Portfolio Management — CFA Level II practice questions

An institutional investor's IPS lists a 5-year minimum time horizon and tolerance for moderate drawdowns up to 15%. Mean-variance optimization yields a portfolio with expected 50% probability of breaching a 20% drawdown. The MOST appropriate response is to:

1. Mean-variance efficient frontier
2. Apply a downside-aware framework
3. Loss aversion in framing choices
4. Information ratio active per risk

Answer: B — Apply a downside-aware framework

A) Mean-variance efficient frontier — wrong optimization framework. B) Correct — this identifies Apply a downside-aware framework. C) Loss aversion in framing choices — wrong behavioral bias. D) Information ratio active per risk — look-alike metric.

A plan sponsor allocates a 300 bps total active risk budget across two managers: Manager X receives 60% of the active risk budget and has an information ratio of 0.50; Manager Y receives 40% of the budget and has an information ratio of 0.30. Using expected active return = information ratio × allocated active risk, the plan's total expected active return is closest to:

1. 2.40%, applying each manager's information ratio to the full 300 bps active risk budget rather than each manager's allocated share
2. 0.80%, summing the two information ratios directly (0.50 + 0.30) and treating the sum itself as a return figure
3. 1.26%, summing each manager's information ratio multiplied by its allocated share of the active risk budget
4. 1.14%, allocating the risk-budget shares to the wrong managers (60% to Manager Y and 40% to Manager X)

Answer: C — 1.26%, summing each manager's information ratio multiplied by its allocated share of the active risk budget

A) Applies each manager's IR to the entire 300 bps budget instead of the manager's own allocated share: 0.50×3.00% + 0.30×3.00% = 2.40%, double-counting the risk budget. B) Treats information ratios — a risk-adjusted metric — as if they were additive return figures, which is not a meaningful calculation. C) Correct — Manager X's allocated risk = 60% × 300 bps = 180 bps, contributing 0.50 × 1.80% = 0.90%; Manager Y's allocated risk = 120 bps, contributing 0.30 × 1.20% = 0.36%; total ≈ 1.26%. D) Swaps the 60%/40% allocation between the two managers, understating the contribution from the higher-IR manager: 0.50×1.20% + 0.30×1.80% = 0.60% + 0.54% = 1.14%.

A 65-year-old retiree with a $2M portfolio has guaranteed pension income covering 60% of expenses. The investor's risk capacity is:

1. HIGHER than for a similar retiree
2. Information ratio active per risk
3. Sharpe ratio total per total risk
4. Strategic asset allocation target

Answer: A — HIGHER than for a similar retiree

A) Correct — this identifies HIGHER than for a similar retiree without pension income. B) Information ratio active per risk — look-alike metric. C) Sharpe ratio total per total risk — look-alike metric. D) Strategic asset allocation target — related concept, not the definition.

A portfolio manager attributes last year's outperformance entirely to 'my superior stock-picking skill,' despite the portfolio being heavily overweight a sector that outperformed the broad market for macro reasons unrelated to individual stock selection. If the manager would likely attribute a future period of underperformance to bad luck or unfavorable market conditions rather than to their own decisions, this pattern is BEST described as:

1. Hindsight bias — believing, after the fact, that past events were more predictable than they actually were
2. Representativeness bias — judging probabilities based on how closely a situation resembles a familiar pattern or stereotype
3. Confirmation bias — selectively seeking out information that supports a pre-existing belief
4. Self-attribution bias — crediting good outcomes to one's own skill while attributing poor outcomes to external factors

Answer: D — Self-attribution bias — crediting good outcomes to one's own skill while attributing poor outcomes to external factors

A) Hindsight bias concerns the false belief that past outcomes were predictable in advance, not the asymmetric attribution of success versus failure described here. B) Representativeness concerns probability judgments based on resemblance to a familiar pattern, which is not what the scenario describes. C) Confirmation bias concerns selectively seeking confirming information, not the specific asymmetric crediting of outcomes to skill versus luck. D) Correct — self-attribution bias is precisely this pattern: taking credit for good outcomes as evidence of skill while blaming poor outcomes on external, uncontrollable factors.

