Comparing performance after adjusting for risk
Series X-A case study · set 3, case 8 of 9 · 5 questions · 2 marks each
Question 1 of 5Case practice
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Over the same year, Portfolio P earns 12% and has annual standard deviation 16%. Portfolio Q earns 10% with standard deviation 8%. The common risk-free rate is 4%. Their estimated betas are 1.2 and 0.6 respectively, and the broad market return is 9%. All figures are on the same annual basis. Use Sharpe ratio as excess return divided by standard deviation. For a separate CAPM comparison, expected return equals the risk-free rate plus beta times the market risk premium. These are retrospective estimates for an educational comparison, not guaranteed future returns. No external cash flows or fee differences affect the supplied returns.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
Over the same year, Portfolio P earns 12% and has annual standard deviation 16%. Portfolio Q earns 10% with standard deviation 8%. The common risk-free rate is 4%. Their estimated betas are 1.2 and 0.6 respectively, and the broad market return is 9%. All figures are on the same annual basis. Use Sharpe ratio as excess return divided by standard deviation. For a separate CAPM comparison, expected return equals the risk-free rate plus beta times the market risk premium. These are retrospective estimates for an educational comparison, not guaranteed future returns. No external cash flows or fee differences affect the supplied returns.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Q1What is Portfolio P’s Sharpe ratio?
Option A. 0.75
Why it is wrong: This divides total return by volatility without subtracting the risk-free rate.
Option B. 0.50 — Correct answer
Option C. 0.25
Why it is wrong: This uses only the risk-free rate in the numerator.
Option D. 2.00
Why it is wrong: This reverses the numerator and denominator.
Answer: B. (12% − 4%)/16% = 0.50. Remember: Sharpe ratio measures excess return per unit of total volatility.
Hint, shown before you answer in practice mode: Use the excess return over 4%.
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Q2What is Portfolio Q’s Sharpe ratio?
Option A. 1.33
Why it is wrong: This reverses volatility and excess return.
Option B. 1.25
Why it is wrong: This divides total return by volatility.
Option C. 0.75 — Correct answer
Option D. 0.50
Why it is wrong: This is Portfolio P’s ratio.
Answer: C. (10% − 4%)/8% = 0.75. Remember: Lower raw return can still produce higher risk-adjusted performance.
Hint, shown before you answer in practice mode: Q earns 6 percentage points over the risk-free rate.
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Q3What CAPM return corresponds to P’s beta of 1.2?
Option A. 6.00%
Why it is wrong: This is only P’s beta-adjusted market premium.
Option B. 14.80%
Why it is wrong: This multiplies beta by the total market return rather than its premium.
Option C. 10% — Correct answer
Option D. 9.00%
Why it is wrong: This is the broad market return, whose beta is one.
Answer: C. 4% + 1.2 × (9% − 4%) = 10%. Remember: CAPM applies beta to the excess market return.
Hint, shown before you answer in practice mode: The market premium is 9% minus 4%.
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Q4What is P’s realised return above that CAPM benchmark?
Option A. −2 percentage points
Why it is wrong: This reverses actual and benchmark returns.
Option B. 3 percentage points
Why it is wrong: This subtracts the raw market return.
Option C. 8 percentage points
Why it is wrong: This subtracts only the risk-free rate.
Option D. 2 percentage points — Correct answer
Answer: D. 12% − 10% = 2 percentage points. This is an estimated alpha under the specified model. Remember: Alpha depends on the chosen risk model and inputs.
Hint, shown before you answer in practice mode: Compare P’s actual 12% with its 10% CAPM benchmark.
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Q5Which conclusion is supported by the Sharpe comparison alone?
Option A. Q must have the higher raw return.
Why it is wrong: Its raw return is 10%, below P’s 12%.
Option B. Q will certainly outperform P next year.
Why it is wrong: Past risk-adjusted results do not guarantee future performance.
Option C. P is risk-free because its alpha is positive.
Why it is wrong: P has substantial reported volatility.
Option D. Q delivered more excess return per unit of total volatility during the measured year. — Correct answer
Answer: D. Q’s Sharpe ratio is 0.75 versus P’s 0.50. That compares the past risk-adjusted outcomes, not future certainty or every kind of risk. Remember: A performance metric supports a limited, clearly defined comparison.
Hint, shown before you answer in practice mode: Keep the conclusion within the measure and time period used.
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