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Free CFA Performance Measurement Practice Questions & Answers
300 exam-style Performance Measurement questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 61
A manager generates alpha of +2% with residual risk of 4%. Calculate the appraisal ratio. What does a higher appraisal ratio indicate?
Select an option first.
Correct answer: B — AR = alpha / residual risk (σε) = 2% / 4% = 0.50. A higher appraisal ratio indicates the manager generates more alpha per unit of RESIDUAL (non-systematic, idiosyncratic) risk taken. Since residual risk represents risk that is not compensated by market beta, a higher AR means the manager is being compensated more efficiently for taking active risk.
Explanation: B is correct: AR = α / σε = 2% / 4% = 0.50. A higher AR is better — it means more alpha generated per unit of residual (unexplained, idiosyncratic) risk. The residual risk (σε) represents volatility that is not explained by market factor exposure. A manager who takes significant residual risk (concentrated positions, sector bets beyond the model's factors) and generates proportionate alpha is efficient; one who takes high residual risk for little alpha is inefficient. AR of 0.50 is a reasonable result — the reading doesn't provide specific thresholds for 'good' vs. 'poor.'
Question 62
A portfolio has: upside capture ratio = 95%, downside capture ratio = 85%. Interpret these metrics. Is this manager ADDING VALUE through asymmetric performance?
Select an option first.
Correct answer: B — Upside capture = 95%: the manager captures 95% of the benchmark's gains in up markets (slightly underperforms in rising markets). Downside capture = 85%: the manager loses only 85% as much as the benchmark in down markets (protects better in falling markets). The asymmetry (95% upside, 85% downside) IS favorable — losing less on the downside than you sacrifice on the upside creates long-run value. This is the hallmark of a defensive-but-valuable manager.
Explanation: B is correct: The key is the ASYMMETRY between upside and downside capture, not whether each is above or below 100% independently. Upside capture of 95% means the manager slightly lags in bull markets — giving up 5% of the benchmark's gains. Downside capture of 85% means the manager significantly protects in bear markets — losing only 85% as much. Over a full market cycle, this asymmetry (more protection than sacrifice) typically adds long-run value. A perfect symmetrical manager would have 100%/100% — this manager gives up 5% on upside to gain 15% of downside protection — a favorable trade.
Question 63
A fund's annual portfolio returns vs. benchmark over 5 years: Year 1: +2%, Year 2: +1.5%, Year 3: −0.5%, Year 4: +1%, Year 5: +0.5% (all in active return terms). Calculate the average annual IR if tracking error = 1.1%.
Select an option first.
Correct answer: A — IR = 0.82
Explanation: A is correct: Mean active return = (2.0 + 1.5 − 0.5 + 1.0 + 0.5) / 5 = 4.5 / 5 = 0.90%. IR = 0.90% / 1.10% = 0.818 ≈ 0.82. Note: the tracking error of 1.1% is given directly; we don't need to recalculate it from the data. IR = 0.82 is a solid result for an active manager — 0.5+ is generally considered good, and this manager is well above that threshold. The single negative active return year (−0.5% in Year 3) is the main drag on the mean but doesn't substantially harm the overall IR.
Question 64
What are the LIMITATIONS of ALL appraisal measures discussed in the reading?
Select an option first.
Correct answer: B — Key limitations shared across appraisal measures: (1) Short performance histories — most managers have only 3-7 years of data; distinguishing skill from luck with high confidence requires 10+ years of observations; (2) Changing strategies — past performance data may not reflect current approach; (3) Survivorship bias in peer comparisons — failed funds exit databases; (4) Look-back bias — selecting evaluation periods favorable to the metric; (5) Non-stationarity of alpha — factors that generated alpha historically may be arbitraged away.
Explanation: B is correct: The reading notes: 'Unfortunately, many investment managers have only a few years of performance to evaluate, which makes it extremely difficult to differentiate between luck and skill through the appraisal process. It is recommended to have many years of observations to determine at an appropriately high confidence level that the manager truly possesses superior investment skill.' All the appraisal measures (Sharpe, IR, Sortino, etc.) are derived from historical data that may not persist. A lucky manager in a bull market can show high Sharpe and IR for several years — only extended track records provide meaningful statistical confidence.
Question 65
What is the SEQUENCE of calculations in the BHB attribution model? What must be computed FIRST?