Two uncorrelated (ρ = 0) strategies have identical expected returns of 8% and identical standalone volatilities of 15%. Combined in a 50/50 portfolio, the portfolio's expected return and volatility are closest to, respectively:

1. 8% return, 10.6% volatility, using the two-asset variance formula, where zero correlation reduces risk below the simple average of the two volatilities
2. 8% return, 15.0% volatility, averaging the two standalone volatilities directly and ignoring the diversification benefit from zero correlation
3. 16% return, 21.2% volatility, doubling both the expected return and the volatility as if the two positions were additive rather than weighted
4. 8% return, 21.2% volatility, computing √(15² + 15²) without applying the 50% portfolio weights to each variance term

Answer: A — 8% return, 10.6% volatility, using the two-asset variance formula, where zero correlation reduces risk below the simple average of the two volatilities

A) Correct — expected return = 0.5×8% + 0.5×8% = 8% (unaffected by correlation); volatility = √(0.5²×15² + 0.5²×15² + 0) = √(56.25 + 56.25) = √112.5 ≈ 10.6%. B) Treats volatility like a linearly averageable quantity, missing the diversification benefit that arises specifically because the two strategies are uncorrelated. C) Incorrectly treats combining two positions as additive (as if holding both at full weight) rather than as a weighted blend, inflating both return and risk. D) Omits the portfolio weights from the variance formula entirely, effectively assuming 100% exposure to each strategy simultaneously rather than 50%.

A retiree with a $2.5 million portfolio plans an initial-year withdrawal of $120,000, with subsequent withdrawals increased 3% annually for inflation. Relative to the traditional ~4% initial safe withdrawal rate guideline, this retiree's plan is BEST characterized as:

1. Conservative relative to the traditional 4% guideline, since the plan's initial withdrawal rate is below typical safe-withdrawal-rate estimates
2. Irrelevant to sustainability analysis, because the safe withdrawal rate framework applies only to fixed-dollar withdrawals, not inflation-adjusted ones
3. Guaranteed to succeed over a 30-year horizon, because the withdrawal rate is close to standard guidance and portfolio balances tend to mean-revert
4. Modestly aggressive relative to the traditional ~4% guideline, since the initial withdrawal rate of 4.8% exceeds it, raising the risk of portfolio depletion under adverse sequence-of-returns scenarios

Answer: D — Modestly aggressive relative to the traditional ~4% guideline, since the initial withdrawal rate of 4.8% exceeds it, raising the risk of portfolio depletion under adverse sequence-of-returns scenarios

A) Reverses the comparison — $120,000/$2,500,000 = 4.8%, which is ABOVE the ~4% guideline, not below it. B) Mischaracterizes the framework — the classic safe-withdrawal-rate research (e.g., the Bengen 4% rule) is specifically built around inflation-adjusted annual withdrawals, not fixed-dollar ones. C) No withdrawal-rate plan can be 'guaranteed' to succeed; sequence-of-returns risk means even withdrawal rates near standard guidance carry a meaningful probability of shortfall, especially when starting above the guideline. D) Correct — an initial withdrawal rate of 4.8% (120,000/2,500,000) exceeds the traditional ~4% guideline, which increases the risk of portfolio depletion, particularly if early returns are poor.

Under the Capital Asset Pricing Model, expected excess return on a security equals:

1. Availability heuristic bias
2. Herding bias among managers
3. Jensen's alpha CAPM residual
4. Beta × market excess return

Answer: D — Beta × market excess return

A) Availability heuristic bias — related concept, not the definition. B) Herding bias among managers — wrong behavioral bias. C) Jensen's alpha CAPM residual — related concept, not the definition. D) Correct — this identifies Beta × market excess return.

