Combining two risky assets
Series XXI-B case study · set 2, case 1 of 6 · 5 questions · 2 marks each
Question 1 of 5Case practice
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The case · stays here for all 5 questions
A manager builds a portfolio from Asset E and Asset D. E has an expected annual return of 16% and annual standard deviation of 20%. D has expected return 8% and standard deviation 10%. The proposed weights are 60% in E and 40% in D, with no leverage or cash position. The estimated correlation is 0.25. Use portfolio variance = wE²σE² + wD²σD² + 2wEwDσEσDρ, with all rates in decimal form. For one sensitivity question, change only correlation to zero. These are forward-looking estimates, not guarantees, and the manager has not assumed that either asset’s credit, liquidity or other risks disappear when the two are combined.
All amounts and contract terms in this case are hypothetical.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
A manager builds a portfolio from Asset E and Asset D. E has an expected annual return of 16% and annual standard deviation of 20%. D has expected return 8% and standard deviation 10%. The proposed weights are 60% in E and 40% in D, with no leverage or cash position. The estimated correlation is 0.25. Use portfolio variance = wE²σE² + wD²σD² + 2wEwDσEσDρ, with all rates in decimal form. For one sensitivity question, change only correlation to zero. These are forward-looking estimates, not guarantees, and the manager has not assumed that either asset’s credit, liquidity or other risks disappear when the two are combined.
All amounts and contract terms in this case are hypothetical.
Q1What is the portfolio’s expected return?
Option A. 12.80% — Correct answer
Option B. 24.00%
Why it is wrong: This adds the two returns without weights.
Option C. 12.00%
Why it is wrong: This gives both assets equal weight.
Option D. 9.60%
Why it is wrong: This counts only E’s contribution.
Answer: A. 60% × 16% + 40% × 8% = 12.80%. Remember: Expected returns combine linearly at fixed weights.
Hint, shown before you answer in practice mode: Take the weighted average of expected returns.
XXIB-S2-C01-Q1easynumerical
Q2What is the covariance between E and D in decimal-return units?
Option A. 0.250
Why it is wrong: This treats correlation as covariance.
Option B. 0.005 — Correct answer
Option C. 0.020
Why it is wrong: This omits correlation.
Option D. 0.050
Why it is wrong: This is ten times the correct result.
Answer: B. Covariance = 0.25 × 0.20 × 0.10 = 0.005. Remember: Correlation is unitless. Covariance also depends on asset volatilities.
Hint, shown before you answer in practice mode: Covariance equals correlation times both standard deviations.
XXIB-S2-C01-Q2mediumnumerical
Q3What is the portfolio variance at correlation 0.25?
Option A. 0.0256
Why it is wrong: This squares the weighted-average standard deviation and ignores covariance structure.
Option B. 0.1840
Why it is wrong: This misplaces a decimal.
Option C. 0.0184 — Correct answer
Option D. 0.0160
Why it is wrong: This assumes zero correlation.
Answer: C. Variance = 0.6²×0.2² + 0.4²×0.1² + 2×0.6×0.4×0.2×0.1×0.25 = 0.0184. Remember: The covariance term is essential in portfolio risk.
Hint, shown before you answer in practice mode: Include both squared-weight terms and the cross term.
XXIB-S2-C01-Q3hardnumerical
Q4What is the resulting portfolio standard deviation?
Option A. About 13.56% — Correct answer
Option B. 16.00%
Why it is wrong: This is the weighted-average volatility, not portfolio volatility.
Option C. 18.40%
Why it is wrong: This multiplies variance by 1,000 rather than taking its square root.
Option D. 1.84%
Why it is wrong: This reports variance as if it were standard deviation.
Answer: A. √0.0184 × 100 = about 13.56%. Remember: Risk measured as standard deviation is the square root of variance.
Hint, shown before you answer in practice mode: Take the square root of the decimal variance, then convert to percent.
XXIB-S2-C01-Q4mediumnumerical
Q5If correlation alone becomes zero, what happens to the estimated standard deviation?
Option A. It stays at 13.56%
Why it is wrong: Correlation changes the cross term.
Option B. It rises to 16%
Why it is wrong: Removing positive covariance lowers risk here.
Option C. It falls to about 12.65% — Correct answer
Option D. It becomes zero
Why it is wrong: Each asset still has its own variance.
Answer: C. New variance is 0.0144 + 0.0016 = 0.016. Its square root is 12.6491%. The expected return remains 12.80% under unchanged return estimates. Remember: Lower correlation can reduce risk without changing weighted expected return.
Hint, shown before you answer in practice mode: Set only the covariance term to zero.
XXIB-S2-C01-Q5hardnumerical
Returns when the client adds money midway
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