Two assets whose risks do not move together
Series X-A case study · set 2, case 8 of 9 · 5 questions · 2 marks each
Question 1 of 5Case practice
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An adviser compares two equally weighted portfolios. Both use assets with expected returns of 12% and 6%, and standard deviations of 20% and 10%, respectively. In Portfolio A, the correlation between the assets is zero. In Portfolio B it is +1. All figures are annual and use the same measurement period. For a separate beta calculation, the first asset has beta 1.2 and the second beta 0.4, against the same market benchmark. There is no leverage or short selling. Treat forecasts and historical estimates as uncertain. Use the two-asset variance formula. Do not simply average standard deviations when correlation is below +1.
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.
An adviser compares two equally weighted portfolios. Both use assets with expected returns of 12% and 6%, and standard deviations of 20% and 10%, respectively. In Portfolio A, the correlation between the assets is zero. In Portfolio B it is +1. All figures are annual and use the same measurement period. For a separate beta calculation, the first asset has beta 1.2 and the second beta 0.4, against the same market benchmark. There is no leverage or short selling. Treat forecasts and historical estimates as uncertain. Use the two-asset variance formula. Do not simply average standard deviations when correlation is below +1.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Q1What expected return do both 50/50 portfolios have?
Option A. 9% — Correct answer
Option B. 12%
Why it is wrong: This ignores the second asset.
Option C. 18%
Why it is wrong: This adds returns without applying weights.
Option D. 6%
Why it is wrong: This ignores the first asset.
Answer: A. 0.50 × 12% + 0.50 × 6% = 9%. Correlation affects risk, not this weighted mean. Remember: Portfolio expected return depends on weights and asset expected returns.
Hint, shown before you answer in practice mode: Use the same weights in both portfolios.
XA-S2-C08-Q1mediumnumerical
Q2What is Portfolio A’s standard deviation, to two decimal percentage points?
Option A. 15.00%
Why it is wrong: This averages standard deviations as if correlation were +1.
Option B. 11.18% — Correct answer
Option C. 5.00%
Why it is wrong: This subtracts weighted risks without justification.
Option D. 12.50%
Why it is wrong: This confuses variance with standard deviation.
Answer: B. Variance = 0.5² × 20² + 0.5² × 10² = 125 in squared percentage units. Standard deviation = √125 = 11.18%. Remember: Diversification requires combining variances and covariance before taking a square root.
Hint, shown before you answer in practice mode: With zero correlation, the covariance term is zero.
XA-S2-C08-Q2hardnumerical
Q3What is Portfolio B’s standard deviation?
Option A. 30%
Why it is wrong: This adds unweighted asset risks.
Option B. 15% — Correct answer
Option C. 11.18%
Why it is wrong: This is the zero-correlation result.
Option D. 10%
Why it is wrong: This ignores the risk contribution of the first asset.
Answer: B. 0.50 × 20% + 0.50 × 10% = 15%. Remember: Perfect positive correlation removes this form of diversification benefit.
Hint, shown before you answer in practice mode: At correlation +1 and positive weights, weighted standard deviations add.
XA-S2-C08-Q3mediumnumerical
Q4What is the beta of either equally weighted portfolio?
Option A. 1.60
Why it is wrong: This adds betas without weights.
Option B. 1.20
Why it is wrong: This uses only the first asset’s beta.
Option C. 0.40
Why it is wrong: This uses only the second asset’s beta.
Option D. 0.80 — Correct answer
Answer: D. 0.50 × 1.2 + 0.50 × 0.4 = 0.80. Remember: Beta measures exposure to the chosen benchmark, not total volatility.
Hint, shown before you answer in practice mode: Portfolio beta is the weighted average of component betas.
XA-S2-C08-Q4mediumnumerical
Q5Using only the supplied expected return and standard deviation, which portfolio offers the better trade-off for a risk-averse client?
Option A. Portfolio A, because it has the same expected return and lower estimated volatility. — Correct answer
Option B. Portfolio B, because +1 correlation guarantees gains.
Why it is wrong: Correlation does not guarantee a positive return.
Option C. Both have equal volatility because weights are equal.
Why it is wrong: Correlation differs and changes portfolio variance.
Option D. Portfolio A, because zero correlation removes all risk.
Why it is wrong: Its standard deviation remains above zero.
Answer: A. Both forecast 9%, but A has about 11.18% volatility versus B’s 15%. On these estimates, A offers the lower risk for the same expected return. Remember: A portfolio can dominate another on a stated risk-return comparison without being risk-free.
Hint, shown before you answer in practice mode: Compare return and risk jointly without making a guarantee.
XA-S2-C08-Q5mediumapplication
A complaint about misleading performance
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