Need answer to the attached 3. There are two portfolios, A and B. Portfolio A ha

Question

Need answer to the attached

3. There are two portfolios, A and B. Portfolio A has an average return of 11% per year, and a market beta of 1.5. Portfolio B on the other hand has a Sharpe ratio of 0.3 Assume that CAPM holds, and the risk-free rate is 2%. (a) Find the expected excess return of the market portfolio. (b) If the market has a Sharpe ratio of 0.5, find the correlation between the returns of portfolio B and the market portfolio (c) Suppose there is an asset C, which is perfectly negatively correlated with asset B, and has a covariance of 0.036 with the market portfolio. What is the standard deviation of stock C? d) What should be the expected return of stock C for it to be correctly priced by CAPM?

Explanation / Answer

a. As per CAPM,

Average Return = Risk free Return + beta * (Market Return - Risk Free Return)

11 = 2 + 1.5 ( Market Return - 2)

( Market Return - 2) = ( 11 - 2 ) / 1.5

   ( Market Return - 2) = 6

Market Return = 6 +2 = 8%

Market Return = 8%

b. As per Sharp Ratio

Sharp Ratio of Market = Expected Return of Market - Risk free Retuen / Standard Deviation of Market

0.5 = ( 8 - 2) / S.D. of Market

S.D. of Market = 6 / 0.5 = 12 %

C.

If Any Assets is perfectly negative correlated then co-relation = -1

Co-relation of Stock C& Market = Co- Variance with Market /( S.D of Market * S.D. of Stock C)

- 1 = 0.036 / (.12 * x)

.12 * x = - 0.036

x = - 0.036 * .12 = - 0.00432

Standard Deviation of Stock C = 0.432%

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