You are a fund manager who has managed two mutual funds. The first is a stock fund; the second is a corporate bond fund. The current risk-free rate is 6%. The expected return and standard deviation for both funds are:

Expected Return Standard Deviation

Stock fund 19% 24%

Bond fund 10% 13%

The correlation between the fund returns is 0.25

Your client wants to invest in both funds but does not know how much he should invest in each fund. Thus, you construct the optimal risky portfolio (shown as the tangent point) for your client. The optimal weight for stock fund is 59% and for bond fund is 41%.

1. Given the optimal weights (59% in stock fund and 41% in bond fund), calculate the expected rate of return and the standard deviation for the optimal risky portfolio.

2. Explain to your client why this portfolio is called the optimal risky portfolio. In other words, from the returns' perspective, explain to your client why he should invest in this portfolio, not any other portfolio.

3. If your client is a rational investor who would like to invest 25% of his $100,000 in risk-free asset and 75% of his $100,000 in the optimal risky portfolio. Where is your client's complete portfolio located in the Capital Allocation Line? Please select the number (1, or 2, or 3) marked on the capital allocation line.

4. Show the portfolio weight and the dollar amount that your client should invest in each asset (risk-free asset, bond fund, and stock fund.)