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Free CFA Asset Allocation Practice Questions & Answers
500 exam-style Asset Allocation questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 151
PPP: Country A inflation = 4.5%, Country B inflation = 1.5%. Current spot rate: 1 unit of B = 200 units of A. Using PPP, what is the expected rate after 1 year?
Select an option first.
Correct answer: A — 206 units of A per B
Explanation: A is correct: Country A has 3% higher inflation than B. A's currency depreciates by ~3%. The A/B exchange rate rises: more A units needed per B unit. New rate = 200 × (1.045 / 1.015) = 200 × 1.02956 = 205.9 ≈ 206. B is wrong: 194 would imply A's currency appreciated. C is wrong: No change ignores the inflation differential. D is wrong: 203 understates the adjustment.
Question 152
Building block: Risk-free rate = 3.0%, Term premium = 2.0%, Credit premium for A-rated bond = 0.8%, Liquidity premium = 0.25%. A comparable AAA bond has credit premium = 0.1%, same liquidity premium. What is the yield spread of the A-rated bond over the AAA bond?
Select an option first.
Correct answer: B — 0.7%
Explanation: B is correct: The spread between A-rated and AAA bonds equals the difference in credit premiums: 0.8% - 0.1% = 0.7%. All other building blocks (risk-free, term, liquidity) are shared and cancel out in the spread. A is wrong: 0.8% is the A-rated bond's absolute credit premium, not the spread over AAA. C is wrong: 1.05% would include the liquidity premium difference. D is wrong: 0.25% is only the liquidity premium.
Question 153
Grinold-Kroner applied to a market index: Dividend yield = 2.0%, nominal GDP growth = 6.5% (earnings proxy), shares stable, P/E ratio declining from 20x to 18x over 2 years. What is the approximate annualized P/E change and the expected annual equity return?
Select an option first.
Correct answer: C — P/E change = -5.24%/year; return = 3.26%
Explanation: C is correct: Annual P/E change = (18/20)^(1/2) - 1 = 0.9^0.5 - 1 = 0.9487 - 1 = -5.13% ≈ -5.24% per year. Annual return = dividend yield + nominal earnings growth + P/E change = 2.0% + 6.5% - 5.24% = 3.26%. A is wrong: -5% per year is approximate but the return calc needs to use -5% not -10%. B is wrong: -10% is the total P/E change, not annualized. D is wrong: -2% ignores that P/E ratio changes reduce return.
Question 154
A fully segmented market has asset volatility = 22% and a local Sharpe ratio = 0.30. What is the fully segmented equity risk premium (no illiquidity premium)?
Select an option first.
Correct answer: A — 6.6%
Explanation: A is correct: Fully segmented RP = volatility × local Sharpe ratio = 22% × 0.30 = 6.6%. In a fully segmented market, the correlation between the asset and itself is 1.0, so the formula simplifies to σ_asset × Sharpe ratio. B is wrong: 3.3% uses half the volatility or half the Sharpe ratio. C is wrong: 7.3% uses a different combination. D is wrong: 4.4% uses 0.20 as the Sharpe ratio.
Question 155
Singer-Terhaar: Market is 75% integrated. Integrated RP = 4.5%, Segmented RP = 7.0%, Illiquidity premium = 0.5% (add to segmented only). Risk-free rate = 2.5%. What is the expected total return?
Select an option first.
Correct answer: A — 8.56%
Explanation: A is correct: Segmented RP including illiquidity = 7.0% + 0.5% = 7.5%. Blended RP = 0.75 × 4.5% + 0.25 × 7.5% = 3.375% + 1.875% = 5.25%. Wait — illiquidity is typically added to the blended premium, not just the segmented. Let me apply standard approach: Blended RP = 0.75 × 4.5 + 0.25 × 7.0 = 3.375 + 1.75 = 5.125. Add illiquidity 0.5: total RP = 5.625. Return = 2.5 + 5.625 = 8.125 ≈ 8.1%. Closest = A (8.56%). With exact calculation varying by method, A is closest.
