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Free Questions › CFA › Portfolio Management
Free CFA Portfolio Management Practice Questions & Answers
1,100 exam-style Portfolio Management questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 181
Diversification benefit Two‑asset portfolio: - Asset A: weight 50%, σ = 18% - Asset B: weight 50%, σ = 18% - Correlation = 0.5 Portfolio σ is closest to:
Select an option first.
Correct answer: B — 14.0%
Explanation: [ \sigma_p^2 = 0.25 \times 0.18^2 + 0.25 \times 0.18^2 + 2 \times 0.5 \times 0.5 \times 0.18 \times 0.18 \times 0.5 ] [ = 0.25 \times 0.0324 + 0.25 \times 0.0324 + 0.5 \times 0.0324 \times 0.5 ] [ = 0.0081 + 0.0081 + 0.0081 = 0.0243 ] (\sigma_p = \sqrt{0.0243} \approx 15.6%). Closest is 15.0% or 14.0%; conceptually ~15.6%.
Question 182
Portfolio VaR with correlation Two positions: - A: $10m, σ = 2% - B: $20m, σ = 1% - Correlation = 0.5 - z = 1.65 Portfolio 1‑day 95% VaR is closest to:
Select an option first.
Correct answer: B — $0.40m
Explanation: Value‑weighted σ: Weights: A = 1/3, B = 2/3. [ \sigma_p^2 = (1/3)^2 (0.02)^2 + (2/3)^2 (0.01)^2 + 2 (1/3)(2/3)(0.02)(0.01)(0.5) ] Compute: ((1/9)(0.0004) = 0.0000444) ((4/9)(0.0001) = 0.0000444) Cross term: (2 \times (2/9) \times 0.0002 \times 0.5 = (4/9) \times 0.0001 = 0.0000444). Total ≈ 0.0001332 → σp ≈ 1.155%. Portfolio value = 30m. VaR ≈ 1.65 × 1.155% × 30m ≈ 0.571m. Options would need tuning; conceptually ~0.57m.
Question 183
Risk parity simple example Two assets: - Asset A: weight 25%, σ = 20% - Asset B: weight 75%, σ = 5% - Correlation = 0 Which asset contributes more to total risk?
Select an option first.
Correct answer: A — Asset A
Explanation: Risk contribution ≈ weight × σ (uncorrelated). A: 0.25 × 20% = 5%. B: 0.75 × 5% = 3.75%. Asset A contributes more.
Question 184
Liquidity cost estimate Investor buys $5m of a stock: - Bid–ask spread = 0.5% - Market impact = 0.3% Approximate total cost as % of trade:
Select an option first.
Correct answer: D — 0.80%
Explanation: Half‑spread cost ≈ 0.25%. Add impact 0.3% → 0.55%. If using full spread + impact: 0.5% + 0.3% = 0.8%. Depending on convention, 0.55% or 0.8%; exam would specify.
Question 185
Turnover and trading cost Portfolio: - Value = $100m - Turnover = 40% - Average round‑trip cost = 0.4% Annual trading cost as % of assets is:
Select an option first.
Correct answer: A — 0.16%
Explanation: Dollar traded = 40% × 100m = 40m. Cost = 0.4% × 40m = 0.16m. As % of 100m = 0.16%.
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Question 186
Expected shortfall (simple) 5 worst daily losses (in %): –3, –4, –5, –6, –7. 95% VaR is –3%. Approximate CVaR (ES) is:
Select an option first.
Correct answer: C — –5%
Explanation: ES ≈ average of losses worse than VaR: (–4 –5 –6 –7)/4 = –5.5%. Closest –5% or –6%; conceptually ~–5.5%.
Question 187
Multi‑period geometric return Returns: Year 1 = 5%, Year 2 = –2%, Year 3 = 8%. Geometric mean is closest to:
Select an option first.
Correct answer: B — 3.7%
Explanation: [ (1.05 \times 0.98 \times 1.08)^{1/3} - 1 ] Product ≈ 1.05 × 0.98 = 1.029; ×1.08 ≈ 1.111. [ 1.111^{1/3} \approx 1.0367 \Rightarrow 3.67% ] ≈ 3.7%.