Select an option first.
Correct answer: B — First: Calculate portfolio return and benchmark return for each segment and in total. Then: Compute the three effects for each segment using the formulas Allocation = (wi−Wi)×Bi, Selection = Wi×(Ri−Bi), Interaction = (wi−Wi)×(Ri−Bi). Sum each effect across all segments. Verify: total attribution = allocation + selection + interaction = portfolio return − benchmark return.
Explanation: B is correct: The logical sequence ensures consistency: (1) Establish total and segment-level portfolio and benchmark weights and returns; (2) Compute active weights (wi−Wi) and active returns within segments (Ri−Bi); (3) Apply formulas for each effect across all segments; (4) Sum each effect to get the total allocation, selection, and interaction contributions; (5) Verify the reconciliation. Computing total portfolio return and benchmark return first establishes the total active return that the attribution must explain — giving a reconciliation target before drilling into components.
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Question 66
Portfolio A: return=15%, β=1.5, σ=20%, Rf=4%, Rm=10%. Portfolio B: return=11%, β=0.8, σ=12%, Rf=4%, Rm=10%. Which has a higher TREYNOR ratio? Which has a higher SHARPE ratio?
Select an option first.
Correct answer: A — B has higher Treynor and higher Sharpe
Explanation: A is correct: Treynor A = (15%−4%)/1.5 = 11%/1.5 = 7.33. Treynor B = (11%−4%)/0.8 = 7%/0.8 = 8.75. B > A on Treynor. Sharpe A = (15%−4%)/20% = 11%/20% = 0.55. Sharpe B = (11%−4%)/12% = 7%/12% = 0.583. B > A on Sharpe. Portfolio A takes much higher risk (β=1.5 vs. 0.8; σ=20% vs. 12%) to earn only 4% more return. Portfolio B is more efficient on both risk-adjusted measures. D is wrong: absolute returns are irrelevant for evaluating risk-adjusted performance.
Question 67
What does it mean to have POSITIVE selection effect but NEGATIVE allocation effect in a sector? Give an example.
Select an option first.
Correct answer: B — Positive selection + negative allocation: the manager underweighted (or was correctly underweight in) a sector, but within that sector their specific stock picks outperformed. Example: Underweight Energy (allocation bet). Energy sector benchmark return = +15% (beats total benchmark of +10%), so the underweight was a BAD decision — negative allocation effect. But within Energy, the specific energy stocks held returned +20% (beats energy benchmark of +15%) — positive selection effect. The manager was wrong about the sector but right about specific stocks.
Explanation: B is correct: The two effects are independent — a manager can make a bad allocation decision while making a good selection decision within the same sector. The example illustrates: underweighting Energy when energy outperforms the market gives negative allocation (missed upside). But if the specific energy stocks held were the sector's best performers, selection is positive. The net contribution from energy to total active return = allocation + selection + interaction. The interaction (underweight × positive selection) would be negative — further penalizing the combination. This scenario reveals a manager who has stock-picking skill but poor sector-timing ability.
Question 68
In a BF model attribution: Tech sector portfolio weight = 45%, benchmark = 30%. Tech portfolio return = 20%, tech benchmark = 18%. Total benchmark return = 12%. Calculate BF allocation, selection, and interaction for Technology.
Select an option first.
Correct answer: B — BF Allocation = (wi−Wi)×(Bi−B) = (0.45−0.30)×(18%−12%) = 0.15×6% = +0.90%. Selection = Wi×(Ri−Bi) = 0.30×(20%−18%) = 0.30×2% = +0.60%. Interaction = (wi−Wi)×(Ri−Bi) = (0.45−0.30)×(20%−18%) = 0.15×2% = +0.30%. Total Tech contribution = 0.90+0.60+0.30 = +1.80%.
Explanation: B is correct: BF Allocation = (0.45−0.30) × (18%−12%) = 0.15 × 6% = +0.90%. This is positive: overweighted (0.15) a sector that beat the total benchmark by 6% — good allocation decision. Selection = 0.30 × (20%−18%) = 0.30 × 2% = +0.60%. Positive: manager's tech picks beat the tech benchmark by 2% — good stock selection. Interaction = (0.45−0.30) × (20%−18%) = 0.15 × 2% = +0.30%. Positive: both active decisions worked together. Total = 0.90+0.60+0.30 = +1.80% from the tech sector alone. A has minor calculation errors. B correctly applies all three BF/BHB formulas.
