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 Treynor measure, which of the three investments offers the highest excess return per unit of systematic risk?
- The Norcliff Global Equity Fund
- The Ardenmead Bond Fund
- The 60/40 combined portfolio
Show answer and explanation
Correct answer: A
Working: Treynor: equity = (12.0 - 3.0)/1.20 = 7.50%; bond = (6.0 - 3.0)/0.50 = 6.00%; portfolio = (9.6 - 3.0)/0.92 = 7.17%; highest is the equity fund.
Explanation: The Treynor measure divides excess return by beta, giving 7.50% for the equity fund, 7.17% for the combined portfolio, and 6.00% for the bond fund, so the equity fund ranks first per unit of systematic risk. The bond fund offers the lowest, not the highest, excess return per unit of beta despite its smaller absolute risk. The combined portfolio's Treynor measure is a beta-weighted blend of the two funds' measures and therefore falls between them, below the equity fund's.
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