Portfolio Risk and Return: Part I: 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 |
The expected return and standard deviation of the proposed 60/40 allocation are closest to:
- 9.6% and 15.2%
- 9.6% and 13.2%
- 8.4% and 13.2%
Show answer and explanation
Correct answer: B
Working: E(Rp) = 0.60(12.0%) + 0.40(6.0%) = 9.6%; sigma_p^2 = (0.60 x 20)^2 + (0.40 x 8)^2 + 2(0.60)(0.40)(0.25)(20)(8) = 144.00 + 10.24 + 19.20 = 173.44; sigma_p = 13.17%, or about 13.2%.
Explanation: The return is the weighted average of the two expected returns, and the variance adds the correlation-adjusted cross term, giving a standard deviation of 13.17% that reflects the diversification benefit of a 0.25 correlation. The 15.2% figure is the weighted average of the two standard deviations, which holds only if the funds were perfectly positively correlated and ignores diversification. The 8.4% return comes from swapping the weights, 0.40(12.0%) + 0.60(6.0%), misapplying the 60/40 allocation.
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