Question

You are a financial advisor who offers investment advice to your clients. There are two risky assets in the market: portfolio X and portfolio Y. X has an expected return of 15% and standard deviation of 35%. The expected return and standard deviation for Y is 20% and 45% respectively. The correlation between the two portfolios is 0.2. The rate of risk-free asset, T-bill, is 5%.

1. a) Peter is one of your clients and he can only invest in T-bill and one of the two risky portfolios. Which risky portfolio should he pick and why?

2. b) Compute the expected return and standard deviation of the optimal risky portfolio if the optimal risky portfolio is given by investing 50.48% in X and 49.52% in Y.

3. c) Mary is also your client and there are no restrictions on her investment. Mary’s risk aversion level is 5. Based on part b, how do you advise Mary to allocate her money among risk-free asset, portfolio X, and portfolio Y?

4. d) Draw the best Capital Allocation Line (CAL) and calculate the slope of that CAL. Furthermore, indicate the positions of portfolios X, Y, and the optimal portfolio you proposed to Mary in part c on the graph.

5. e) Suppose the return of market portfolio is 17.48%, under CAPM, what are the betas for X and Y if they are in equilibrium?

6. f) If the beta of portfolio X turns out to be 0.9 and Y is in equilibrium, is there any arbitrage opportunity? If yes, how to exploit such opportunity using the existing assets?

Answer 1

(a) let's assume we invest 50% in riskfree asset and 50% in risky asset

expected return and risk of a risk-free asset with risky portfolio X

Expected Return = 0.5*0.15+ 0.5*.0.05

=10%

Risk = 0.5*0.35

=17.5%

expected return and risk of risk-free asset with risky portfolio Y

Expected Return= 0.5*0.2+ 0.5*0.05

=12.5%

Risk = 0.5* 0.45

=22.5%

In my opinion Peter should choose portfolio X with risk free asset

(b) Expected Return = W1R1 + W2R2

W1& W2 are the proportion of the portfolio invested

R1 & R2 are expected return of portfolio X and Y

Expected Return = 0.5048* 0.15 + 0.4952*0.2

= 17.476%

Standard Deviation = square root of (0.5048)^2* (0.35)^2 + (0.4952)^2* (0.45)^2 +2*0.5048*0.4952*0.35*0.45*0.2

26.17%

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