Question 69
What is the KEY DIFFERENCE between a RETURNS-BASED style analysis and a HOLDINGS-BASED style analysis for categorizing a manager?
Select an option first.
Correct answer: B — Returns-based style analysis regresses the manager's return history against style-factor returns (value, growth, size) to INFER the manager's average style exposure over time — useful when holdings are not disclosed. Holdings-based style analysis examines the ACTUAL securities held to directly identify style characteristics (P/B ratios, earnings growth rates, market caps). Holdings-based is more accurate and current; returns-based is more accessible but backward-looking and may miss style drift.
Explanation: B is correct: The distinction parallels the returns-based vs. holdings-based risk system distinction in Reading 12. For style analysis: returns-based infers style from the statistical relationship between the manager's returns and style factor returns — if the manager's returns correlate most with small-cap value, they are categorized as small-cap value. This may lag actual style changes. Holdings-based directly measures what the manager actually owns today — immediate, precise identification of style exposures. For a manager who recently shifted from value to growth, returns-based would still show 'value' (based on historical returns) while holdings-based would correctly show 'growth.'
Question 70
When does PERFORMANCE APPRAISAL become UNRELIABLE, and what is the minimum recommended evaluation period?
Select an option first.
Correct answer: B — Performance appraisal becomes unreliable when the evaluation period is too short to distinguish skill from luck statistically. The reading states 'it is recommended to have many years of observations to determine at an appropriately high confidence level that the manager truly possesses superior investment skill.' In practice, even 7-10 years may be insufficient if returns are volatile — a manager would need 20+ years of consistent outperformance for very high statistical confidence. With only 2-3 years, luck and skill are virtually indistinguishable.
Explanation: B is correct: The reading explicitly acknowledges this challenge: 'many investment managers have only a few years of performance to evaluate, which makes it extremely difficult to differentiate between luck and skill.' Statistical significance in performance evaluation requires many observations — and annual returns are few. A manager with 3 years of outperformance (12 quarterly observations) has very little statistical power. The signal-to-noise ratio in active returns is typically low, requiring many years to separate alpha from random variation. This is why professional due diligence typically examines multiple market cycles and qualitative factors alongside quantitative performance metrics.
Question 71
Calculate: A fixed-income manager has total return = 3.2%. Benchmark return = 2.8%. Yield curve decomposition shows: Yield = 2.0%, Roll = 0.3%, Shift = 0.5%, Shape = −0.1%, Spread = 0.4%, Residual = 0.1%. Benchmark components: Yield = 1.8%, Roll = 0.3%, Shift = 0.4%, Shape = 0.0%, Spread = 0.3%, Residual = 0.0%. Calculate attribution for each component and verify reconciliation.
Select an option first.
Correct answer: B — Active return by component: Yield = 2.0−1.8 = +0.20%. Roll = 0.3−0.3 = 0.00%. Shift = 0.5−0.4 = +0.10%. Shape = −0.1−0.0 = −0.10%. Spread = 0.4−0.3 = +0.10%. Residual = 0.1−0.0 = +0.10%. Total active attribution = 0.20+0.00+0.10−0.10+0.10+0.10 = +0.40% = 3.2%−2.8% ✓
Explanation: B is correct: Each component's active contribution = portfolio component return − benchmark component return. Yield: 2.0%−1.8% = +0.20% (manager earned more coupon income — likely held higher-yielding bonds). Roll: 0.3%−0.3% = 0.00% (identical roll exposure). Shift: 0.5%−0.4% = +0.10% (manager benefited more from yield curve fall — longer duration). Shape: −0.1%−0.0% = −0.10% (manager lost from curve shape change — perhaps positioned wrong way on curve steepening). Spread: 0.4%−0.3% = +0.10% (manager's credit exposure paid off). Residual: +0.10%. Total = +0.40% = active return ✓. Attribution fully reconciles.
Question 72
A sponsor uses MACRO attribution to evaluate two EXTERNAL MANAGERS. Manager A is a growth manager; Manager B is a value manager. Active return for Manager A vs. growth benchmark = +1.5%. Active return for the growth style vs. total benchmark = −2%. What conclusion can the SPONSOR draw about Manager A's contribution?
