Question

5)

- A portfolio that combines the risk free asset and the market portfolio has an expected return of 7% and a standard deviation of 10%. The risk free rate is 4%, and the market returns (expected) is 12%. What expected return would a security earn if it had a correlation of 0.45 ewth the market portfolio and a standard deviation of 55%.?

- Suppose the risk free rate is 4.8% and the market portfolio has an expected return of 11.4%. the market portfolio has a variance of 0.0429. Portfolio Z has a correlation coefficient of 0.39 with the market, and a variance of 0.1783. What is the expected return on Z?

Answer #1

a. Let the allocation to risk free portfolio be x. Allociation to market portfolio is 1-x

0.07 = .04x +.12(1-x)

Which implies x = .625

Therefore allociation to risk free portfoliio is 62.5% and to market portfolio is 37.5%

Standard devaition (SD) of this portfolio = 0.1 = .375 * SD of market portfolio

SD of market portfolio = 0.2667

The Beta of the security = Correlation * (SD of security/SD of market) = 0.45 * .55/.2667 = 0.9280

Therefore the expected return on the security as per CAPM = 0.04
+ (.12-.04)*0.928 = **11.42%**

b. The Beta of portfolio Z = Correlation * (SD of portfolio/SD of market) = 0.39 * sqrt(.1783)/sqrt(0.0429) = 0.795 (Since SD is sqare root of variance)

The expected return on the portfolio = 0.048 +
(.114-0.048)*0.795 = **10.05%**

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