Portfolio Risk and Return: Part II: practice question
Lakemont University endowment — two-fund allocation
Danielle Osei, CFA, is a portfolio manager at Whitmore & Vale Advisors, where she is responsible for the Lakemont University endowment. The endowment distributes 4% of its market value each year to fund scholarships, pays no income taxes, and has an essentially perpetual time horizon. Osei is updating the endowment's investment policy statement while she evaluates a simple two-fund allocation for the portfolio.
The proposed allocation places 60% of the endowment in the Norcliff Global Equity Fund and 40% in the Ardenmead Bond Fund. Osei's capital market assumptions, together with each fund's expected return, standard deviation, beta, and proposed weight, are shown in Exhibits 1 and 2. She assumes returns on the two funds are jointly normally distributed.
Osei computes the combined portfolio's expected return and standard deviation, derives its beta and the return the capital asset pricing model requires, and ranks the three investments with the Sharpe and Treynor measures before finalizing her recommendation to the endowment's trustees.
| Fund | Expected return | Standard deviation | Beta | Weight |
|---|---|---|---|---|
| Norcliff Global Equity Fund | 12.0% | 20.0% | 1.20 | 60% |
| Ardenmead Bond Fund | 6.0% | 8.0% | 0.50 | 40% |
| Assumption | Value |
|---|---|
| Risk-free rate | 3.0% |
| Expected return on the market portfolio | 9.0% |
| Correlation between the two funds' returns | 0.25 |
Using the CAPM and the beta of the combined portfolio, the required return for the endowment portfolio is closest to:
- 8.10%
- 10.20%
- 8.52%
Show answer and explanation
Correct answer: C
Working: Beta_p = 0.60(1.20) + 0.40(0.50) = 0.92; E(R) = 3.0% + 0.92(9.0% - 3.0%) = 3.0% + 5.52% = 8.52%.
Explanation: Portfolio beta is the weighted average of the fund betas, 0.92, and applying it to a 6% market risk premium gives 3.0% + 5.52% = 8.52%. The 10.20% figure uses the equity fund's beta of 1.20 alone, overstating the portfolio's systematic risk. The 8.10% figure uses the simple average beta of 0.85, (1.20 + 0.50)/2, which ignores the 60/40 weighting.
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