Question: 1. The expected returns and standard deviations for a stock fund (S), a bond fund (B) and the T-bill, which is the risk-free asset (f),

1. The expected returns and standard deviations for a stock fund (S), a bond fund (B) and the T-bill, which is the risk-free asset (f), are given below.

Fund	Expected return	SD
S	10%	19%
B	5%	8%
f	3%	0%

We construct the optimal risky portfolio using the stock and bond funds. We calculate the weights of the stock and bond funds in the optimal risky portfolios using the formula for the weight of the optimal portfolio of two risky assets (Equation 6.10). Accordingly, we find that the optimal weight of the stock fund is 43.2% and the optimal weight of the bond fund is 56.8%.

(1) Calculate the expected return of the optimal risky portfolio

(2) Calculate the standard deviation of the optimal risky portfolio

(3) Calculate the Sharpe ratio of the optimal risky portfolio

(4) Answer (4.1) to (4.4) based on the following information.

Your job as financial planner is to create the complete portfolio for the client, which meets the expected return and standard deviation targets of your client by mixing the optimal risky portfolio and the risk-free asset. Your client expects a 5.29% expected return and a 5.58% standard deviation on the complete portfolio.

(4-1) Calculate the weight of the optimal risky portfolio in the complete portfolio.

(4-2) Calculate the weight of the risk-free asset in the complete portfolio.

(4.3) Calculate the weight of the stock fund in the complete portfolio.

(4.4) Calculate the weight of the bond fund in the complete portfolio.

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