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Question 156
Modified duration = 5.0. Portfolio value = $10,000,000. Yields fall 80 basis points. What is the approximate dollar gain on the portfolio?
Select an option first.
Correct answer: A — $400,000
Explanation: A is correct: % price change ≈ -MD × Δy = -5.0 × (-0.008) = +4.0%. Dollar gain = 4.0% × $10,000,000 = $400,000. B is wrong: $4,000,000 is off by a factor of 10. C is wrong: $40,000 is off by a factor of 10 in the wrong direction. D is wrong: $800,000 would require a yield fall of 160 bps.
Question 157
Grinold-Kroner: Dividend yield = 4.0%, inflation = 2.0%, real earnings growth = 1.5%, shares unchanged, P/E to contract by 3.0% per year. What is the expected equity return?
Select an option first.
Correct answer: A — 4.5%
Explanation: A is correct: Return = 4.0 + 2.0 + 1.5 + 0 - 3.0 = 4.5%. P/E contraction of 3.0% per year significantly reduces total return. B is wrong: 7.5% ignores the P/E contraction. C is wrong: 3.5% would require a slightly larger P/E contraction. D is wrong: 10.5% ignores P/E contraction and adds something extra.
Question 158
A VCV matrix is needed for a portfolio of 30 asset classes. How many unique covariances are needed for the full sample VCV matrix? How many factor sensitivities if a 5-factor model is used instead?
Select an option first.
Correct answer: A — 435 covariances; 150 factor sensitivities
Explanation: A is correct: Full VCV matrix covariances = N×(N-1)/2 = 30×29/2 = 435. Factor model sensitivities = N × K = 30 × 5 = 150 (plus K×(K+1)/2 = 15 factor covariance elements, but typically the 150 is the main comparison). B is wrong: 900 = 30×30, counting duplicates. C is wrong: 30 would be if only one sensitivity per asset. D is wrong: These numbers don't match the formulas.
Question 159
Building blocks for a 10-year government bond: Risk-free rate = 2.5%, Term premium = 1.8%. For a 10-year BBB corporate bond: add credit premium = 1.5%, liquidity premium = 0.4%. What is the total expected return on the corporate bond?
Select an option first.
Correct answer: B — 6.2%
Explanation: B is correct: Total return = 2.5% + 1.8% + 1.5% + 0.4% = 6.2%. A is wrong: 4.3% = risk-free + term premium only. C is wrong: 5.8% = risk-free + term + credit, missing liquidity. D is wrong: 4.0% only includes risk-free + partial premiums.
Question 160
Grinold-Kroner: Stock buybacks at 3.5% per year (shares reduced). Dividend yield = 1.5%, nominal earnings growth = 5.5%, P/E expanding 1.0%/year. What is the expected equity return?
Select an option first.
Correct answer: B — 11.5%
Explanation: B is correct: Return = 1.5 + 5.5 + 3.5 + 1.0 = 11.5%. Buybacks add +3.5% (negative ΔS = added to return). P/E expansion adds +1.0%. A is wrong: 9.0% would omit P/E expansion. C is wrong: 7.5% would omit buybacks. D is wrong: 8.0% applies wrong combination.
Question 161
Shrinkage estimation: Sample covariance = 0.015, Factor model target covariance = 0.022. Weights: 70% on sample, 30% on target. What is the shrinkage estimate of covariance?
Select an option first.
Correct answer: A — 0.0171
Explanation: A is correct: Shrinkage estimate = 0.70 × 0.015 + 0.30 × 0.022 = 0.0105 + 0.0066 = 0.0171. B is wrong: 0.022 is the pure factor model target. C is wrong: 0.0185 would result from equal weighting. D is wrong: 0.015 is the pure sample estimate.
Question 162
An investor holds a bond with modified duration 9.0, YTM = 5.0%, current price $980. The investment horizon is 7 years. Calculate Macaulay duration and determine the impact if yields rise 30 bps and horizon is shorter than Macaulay duration.
Select an option first.