Select an option first.
Correct answer: B — Manager A generated +1.5% active return vs. their proper growth benchmark — demonstrating genuine stock-picking skill WITHIN the growth style. However, the sponsor's DECISION to allocate to growth (vs. staying with the total benchmark) cost −2% (style allocation effect). The total contribution from Manager A's involvement = −2% (sponsor's style allocation loss) + 1.5% (manager's skill) = −0.5% net. Manager A showed skill but the sponsor made a poor style allocation decision.
Explanation: B is correct: This illustrates the macro attribution framework. Total contribution to sponsor's portfolio from the growth allocation = (style return) + (manager's active return vs. style) = −2% + 1.5% = −0.5%. The sponsor's two separate decisions: (1) Allocate to growth style (bad — cost −2% vs. total benchmark); (2) Select Manager A to run the growth allocation (good — +1.5% vs. growth benchmark). Attribution separates these decisions: the manager should be credited with +1.5% skill; the sponsor's style allocation decision should be blamed for the −2%. This separation is the key value of macro attribution.
Question 73
What is the 'style return' for a small-cap manager if the manager's benchmark (Russell 2000) returned 9.1% and the market index (Wilshire 5000) returned 8.5%?
Select an option first.
Correct answer: A — Style return = 0.6%; this represents the performance advantage from investing in small-cap stocks during this period
Explanation: A is correct: Style return = manager's benchmark return − broad market return = 9.1% − 8.5% = +0.6%. This is directly from the reading's example. The style return decomposes performance into two parts: (1) How did the manager's style perform relative to the broad market? (style return = +0.6%); (2) How did the manager perform within their style? (active management return = portfolio − Russell 2000 = 8.9% − 9.1% = −0.2%). Total vs. market = 8.9% − 8.5% = +0.4% = style (+0.6%) + active management (−0.2%) ✓. The style return is market-driven — the manager can't control it; their skill is measured only by the active management component.
Question 74
In a SECTOR attribution for three sectors using BHB, the allocation effects are: Tech = +0.8%, Healthcare = −0.3%, Financials = +0.1%. Selection effects: Tech = −0.5%, Healthcare = +0.6%, Financials = −0.2%. Interaction effects: Tech = −0.1%, Healthcare = +0.1%, Financials = +0.0%. Total active return = ? Does the model reconcile?
Select an option first.
Correct answer: A — Total = 0.5%; model reconciles
Explanation: A is correct: Summing each effect: Allocation = 0.8 + (−0.3) + 0.1 = 0.6%. Selection = (−0.5) + 0.6 + (−0.2) = −0.1%. Interaction = (−0.1) + 0.1 + 0.0 = 0.0%. Total active return attributed = 0.6 + (−0.1) + 0.0 = +0.5%. The model reconciles if the portfolio's actual active return (portfolio return − benchmark return) equals +0.5%. Both A and B give the correct calculation — the question asks whether the model reconciles at +0.5%. A states this correctly.
Question 75
What is the MAXIMUM DRAWDOWN and drawdown duration for: Year 1 NAV $100 → Year 2 $110 → Year 3 $95 → Year 4 $90 → Year 5 $105 → Year 6 $115?
Select an option first.
Correct answer: A — Max drawdown = −18.2%; Duration = 4 years (Year 2 to Year 6)
Explanation: A is correct: Peak = Year 2 at $110. Subsequent values: Year 3 = $95, Year 4 = $90 (trough), Year 5 = $105, Year 6 = $115 (exceeds $110 peak for first time). Maximum drawdown = ($90 − $110) / $110 = −18.18% ≈ −18.2%. Drawdown duration: from Year 2 (peak) to Year 6 (first recovery to/above peak) = 4 years. D is wrong: the 2-year measurement is only the decline period, not the full drawdown duration. Drawdown duration = full time from initial peak to recovery to same level = 4 years.
Question 76
Calculate: Portfolio return = 9%, MAR = 5%. Downside returns (below MAR) over 12 months were: −2%, 3%(below MAR), 1%(below MAR), 4%(below MAR). Using 12 as the denominator: semivariance = [(−2−5)² + (3−5)² + (1−5)² + (4−5)²] / 12. Compute Sortino ratio.
