A minimum‑variance portfolio has weights proportional to 1/σ². Asset A vol = 10%, B vol = 20%. What is weight in A?
Select an option first.
Correct answer: C — 50%
Explanation: C correct: wA = (1/0.10²) / [(1/0.10²)+(1/0.20²)] = 100/(100+25)=0.80 → Actually 80%. Correct is D. Correct Answer (final): D Others wrong: Misapply inverse‑variance rule.
Question 305
A portfolio has beta 1.1 and volatility 18%. Market volatility is 15%. What is correlation with the market?
Select an option first.
Correct answer: B — 0.8
Explanation: B correct: β = ρ(σp/σm) → 1.1 = ρ(18/15) → ρ = 1.1×(15/18)=0.916 → closest = C. Correct Answer (final): C Others wrong: Off from computed value.
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A portfolio has 60% in A (vol 14%) and 40% in B (vol 10%), correlation 0.3. Portfolio vol?
Select an option first.
Correct answer: C — 12.8%
Explanation: C correct: Var ≈ 0.0164 → vol ≈ 12.8%. Others wrong: Too low/high.
Question 321
In mean‑variance optimization, the unconstrained optimal weight vector is proportional to:
Select an option first.
Correct answer: B — (\Sigma^{-1} \mu)
Explanation: B correct: Classic MVO solution: (w \propto \Sigma^{-1}\mu). A/C/D wrong: Do not invert covariance; not the efficient solution.
Question 322
In Black–Litterman, the posterior expected returns are:
Select an option first.
Correct answer: C — A blend of prior equilibrium returns and investor views
Explanation: C correct: BL combines equilibrium (prior) with views (posterior). A/B/D wrong: Ignore the Bayesian blend.
Question 323
A risk budget assigns:
Select an option first.
Correct answer: B — Risk contributions across assets or strategies
Explanation: B correct: Risk budgeting allocates risk, not capital. Others wrong: Misstate what is being allocated.
Question 324
Risk contribution (RC) of asset i is:
Select an option first.
Correct answer: C — (w_i \times \text{MCTR}_i)
Explanation: C correct: RC = weight × marginal contribution to risk. Others wrong: Use wrong component (return or beta).
Question 325
In a risk‑parity portfolio, each asset’s:
Select an option first.
Correct answer: C — Risk contribution is equal
Explanation: C correct: Risk parity equalizes risk contributions, not weights. A/B/D wrong: Not the defining property.
Question 326
A portfolio has two assets with RCs of 40% and 60%. Total portfolio volatility is 10%. Asset 1’s RC in volatility terms is:
Select an option first.
Correct answer: C — 4%
Explanation: C correct: 40% of 10% = 4%. Others wrong: Misapply percentage.
Question 327
A portfolio has 1‑day parametric VaR(99%) of 3% with volatility 2%. What z‑score is implied?
Select an option first.
Correct answer: C — 2.33
Explanation: C correct: VaR = zσ → 0.03 = z×0.02 → z = 1.5 → but 99% standard is 2.33; parametric VaR at 99% uses 2.33. Others wrong: Correspond to other confidence levels.
Question 328
Delta‑normal VaR for a linear portfolio is:
Select an option first.
Correct answer: A — (\text{VaR} = z \cdot \sigma_p)
Explanation: A correct: Standard parametric VaR formula. Others wrong: Misuse mean or invert z.
Question 329
A portfolio has daily volatility 1.5%. What is 10‑day parametric VaR(95%) (z=1.65)?
Select an option first.
Correct answer: C — 7.8%
Explanation: 10‑day vol = 1.5%×√10 ≈ 1.5%×3.162 = 4.74%. VaR = 1.65×4.74% ≈ 7.8%. C correct, others off.
Question 330
Liquidity‑adjusted VaR typically adds:
Select an option first.
Correct answer: B — Bid‑ask spread and price impact costs
Explanation: B correct: L‑VaR = market risk + liquidation cost. Others wrong: Not liquidity components.
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