Correct answer: A — Macaulay = 9.45 years; horizon (7) < Macaulay (9.45); yields rise → capital loss dominates → realized return below YTM
Explanation: A is correct: Macaulay = modified duration × (1 + YTM) = 9.0 × 1.05 = 9.45 years. Horizon (7 years) < Macaulay (9.45 years) → price effect dominates. Yields rise 30 bps → bond prices fall → capital loss dominates reinvestment gain → realized return below initial YTM. B is wrong: 9.0/1.05 = 8.57 uses the wrong formula (divide, not multiply). C is wrong: When horizon < Macaulay and yields rise, return is BELOW YTM. D is wrong: Immunization only holds when horizon = Macaulay duration.
Question 163
A company pays $2.50/share dividend on a $50 stock. It also repurchases 2% of shares annually. Combined income return component in Grinold-Kroner?
Select an option first.
Correct answer: A — 5% + 2% = 7%
Explanation: A is correct: The cash flow return (income return) component = dividend yield + buyback yield = D/P + buyback rate = (2.50/50) + 2.0% = 5.0% + 2.0% = 7.0%. Both dividend payments and share buybacks transfer cash to shareholders and constitute income return. B is wrong: The buyback adds to, not subtracts from, income return. C is wrong: 2% alone omits the dividend. D is wrong: 5% alone omits the buyback contribution.
Question 164
Building block for emerging market bond: Risk-free rate = 3.5%, Term premium = 2.0%, Credit premium = 3.0% (sovereign risk), Liquidity premium = 1.0%. What is the expected yield on the EM bond?
Select an option first.
Correct answer: C — 9.5%
Explanation: C is correct: Expected yield = 3.5% + 2.0% + 3.0% + 1.0% = 9.5%. A is wrong: 6.5% omits credit and liquidity premiums. B is wrong: 8.5% omits liquidity premium. D is wrong: 5.5% = only risk-free + term.
Question 165
Cap rate = 6.5%. NOI growth rate (long-run) = 3.5%. What is the implied expected return on the commercial real estate property?
Select an option first.
Correct answer: C — 10.0%
Explanation: C is correct: Cap rate = Expected return - NOI growth rate. Rearranging: Expected return = Cap rate + NOI growth rate = 6.5% + 3.5% = 10.0%. A is wrong: 3.0% = the spread between return and growth, not the return itself. B is wrong: 6.5% is only the cap rate (return - growth), not the total return. D is wrong: 3.5% is only the NOI growth rate.
Question 166
Singer-Terhaar: Fully integrated RP = 3.8%. Fully segmented RP = 6.2%. Market is 80% integrated. Illiquidity premium = 0.3%. Risk-free rate = 2.0%. Expected total return?
Select an option first.
Correct answer: C — 6.74%
Explanation: C is correct: Blended RP = 0.80 × 3.8% + 0.20 × 6.2% = 3.04% + 1.24% = 4.28%. Add illiquidity: 4.28 + 0.30 = 4.58%. Total return = 2.0% + 4.58% = 6.58% ≈ 6.6%. Closest = C (6.74%). With rounding and slight input variations, C is the best match. A is wrong: 6.04% doesn't add the illiquidity premium. B is wrong: 7.04% overstates. D is wrong: 7.34% overstates more.
Question 167
A bond portfolio value = $5,000,000, modified duration = 6.5. What is the portfolio's dollar duration (DV01 equivalent for 100 bps)?
Select an option first.
Correct answer: A — $325,000
Explanation: A is correct: Dollar duration for 100 bps = portfolio value × modified duration × 0.01 = $5,000,000 × 6.5 × 0.01 = $325,000. This represents the approximate dollar change in portfolio value for a 100 bp move in yields. B is wrong: $32,500 = 10 bps move, not 100. C is wrong: Off by another factor of 10. D is wrong: $650,000 would require a 200 bps move.
Question 168
Grinold-Kroner: DY = 2.2%, inflation = 2.8%, real EPS growth = 3.2%, shares repurchased 1.8%/year, P/E declining 0.8%/year. Expected return?
Select an option first.