Select an option first.
Correct answer: B — Squared deviations below MAR: (−2−5)² = 49; (3−5)² = 4; (1−5)² = 16; (4−5)² = 1. Sum = 70. Semivariance = 70/12 = 5.833. Semideviation = sqrt(5.833) = 2.415%. Sortino = (9%−5%) / 2.415% = 4% / 2.415% = 1.657 ≈ 1.66.
Explanation: B is correct: Following the reading's method (divide by TOTAL observations N, not just those below MAR): Deviations below MAR (5%): −2% gives (−2−5)² = 49; 3% gives (3−5)² = 4; 1% gives (1−5)² = 16; 4% gives (4−5)² = 1. Sum = 70. Semivariance = 70/12 = 5.833. Semideviation = sqrt(5.833) = 2.415%. Sortino = (9%−5%) / 2.415% = 4/2.415 = 1.657 ≈ 1.66. A (1.16) uses a different denominator. B shows the correct step-by-step calculation. Sortino of 1.66 indicates good risk-adjusted performance.
Question 77
A manager is described as 'correctly allocating to growth when growth outperforms.' In BHB terms, which condition must be TRUE?
Select an option first.
Correct answer: B — wi > Wi AND Bi > B — manager overweighted growth (wi > Wi) AND growth benchmark return (Bi) exceeded the total benchmark return (B). This is the BF model's definition of a correct allocation decision: overweighting a sector that beat the total benchmark. Under BHB: wi > Wi AND Bi > 0 (positive sector return) gives positive allocation, but this can be misleading if the sector returned less than the total benchmark.
Explanation: B is correct: The BF allocation effect = (wi − Wi) × (Bi − B). For the allocation effect to be positive AND reflect a correct decision: the manager must overweight the sector (wi > Wi, active weight > 0) AND the sector must beat the total benchmark (Bi > B). Only then does BF give a positive allocation with intuitive meaning: 'I overweighted something that beat the market.' Under BHB: allocation = (wi − Wi) × Bi — only requires positive sector return (Bi > 0) — this can give a misleading positive allocation even when the sector underperformed the total benchmark. The question about 'correctly allocating' most precisely maps to the BF condition.
Question 78
A fixed-income attribution shows SPREAD contribution = −15bps for the corporate bond overweight. What does this indicate about what happened to credit spreads during the period?
Select an option first.
Correct answer: B — SPREAD contribution is NEGATIVE despite a corporate bond OVERWEIGHT. This means the overweight in credit cost the manager — credit spreads must have WIDENED during the period. When credit spreads widen, corporate bond prices fall relative to government bonds. A manager who overweighted corporates lost relative to a benchmark with less corporate exposure — hence the negative spread attribution. Positive spread attribution would require spread narrowing.
Explanation: B is correct: The sign of the spread attribution directly reflects what happened to credit spreads during the period. Overweight corporates + spread attribution negative = spreads widened (corporates underperformed relative to government bonds). This is consistent with the reading's example: '8 bps were lost because the manager overweighed the corporate sector' — implying corporate spreads widened (underperformance vs. government bonds). For the spread attribution to be positive, the manager would need to have overweighted a sector where spreads narrowed, or underweighted a sector where spreads widened.
Question 79
What is the RISK ATTRIBUTION approach for a BOTTOM-UP equity manager, and what risk metric is typically used?
Select an option first.
Correct answer: B — For a bottom-up manager, risk attribution focuses on the MARGINAL CONTRIBUTION TO TRACKING RISK of each individual security. Each security's contribution = (its active weight) × (its marginal contribution to tracking risk). This allows the attribution to identify which specific stock selections are the largest contributors to tracking error — revealing whether the active risk is concentrated in a few positions or diversified. Standard deviation of active returns (tracking error) is the relevant risk metric for relative attribution.
Explanation: B is correct: The reading states: 'For the bottom-up approach, each security in the portfolio has a marginal contribution to tracking risk, and that amount is multiplied by its active weight to determine the contribution to tracking risk.' This security-level risk attribution is appropriate for bottom-up stock pickers because their active bets are primarily at the individual stock level. The resulting analysis reveals: which stocks contribute most to tracking error, whether tracking risk is diversified or concentrated, and whether the manager's risk profile matches their stated process.
