IMC Performance Measurement and Attribution 2 — Questions and Answers
Question 1: The Sharpe ratio measures excess return per unit of which type of risk?
- Systematic risk (beta)
- Total risk (standard deviation) (Correct answer)
- Tracking error
- Downside deviation
Correct answer: Total risk (standard deviation)
Sharpe ratio = (Portfolio return − Risk-free rate) / Standard deviation of portfolio returns, capturing return per unit of total risk.
Question 2: A portfolio returns 15%, the risk-free rate is 4%, and the portfolio's beta is 1.1. What is the Treynor ratio?
- 11.0
- 10.0 (Correct answer)
- 13.6
- 8.0
Correct answer: 10.0
Treynor ratio = (Portfolio return − Risk-free rate) / Beta = (15% − 4%) / 1.1 = 10.0.
Question 3: Jensen's alpha is best described as:
- Excess return over the risk-free rate divided by beta
- The portfolio's actual return minus its CAPM-expected return given its level of systematic risk (Correct answer)
- The difference between portfolio return and benchmark return divided by tracking error
- Portfolio return divided by its standard deviation
Correct answer: The portfolio's actual return minus its CAPM-expected return given its level of systematic risk
Jensen's alpha = Actual return − [Risk-free rate + beta × (Market return − Risk-free rate)], measuring outperformance relative to what CAPM predicts.
Question 4: Tracking error is defined as the standard deviation of:
- Portfolio absolute returns over time
- Benchmark returns over time
- Active returns (portfolio return minus benchmark return) (Correct answer)
- Risk-free rate deviations from expectations
Correct answer: Active returns (portfolio return minus benchmark return)
Tracking error measures the variability of a portfolio's returns relative to its benchmark, quantifying active risk.
Question 5: The information ratio is calculated as:
- Active return / Portfolio standard deviation
- Active return / Tracking error (Correct answer)
- Portfolio return / Benchmark return
- Excess return / Beta
Correct answer: Active return / Tracking error
Information ratio = Active return / Tracking error, measuring the reward earned per unit of active risk taken relative to the benchmark.
Question 6: Which risk-adjusted performance measure is most appropriate when evaluating a portfolio that forms one component of a larger, well-diversified overall portfolio?
- Sharpe ratio
- Treynor ratio (Correct answer)
- Information ratio
- Sortino ratio
Correct answer: Treynor ratio
The Treynor ratio uses systematic risk (beta) in its denominator and is the preferred measure when the portfolio is a component of a broader diversified portfolio where unsystematic risk is already eliminated.
Question 7: A portfolio manager achieves a Sharpe ratio of 0.85 compared to the market's Sharpe ratio of 0.60. What does this indicate?
- The portfolio has higher absolute returns than the market
- The portfolio has earned more excess return per unit of total risk than the market (Correct answer)
- The portfolio has a higher beta than the market
- The portfolio holds less systematic risk than the market
Correct answer: The portfolio has earned more excess return per unit of total risk than the market
A higher Sharpe ratio means the portfolio has generated more excess return above the risk-free rate for each unit of total risk (standard deviation) relative to the market.
IMC Performance Measurement and Attribution 2
The Sharpe ratio measures excess return per unit of which type of risk?