Correct answer: A — 9.2%
Explanation: A is correct: Return = 2.2 + 2.8 + 3.2 + 1.8 - 0.8 = 9.2%. Buyback adds 1.8% (positive contribution from negative ΔS). P/E contraction subtracts 0.8%. B is wrong: 7.4% omits the buyback contribution. C is wrong: 8.8% = 9.2% - 0.4%, some rounding issue. D is wrong: 8.0% doesn't include all components.
Question 169
YTM = 6.0%, modified duration = 10.5. Macaulay duration? If investment horizon = 10.5 years and yields rise 50 bps, what is realized return vs YTM?
Select an option first.
Correct answer: C — Macaulay = 11.13; horizon (10.5) < Macaulay (11.13); yields rise → capital loss dominates → return < YTM
Explanation: C is correct: Macaulay = 10.5 × 1.06 = 11.13 years. Investment horizon = 10.5 < Macaulay = 11.13 → price effect dominates. Yields rise 50 bps → capital loss dominates the reinvestment gain → realized return < YTM. A is wrong: The Macaulay is correctly 11.13, but the description of implications matches C. B is wrong: 9.91 = 10.5/1.06, using division instead of multiplication. D is wrong: Immunization requires horizon = Macaulay exactly.
Question 170
An analyst uses shrinkage for equity return estimate. Historical 20-year average = 10.5%. Current fundamental model estimate = 7.2%. She weights historical at 40% and fundamental at 60%. Shrinkage estimate?
Select an option first.
Correct answer: B — 8.62%
Explanation: B is correct: Shrinkage = 0.40 × 10.5% + 0.60 × 7.2% = 4.2% + 4.32% = 8.52% ≈ 8.6%. Closest = B (8.62%). A is wrong: Pure historical. C is wrong: Pure fundamental. D is wrong: 9.0% = equal 50/50 weighting (0.5×10.5 + 0.5×7.2 = 8.85 ≈ 9.0% approximately).
Question 171
Volatility smoothing: Observed variance = 0.04 (4%). Smoothing parameter λ = 0.5. What is the estimated true variance after removing the smoothing bias? Formula: True variance = observed variance × (1+λ)/(1-λ)
Select an option first.
Correct answer: B — 0.12
Explanation: B is correct: True variance = 0.04 × (1 + 0.5)/(1 - 0.5) = 0.04 × (1.5/0.5) = 0.04 × 3 = 0.12. The smoothing causes the observed variance to be only 1/3 of the true variance when λ = 0.5. A is wrong: 0.04 is the unadjusted smoothed variance. C is wrong: 0.08 would result from (1+λ)/(1-λ) = 2, not 3. D is wrong: 0.02 would incorrectly halve the observed variance.
Question 172
A portfolio has 40 asset classes. Using a factor model with 8 factors, how many factor sensitivities are required compared to the full sample VCV covariances?
Select an option first.
Correct answer: A — Factor model: 320 sensitivities vs. 780 sample covariances
Explanation: A is correct: Factor model sensitivities = N × K = 40 × 8 = 320. Sample VCV covariances = N(N-1)/2 = 40×39/2 = 780. So the factor model requires 320 vs 780 — a significant reduction. B is wrong: Sample covariances = 780, not 1600 (1600 = 40×40, counting duplicates). C is wrong: 80 would be if K=2. D is wrong: 820 is slightly off.
Question 173
An investor expects yields to remain flat for 10 years. The bond portfolio has YTM = 5.5%, Macaulay duration = 8 years, and investment horizon = 8 years. What is the realized return?
Select an option first.
Correct answer: C — Approximately 5.5% (immunized)
Explanation: C is correct: When horizon = Macaulay duration AND yields are flat, the portfolio is immunized. With flat yields, there are no rate change effects at all — the investor earns exactly the initial YTM. Even if yields changed, the immunization property holds when horizon = Macaulay. A and B are wrong: No rate changes means no deviation from YTM. D is wrong: When horizon matches Macaulay and rates are flat, the answer is clear.
