21.00%

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Answer #1

Beta of the well-diversified portfolio = βP = 0.9

Correlation between the well-diversified portfolio and the market = ρ = 1 [A well-diversified portfolio will be almost similar to a market portfolio. Hence, its correlation with the market will be 1]

Standard deviation of the portfolio = σP

Standard devaition of the market = σM = 20%

Beta of the portfolio is calculated using the formula:

βP = (ρ*σP)/σM

0.9 = (1*σP)/20%

σP = 0.9*20% = 18%

Answer -> 18% (option d)

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