CFA Level IPortfolio ManagementHard
Two actively managed, well-diversified portfolios are being compared. Portfolio A has a return of 15%, a beta of 1.2; Portfolio B has a return of 18%, a beta of 1.8. The risk-free rate is 3%. Which portfolio performed better on a risk-adjusted basis using the appropriate measure for well-diversified portfolios, and what are the respective values?
- APortfolio B is better; Treynor A = 10.0, Treynor B = 8.33
- BPortfolio B is better; Sharpe A = 0.75, Sharpe B = 0.83
- CPortfolio A is better; Treynor A = 10.0, Treynor B = 8.33
- DPortfolio A is better; Sharpe A = 0.75, Sharpe B = 0.83
Show answer & explanationAnswer & explanation
Correct answer: C. Portfolio A is better; Treynor A = 10.0, Treynor B = 8.33
For well-diversified portfolios, the Treynor ratio (using systematic risk/beta) is the appropriate measure. Treynor A = (15%−3%)/1.2 = 10.0; Treynor B = (18%−3%)/1.8 = 8.33. Despite B's higher raw return, A delivers more excess return per unit of systematic risk, making it the better risk-adjusted performer.
Why the other options are wrong
- A. Correct calculations but incorrect conclusion—A actually has the higher Treynor ratio.
- B. Uses Sharpe ratio, which is less appropriate here since unsystematic risk should be diversified away in these portfolios; std devs weren't even given.
- D. Uses Sharpe ratio, which is inappropriate for well-diversified portfolios, and lacks needed standard deviation data to even compute it.
Treynor Ratio for Diversified Portfolios
The Treynor ratio measures excess return per unit of systematic risk (beta) and is most appropriate for evaluating well-diversified portfolios where unsystematic risk has been eliminated.
- Formula: (Rp − Rf) / βp
- Appropriate when portfolios are well-diversified (no unsystematic risk remains)
- Sharpe ratio is preferred for non-diversified or total portfolios using standard deviation
Memory trick: Diversified? Trust Treynor's beta-based test