Problem 3 (20 marks). A stock has a beta of 1.2 and an expected return of 16%. T

Question

Problem 3 (20 marks). A stock has a beta of 1.2 and an expected return of 16%. The risk-free asset currently earns 5%. a) What is the expected return on a portfolio that is equally invested in the two assets? 5 marks b) If a portfolio of the two assets has a beta of 0.75, what are the portfolio weights? 5 marks] c) If a portfolio of the two assets has an expected return of 8%, what is its beta? 5 marks] d) If a portfolio of the two assets has a beta of 2.3, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.[5 marks]

Explanation / Answer

Part A:

Expected Ret = Weighted Avg return of all securities in that portfolio.

Part B:

Portfolio Beta = Weight of stock * Beta of that stock ( As Risk free asset beta is "Zero")

0.75 = Weight of stock * 1.2

Weight of stock in portfolio = 0.75 / 1.2

= 0.625 i.e 62.5%

Part C:

Expected ret = Weighted Avg return of stocks in that portfolio

let X be the weight of stock in portfolio & "1-X" be the weight of risk free asset

Thus 0.05 + 0.11X = 0.08

0.11X = 0.03

X = 3/11

Portfolio beta = Weight of Risky Asset * Beta of that Asset

= (3 / 11 ) * 1.2

= 0.3273

Part D:

Portfolio Beta = Weight of stock * Beta of that stock ( As Risk free asset beta is "Zero")

2.3 = Weight of stock * 1.2

Weight of stock in portfolio = 2.30 / 1.2

= 1.9167 i.e 191.67%

Weight of stock = 191.67%

Weight of Risk free Asset = - 91.67%

.

Pls comment, if any further assistance is required.

Thank you

Asset Weight Return Weighted ret Stock 0.5 16% 8.00% Risk free asset 0.5 5% 2.50% Portfolio return 10.50%

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