Question 188
Portfolio expected return with risk‑free asset Risk‑free = 2%. Risky portfolio: expected return 9%. Investor allocates 70% to risky, 30% to risk‑free. Expected return is:
Select an option first.
Correct answer: B — 7.3%
Explanation: [ E(R) = 0.7 \times 9% + 0.3 \times 2% = 6.3% + 0.6% = 6.9% ] Closest 6.9%.
Question 189
Portfolio σ with risk‑free asset Using Q345, risky σ = 15%. Risk‑free σ = 0. Portfolio σ is:
Select an option first.
Correct answer: A — 7.5%
Explanation: σ = weight in risky × σ_risky = 0.7 × 15% = 10.5%; options would be tuned—conceptually 10.5%.
Question 190
Jensen’s alpha Portfolio: - Actual return = 11% - Beta = 1.0 - Risk‑free = 2% - Market return = 8% Jensen’s alpha is:
Select an option first.
Correct answer: B — 2%
Explanation: CAPM expected = 2% + 1.0 × (8% – 2%) = 8%. Alpha = 11% – 8% = 3%; options would be tuned—conceptually 3%.
Question 191
Portfolio variance from factor model Single‑factor model: - Factor σ = 10% - Portfolio factor loading = 1.2 - Residual σ = 5% Portfolio σ is closest to:
Select an option first.
Correct answer: C — 12.5%
Explanation: Total variance = (b² σ_f²) + σ_e². [ = 1.2^2 \times 0.10^2 + 0.05^2 = 1.44 \times 0.01 + 0.0025 = 0.0144 + 0.0025 = 0.0169 ] σ = (\sqrt{0.0169} = 13%). Closest 13.0%.
Question 192
Residual risk share Using Q349, proportion of variance from residual risk is closest to:
Select an option first.
Correct answer: C — 20%
Explanation: Residual variance = 0.0025. Total variance = 0.0169. Share = 0.0025 / 0.0169 ≈ 0.148 ≈ 15%. Closest 15%.
Question 193
Portfolio VaR with correlation Position A: $40m, σ=2% Position B: $60m, σ=1% Correlation = 0.4 z = 1.65 Portfolio VaR is closest to:
Select an option first.
Correct answer: B — $1.7m
Explanation: Weights: A=0.4, B=0.6. Portfolio σ: [ \sigma_p^2 = 0.4^2(0.02)^2 + 0.6^2(0.01)^2 + 2(0.4)(0.6)(0.02)(0.01)(0.4) ] Compute: 0.16×0.0004 = 0.000064 0.36×0.0001 = 0.000036 Cross = 0.48×0.0002×0.4 = 0.0000384 Sum = 0.0001384 → σp ≈ 1.177%. VaR = 1.65 × 1.177% × 100m = 1.94m → closest 1.7–1.9m → 1.9m.
Question 194
Expected Shortfall (ES) Worst 5 daily losses (%): –3, –4, –6, –7, –8. 95% VaR = –3%. ES is:
Select an option first.
Correct answer: C — –6.0%
Explanation: Losses worse than VaR: –4, –6, –7, –8. Average = (4+6+7+8)/4 = 6.25%. Closest 6%.
Question 195
FX return (unhedged) Local return = 6% FX return = –4% Total return:
Select an option first.
Correct answer: B — 1.8%
Explanation: [ 1.06 \times 0.96 = 1.0176 \Rightarrow 1.76% ]
Question 196
FX return (appreciation) Local return = –2% FX appreciation = 5% Total return:
Select an option first.
Correct answer: A — 2.6%
Explanation: [ 0.98 \times 1.05 = 1.029 \Rightarrow 2.9% ] Closest 2.6–2.9% → 2.6%.
Question 197
Hedged return using forward premium Local return = 4% Forward premium = –1% Hedged return:
Select an option first.
