Unit study guide · NISM Series XXI-B
Performance measurement and evaluation of Portfolio Managers
8 questions in this unit
What this unit covers
- Which return measure neutralises client-controlled external cash-flow timing when evaluating the manager’s investment performance?
- What is a central aim of the Global Investment Performance Standards?
- A portfolio gains 20% in year one and loses 20% in year two, with no cash flows. What is its geometric annual return?
- A performance review uses annual portfolio return of 14%, risk-free return of 5% and portfolio standard deviation of 18%. The measures cover the same period and use the same frequency. What is the Sharpe ratio?
- The same performance review records annual return of 14%, risk-free return of 5% and portfolio beta of 1.2. All inputs are measured consistently. What is the Treynor measure, expressed as return per unit of beta?
- The performance review reports portfolio return of 14% and benchmark return of 11%. Tracking error, the standard deviation of active returns, is 3% on the same annual basis. What is the information ratio?
- The performance review records portfolio return of 14%, benchmark market return of 11%, risk-free return of 5% and beta of 1.2. Treat the benchmark as the market proxy for the stated capital asset pricing model. What is Jensen’s alpha?
- The review shows portfolio return of 14%, risk-free return of 5%, portfolio volatility of 18% and benchmark volatility of 12%. Use the same period and assume risk-free mixing is feasible. What is the M² risk-adjusted return level, not its difference from benchmark return?
Key ideas
From the practice bank · 1
Which return measure neutralises client-controlled external cash-flow timing when evaluating the manager’s investment performance?
Time-weighted return links subperiod returns around external cash flows so their timing does not drive the performance measure. Money-weighted return instead reflects the investor’s cash-flow experience. Remember: The choice of return measure should reflect who controls external cash flows.
Hint Consider a measure that links returns between external cash-flow events. Common mistake: Using total rupee profit to compare managers handling different contribution schedules.
XXI-B-137From the practice bank · 2
What is a central aim of the Global Investment Performance Standards?
The standards promote fair representation and full disclosure of investment performance. They should not be described as a guarantee of returns or investment suitability. Remember: Performance standards improve reporting discipline rather than assure future investment success.
Hint Separate standards for reporting results from promises about the results themselves. Common mistake: Treating a standards claim as proof that a portfolio cannot lose money.
XXI-B-138From the practice bank · 3
A portfolio gains 20% in year one and loses 20% in year two, with no cash flows. What is its geometric annual return?
The geometric annual return is approximately −2.02% because wealth ends at 96% of its starting value. Two-year growth factor = 1.20 × 0.80 = 0.96. Annual geometric return = √0.96 − 1 = −0.020204, or about −2.02%. Remember: Equal percentage gains and losses do not cancel when compounded.
Hint Find the ending wealth factor before converting it to a constant annual rate. Common mistake: Using the arithmetic average to describe multi-year wealth growth.
XXI-B-139From the practice bank · 4
A performance review uses annual portfolio return of 14%, risk-free return of 5% and portfolio standard deviation of 18%. The measures cover the same period and use the same frequency. What is the Sharpe ratio?
The Sharpe ratio is 0.50 because the 9% excess return is half the 18% standard deviation. Working: (14% − 5%) ÷ 18% = 9% ÷ 18% = 0.50. Remember: Sharpe measures excess return per unit of total return volatility.
Hint Identify the return above the baseline and the measure of total volatility. Common mistake: Using total return rather than excess return in the numerator.
XXI-B-140From the practice bank · 5
The same performance review records annual return of 14%, risk-free return of 5% and portfolio beta of 1.2. All inputs are measured consistently. What is the Treynor measure, expressed as return per unit of beta?
The Treynor measure is 7.50% per unit of beta because the excess return is 9%. Working: (14% − 5%) ÷ 1.2 = 7.50%. Remember: Treynor and Sharpe use different risk denominators.
Hint Use systematic market sensitivity rather than total portfolio volatility. Common mistake: Replacing beta with standard deviation or multiplying by beta.
XXI-B-141From the practice bank · 6
The performance review reports portfolio return of 14% and benchmark return of 11%. Tracking error, the standard deviation of active returns, is 3% on the same annual basis. What is the information ratio?
The information ratio is 1.00 because the 3% active return equals the 3% tracking error. Working: (14% − 11%) ÷ 3% = 1.00. Remember: The information ratio compares benchmark-relative return with benchmark-relative risk.
Hint Use the benchmark difference and the variability of that difference. Common mistake: Using the risk-free rate or total portfolio return in place of benchmark-relative return.
XXI-B-142From the practice bank · 7
The performance review records portfolio return of 14%, benchmark market return of 11%, risk-free return of 5% and beta of 1.2. Treat the benchmark as the market proxy for the stated capital asset pricing model. What is Jensen’s alpha?
Jensen’s alpha is 1.80 percentage points because the portfolio exceeds its 12.20% model-required return. Market premium = 11% − 5% = 6%. Required return = 5% + 1.2 × 6% = 12.20%. Alpha = 14% − 12.20% = 1.80 percentage points. Remember: Jensen’s alpha adjusts the return comparison for systematic market exposure.
Hint Find the model-required return at this beta before evaluating the residual. Common mistake: Calling raw outperformance over the market the same thing as beta-adjusted alpha.
XXI-B-143From the practice bank · 8
The review shows portfolio return of 14%, risk-free return of 5%, portfolio volatility of 18% and benchmark volatility of 12%. Use the same period and assume risk-free mixing is feasible. What is the M² risk-adjusted return level, not its difference from benchmark return?
The M² adjusted return level is 11.00% because the portfolio’s excess return is scaled down to benchmark volatility. Excess return = 14% − 5% = 9%. Volatility ratio = 12% ÷ 18% = 2/3. Adjusted return = 5% + 9% × 2/3 = 11%. This answer is the adjusted return level, not the benchmark-relative M² difference. Remember: State whether M² refers to an adjusted return level or its benchmark-relative difference.
Hint Scale the portfolio’s excess return to benchmark volatility, then restore the baseline. Common mistake: Reversing the volatility ratio or omitting the risk-free component.
XXI-B-144