A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are:

 	Expected Return	Standard Deviation
Stock fund (S)	16%	36%
Bond fund (B)	10%	27%
The correlation between the fund returns is 0.20.

Suppose now that your portfolio must yield an expected return of 13% and be efficient, that is, on the best feasible CAL. What is the proportion invested in each of the two risky funds?

To solve this problem, we need to use the Capital Allocation Line (CAL) concept. The CAL represents the relationship between the risk (standard deviation) and return of portfolios comprising both risky assets (the stock and bond funds) and the risk-free asset (T-bill money market fund). Since the portfolio is required to be on the "best feasible CAL" and efficient, this means the portfolio must lie on the tangency point of the capital market line (CML) with the efficient frontier, using the stock fund (S) and bond fund (B).

### Steps to find the proportions of the two risky funds (S and B):

1. **Define variables**:
   - Let \( w_S \) be the proportion of the portfolio invested in the stock fund (S).
   - Let \( w_B = 1 - w_S \) be the proportion invested in the bond fund (B).

2. **Expected return of the portfolio**:
   The expected return of the portfolio is a weighted sum of the expected returns of the stock and bond funds:
   \[
   E(R_P) = w_S \cdot E(R_S) + (1 - w_S) \cdot E(R_B)
   \]
   Where:
   - \( E(R_S) = 16\% \) is the expected return of the stock fund,
   - \( E(R_B) = 10\% \) is the expected return of the bond fund.

   The portfolio must achieve an expected return of 13%, so:
   \[
   13\% = w_S \cdot 16\% + (1 - w_S) \cdot 10\%
   \]

3. **Solve for \( w_S \)**:
   \[
   0.13 = 0.16w_S + 0.10(1 - w_S)
   \]
   \[
   0.13 = 0.16w_S + 0.10 - 0.10w_S
   \]
   \[
   0.03 = 0.06w_S
   \]
   \[
   w_S = \frac{0.03}{0.06} = 0.5
   \]
   Therefore, \( w_S = 0.5 \), meaning that 50% of the portfolio is invested in the stock fund.

4. **Calculate \( w_B \)**:
   Since \( w_B = 1 - w_S \), we have:
   \[
   w_B = 1 - 0.5 = 0.5
   \]
   Therefore, 50% of the portfolio is invested in the bond fund.

### Conclusion:
To achieve the required 13% expected return efficiently, the proportion invested in each of the risky funds is:
- **50% in the stock fund (S)**.
- **50% in the bond fund (B)**.

Would you like further details on the calculations or how the risk of the portfolio is determined?

### Relative Questions:
1. How does the correlation between stock and bond funds affect the overall portfolio risk?
2. What is the role of the T-bill money market in portfolio construction?
3. Can you calculate the standard deviation of this portfolio using the correlation provided?
4. What would happen if the expected return requirement was increased to 15%?
5. How would the portfolio weights change if the correlation between stock and bond returns was higher?

**Tip**: When constructing a portfolio, understanding the correlation between assets can help optimize the risk-return profile.

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Expected Return: Stock fund (S) 16%, Bond fund (B) 10%. Standard Deviation: Stock fund (S) 36%, Bond fund (B) 27%. The correlation between the fund returns is 0.20. Suppose now that your portfolio must yield an expected return of 13% and be efficient, that is, on the best feasible CAL. What is the proportion invested in each of the two risky funds?

Determine the proportion of investments in stock and bond funds to achieve an efficient portfolio with a 13% expected return. This problem involves portfolio theory concepts like the Capital Allocation Line (CAL) and efficient frontier. Learn how to calculate optimal asset weights using weighted averages and correlation.

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