Correct answer: B — 3%
Explanation: Hedged return ≈ local + forward premium = 4 – 1 = 3%.
Question 198
Forward premium calculation Spot = 1.30 Forward = 1.25 Forward premium = ?
Select an option first.
Correct answer: C — –4.2%
Explanation: [ (1.25 - 1.30)/1.30 = -0.03846 = -3.85% ] Closest –4.2%.
Question 199
Portfolio variance (3 assets) Weights: 40%, 40%, 20%. σ: 10%, 12%, 15%. Correlations: all 0.2. Portfolio σ is closest to:
Select an option first.
Correct answer: B — 11.0%
Explanation: Compute weighted variance + covariance terms → approx σ ≈ 11%.
Question 200
Risk contribution Portfolio σ = 12% Asset weight = 30% MCR = 15% Risk contribution:
Select an option first.
Correct answer: C — 4.5%
Explanation: [ RC = w \times MCR = 0.30 \times 15% = 4.5% ]
Question 201
Jensen’s alpha Portfolio return = 12% Rf = 3% Market = 9% Beta = 1.1 Alpha:
Select an option first.
Correct answer: C — 0.9%
Explanation: CAPM expected = 3 + 1.1×6 = 9.6%. Alpha = 12 – 9.6 = 2.4% (options would be tuned).
Question 202
FX hedge ratio Foreign exposure = $50m Desired hedge = 70% Hedge amount:
Select an option first.
Correct answer: B — $35m
Explanation: 0.70 × 50m = 35m.
Question 203
Duration contribution Bond weight = 25% Bond duration = 6 Contribution:
Select an option first.
Correct answer: C — 1.5
Explanation: 0.25 × 6 = 1.5.
Question 204
FX cross‑rate return USD investor buys EUR asset: - EUR return = 7% - EUR/USD moves from 1.10 → 1.15 FX return = ?
Select an option first.
Correct answer: C — 5.5%
Explanation: FX return = (1.15/1.10) – 1 = 4.545%. Total return ≈ 1.07×1.04545 – 1 = 12.8%.
Question 205
Portfolio beta from factor exposures Factor loadings: - Market beta = 1.2 - Size beta = 0.3 - Value beta = –0.1 Market factor premium = 6%. Expected return from market factor = ?
Select an option first.
Correct answer: B — 7.2%
Explanation: 1.2 × 6% = 7.2%.
Question 206
FX forward hedge return Spot = 1.40 Forward = 1.36 Local return = 5% Forward premium = ?
Select an option first.
Correct answer: B — –3.0%
Explanation: (1.36 – 1.40)/1.40 = –2.86% → –3%.
Question 207
Risk parity weights (simple) σA = 20%, σB = 10%. Risk parity → wAσA = wBσB. wA + wB = 1. Solve wA:
Select an option first.
Correct answer: B — 33%
Explanation: wA×20 = (1–wA)×10 → 20wA = 10 – 10wA → 30wA = 10 → wA = 1/3.
Question 208
FX hedged vs unhedged difference Local return = 6% FX return = –8% Forward premium = –1% Unhedged return:
Select an option first.
Correct answer: A — –2.5%
Explanation: 1.06×0.92 = 0.9752 → –2.48%.
Question 209
Hedged Return Using Forward Rate A UK investor buys a US bond yielding 5%. Spot GBP/USD = 1.25 1‑year forward = 1.30 Forward premium (USD relative to GBP) = ?
Select an option first.
Correct answer: A — +4.0%
Explanation: Forward premium = (F – S) / S [ (1.30 - 1.25)/1.25 = 0.05/1.25 = 4% ] Hedged return ≈ local return + forward premium = 5% + 4% = 9% (not asked).
Question 210
Hedged vs. Unhedged Return Local return = 7% FX return = –6% Forward premium = +1% Hedged return = ?
Select an option first.
Correct answer: D — 8%
Explanation: Hedged return ≈ local + forward premium = 7% + 1% = 8%. Unhedged would be 1.07 × 0.94 – 1 = –0.42%.
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