Use the stated covariance model
Each question supplies the relevant model condition. Volatility contributions refer to the weighted Euler decomposition, not a standalone risk number or a capital percentage. Do not assume every component is positive.
Explain the missing condition
The wrong alternatives remove a required weight, change a signed quantity into an absolute one or divide by zero. A coherence check also needs the joint matrix rather than only individual correlation labels.
Try the questions
For positive portfolio volatility, which expression is the weighted Euler contribution of asset i?
- A.
Cov(Ri,RP)/σP
- B.
wi Cov(Ri,RP)/σP
- C.
wi σi in every model
Answer and explanation
Answer: B
Weighted contributions sum to portfolio volatility in the stated homogeneous model.
- A
This is the marginal contribution before applying capital weight.
- B
The weight turns the marginal quantity into the component.
- C
This drops covariance with the portfolio.
Two components are +8 and −6 percentage points. What is their signed total?
- A.
14 percentage points
- B.
2 percentage points
- C.
0 because a negative component is invalid
Answer and explanation
Answer: B
Positive capital weights can still have negative risk contributions.
- A
This adds magnitudes and removes the offset.
- B
The negative term remains negative.
- C
Negative covariance can produce a negative component.
Total portfolio volatility is exactly zero. How should volatility-based contribution shares be handled?
- A.
Assign 50% each automatically
- B.
Mark them undefined
- C.
Take absolute values first
Answer and explanation
Answer: B
The variance and standard deviation can be defined as zero while these ratios are undefined.
- A
That invents shares without a defined denominator.
- B
The relevant ratio divides by zero.
- C
That does not resolve the zero denominator.
Every individual pair correlation lies in [−1,1]. Does that establish a valid larger covariance matrix?
- A.
Yes, because the pair bounds are sufficient
- B.
No; joint coherence needs assessment
- C.
Yes if the matrix has more than two assets
Answer and explanation
Answer: B
A valid joint model must produce nonnegative quadratic variance for every weight vector.
- A
The joint matrix can still fail positive semidefiniteness.
- B
The three-asset −0.8 counterexample produces negative variance.
- C
Adding assets increases the need for a joint check.