In a two-asset portfolio, Asset A (70% weight) has a marginal contribution to total risk (MCTR) of 12%, and Asset B (30% weight) has an MCTR of 20%. Asset B's contribution to total portfolio risk, as a percentage of total portfolio volatility, is closest to:

1. 30.0%, using Asset B's capital weight directly as its risk contribution
2. 20.0%, using Asset B's MCTR directly as its percentage risk contribution
3. 41.7%, using (weight × MCTR) for each asset divided by total portfolio risk
4. 58.3%, which is actually Asset A's contribution to total risk, not Asset B's

Answer: C — 41.7%, using (weight × MCTR) for each asset divided by total portfolio risk

A) Capital weight and risk contribution differ whenever assets have different volatilities/correlations; 30% ignores B's risk contribution entirely. B) MCTR alone is not a percentage contribution; it must be weighted by position size and scaled by total risk. C) Correct — total risk = (0.70×12) + (0.30×20) = 8.4 + 6.0 = 14.4; Asset B's share = 6.0/14.4 ≈ 41.7%. D) 8.4/14.4 ≈ 58.3% is Asset A's contribution — this answers the wrong asset.

A USD-based investor holds a EUR-denominated equity portfolio. If the EUR APPRECIATES against the USD by 5% while the portfolio's local-currency return is 8%, the USD return is approximately:

1. 1.16% per calc approx (rounded)
2. 0.95% per calc approx (rounded)
3. 1.05 × 1.08 − 1 = 13.4% approx
4. 1.26% per calc approx (rounded)

Answer: C — 1.05 × 1.08 − 1 = 13.4% approx

A) 1.16% per calc approx (rounded) — off-by-percent numeric trap. B) 0.95% per calc approx (rounded) — off-by-percent numeric trap. C) Correct — the computed value is 1.05 × 1.08 − 1 = 13.4%. D) 1.26% per calc approx (rounded) — off-by-percent numeric trap.

A risk parity strategy allocates between two uncorrelated assets so that each contributes equally to total portfolio risk. Asset 1 has a volatility of 10% and Asset 2 has a volatility of 25%. Using the simplified inverse-volatility approximation, Asset 1's approximate portfolio weight is closest to:

1. 71.4%, weighting each asset inversely proportional to its volatility and normalizing so the weights sum to 100%
2. 28.6%, inverting the weighting rule so the higher-volatility asset receives the larger allocation
3. 50.0%, allocating capital equally between the two assets regardless of their volatility difference
4. 86.2%, using inverse-variance (1/σ²) weighting rather than inverse-volatility (1/σ) weighting

Answer: A — 71.4%, weighting each asset inversely proportional to its volatility and normalizing so the weights sum to 100%

A) Correct — inverse-volatility weights: w1 ∝ 1/10 = 0.10, w2 ∝ 1/25 = 0.04; normalized, w1 = 0.10/(0.10+0.04) ≈ 71.4%. B) Applies the opposite rule, giving the higher-volatility asset (Asset 2) the larger weight, which would concentrate rather than equalize risk contribution. C) Naive equal-weighting ignores the volatility difference entirely and does not equalize each asset's contribution to total portfolio risk. D) Uses inverse-variance weighting (a minimum-variance-style approach) instead of the inverse-volatility approximation that risk parity typically uses, producing an overly concentrated 86.2% weight in the lower-volatility asset.

In a vignette: analyst is asked about implementing CFA Code while breaking firm policy. What's the priority?

CFA Code is the higher standard. If firm policy conflicts, member must follow CFA Code (and likely seek to change firm policy or disassociate from violations).

What is core-satellite portfolio?

Passive low-cost core (broad market) surrounded by active satellites pursuing alpha. Balances cost-efficiency and active management opportunities.

What are the components of the Treynor-Mazuy model?

Tests for market timing: r_p − r_f = α + β(r_m − r_f) + γ(r_m − r_f)². Significant γ > 0 implies market-timing skill.

In a vignette: a valuator applies the build-up method to estimate the cost of equity for a private company with no comparable public beta. What components are typically summed?

Risk-free rate + equity risk premium + size premium + company-specific (unsystematic) risk premium, plus an industry risk premium if used. Unlike CAPM, no beta adjustment is applied to the equity risk premium.