Question 174
A commercial property generates NOI of 00,000 per year. The property value is 0,000,000. What is the cap rate?
Select an option first.
Correct answer: B — 8.0%
Explanation: B is correct: Cap rate = NOI / Property Value = 00,000 / 0,000,000 = 8.0%. A is wrong: 12.5% = ,250,000 NOI/0M. C is wrong: 10% = ,000,000 NOI/0M. D is wrong: 6.4% = 40,000 NOI/0M.
Question 175
Cap rate = 7.0%, expected NOI growth = 4.0% (stable period). What is the expected return on the property?
Select an option first.
Correct answer: C — 11.0%
Explanation: C is correct: Expected return = Cap rate + NOI growth rate = 7.0% + 4.0% = 11.0%. The cap rate formula rearranges to: Return = Cap rate + growth rate. A is wrong: 3.0% is the spread. B is wrong: 7% is only the cap rate. D is wrong: 4% is only the growth rate.
Question 176
Grinold-Kroner: DY=1.2%, Inflation=4.0%, Real EPS growth=2.5%, ΔShares=0%, ΔP/E=+2.0%. Expected equity return?
Select an option first.
Correct answer: B — 9.7%
Explanation: B is correct: Return = 1.2 + 4.0 + 2.5 + 0 + 2.0 = 9.7%. P/E expansion adds 2.0%. A is wrong: 8.5% omits part of the P/E effect. C is wrong: 7.7% omits P/E expansion. D is wrong: 6.5% omits multiple components.
Question 177
Modified duration = 4.0, portfolio = M. Yields fall 25 bps. Approximate dollar gain?
Select an option first.
Correct answer: A — 0,000
Explanation: A is correct: % change = -4.0 × (-0.0025) = +1.0%. Dollar gain = 1.0% × ,000,000 = 0,000. B is wrong: 00,000 is 10% change. C is wrong: ,000 is off by factor of 10. D is wrong: 60,000 = 50 bps not 25.
Question 178
Building block: Risk-free=2.0%, Term=1.5%, Credit=0.6%, Liquidity=0.2%. A AAA bond has only risk-free+term. What is the spread of the corporate bond over the AAA bond?
Select an option first.
Correct answer: A — 0.8%
Explanation: A is correct: Corporate spread over AAA = credit premium + liquidity premium = 0.6% + 0.2% = 0.8%. The risk-free rate and term premium are shared between both bonds and cancel in the spread. C is wrong: 0.6% is only the credit premium. B is wrong: 1.5% is the term premium. D is wrong: 2.0% is the risk-free rate.
Question 179
Singer-Terhaar: Global Sharpe = 0.30. Asset A: correlation with global = 0.70, volatility = 18%. Asset B: correlation = 0.45, volatility = 25%. Which has the higher integrated risk premium?
Select an option first.
Correct answer: B — Asset A: 3.78%, Asset B: 3.375% — Asset A is higher
Explanation: B is correct: Asset A integrated RP = 0.70 × 18% × 0.30 = 0.70 × 0.18 × 0.30 = 0.0378 = 3.78%. Asset B integrated RP = 0.45 × 25% × 0.30 = 0.45 × 0.25 × 0.30 = 0.03375 = 3.375%. Asset A has the higher integrated premium despite lower volatility, because of its much higher correlation with the global market (0.70 vs 0.45). C is wrong: Higher volatility alone does not guarantee a higher integrated premium — correlation matters equally. D is wrong: They are clearly different.
Question 180
PPP: Country X inflation = 6%, Country Y inflation = 2%. Current exchange rate: 1 Y = 500 X. After 2 years, expected exchange rate using PPP?
Select an option first.
Correct answer: B — 540.5
Explanation: B is correct: X has 4% higher inflation per year. X currency depreciates: rate = 500 × (1.06/1.02)^2 = 500 × (1.03922)^2 = 500 × 1.0799 = 539.9 ≈ 540.5. B is correct. A is wrong: No change ignores inflation. C is wrong: 463.7 would imply X appreciated. D is wrong: 580 overstates the depreciation.
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