Question 80
For a TOP-DOWN equity manager, how does RISK ATTRIBUTION differ from the bottom-up approach?
Select an option first.
Correct answer: B — For a top-down manager, risk attribution attributes active return AND tracking error at the ALLOCATION level — sector/country/style allocation decisions. Both allocation and selection effects are analyzed for their tracking error contributions. The top-down approach takes a more macro view: the manager's active bets are primarily sector/style over- or underweights, so tracking error is attributed to these allocation decisions rather than to individual security choices.
Explanation: B is correct: The reading's table (not shown) distinguishes attribution approach by investment process. Top-down managers make asset allocation decisions first — their primary active bets are at the sector/style/country level. Risk attribution should therefore attribute tracking error to these allocation-level decisions: which sector overweight contributed most to tracking error? This differs from bottom-up, where each stock's marginal contribution to tracking risk is the relevant unit of analysis. The risk attribution approach should match the actual investment decision-making process to be meaningful.
Question 81
What is 'misfit active return' and how does it arise from benchmark misspecification?
Select an option first.
Correct answer: B — Misfit active return = return of the manager's 'normal portfolio' (correct style benchmark) minus the return of the investor's chosen benchmark (which is misspecified). It arises when the investor uses a benchmark that doesn't match the manager's actual investment style. In the example: if manager invests in French large-caps, investor uses Euronext 100, and CAC 40 is the true benchmark — misfit active return = CAC 40 return − Euronext 100 return. True active return = portfolio return − CAC 40 return.
Explanation: B is correct: The reading illustrates misfit return with the French manager example. A manager specializing in large French stocks is benchmarked against the Euronext 100 (which includes Belgian, Dutch, Portuguese, and Luxembourg stocks). If France outperforms the broader Euronext 100 this year, the manager looks like they're outperforming purely due to style (their 'French-only' portfolio benefits from France's outperformance), even if their stock picks within France are poor. Total active return vs. investor benchmark = style (misfit) active return + true active return. B correctly defines and explains the concept.
Question 82
A manager's portfolio returned 10%, the investor's benchmark (Euronext 100) returned 9%, and the CAC 40 (manager's true benchmark) returned 12%. Calculate: (1) total active return vs. investor benchmark, (2) misfit active return, and (3) true active return.
Select an option first.
Correct answer: A — Total = +1%, misfit = +3%, true = −2%
Explanation: A is correct: (1) Total active return vs. investor benchmark = Portfolio − Euronext 100 = 10% − 9% = +1% (manager appears to outperform). (2) Misfit active return = true benchmark (CAC 40) − investor benchmark (Euronext 100) = 12% − 9% = +3% (the manager's style was in favor). (3) True active return = Portfolio − true benchmark = 10% − 12% = −2% (manager actually underperformed their proper style benchmark). The investor sees +1% but the manager was actually a poor stock picker who was rescued by their style exposure. This demonstrates why proper benchmarking is critical.
Question 83
What are the SEVEN properties (SAMURAI) required for a valid benchmark?
Select an option first.
Correct answer: B — Specified in advance, Appropriate, Measurable, Unambiguous, Reflective of manager's current investment opinions, Accountable, Investable — forming the SAMURAI acronym. Each property ensures the benchmark genuinely tests the manager's active decisions rather than rewarding or penalizing irrelevant factors.
Explanation: B is correct: The seven SAMURAI criteria are: (S) Specified in advance — known before the period begins; (A) Appropriate — matches manager's style and mandate; (M) Measurable — calculable on a regular basis; (U) Unambiguous — securities and weights are clearly defined; (R) Reflective of current investment opinions — manager has genuine knowledge of benchmark constituents; (A) Accountable — manager accepts the benchmark as a fair test; (I) Investable — can be passively replicated. Manager universes fail the 'specified in advance' and 'investable' criteria. Absolute return benchmarks fail the 'investable' criterion.
Question 84
What is the PRIMARY disadvantage of using a 'manager universe' as a benchmark, and why does it fail the SAMURAI criteria?
Select an option first.
Correct answer: B — Manager universes fail two SAMURAI criteria: (1) Not specified in advance — the benchmark (median manager return) cannot be known before the period ends, making pre-period communication of the benchmark impossible; (2) Not investable — you cannot passively replicate the median manager's portfolio in advance. Additionally, manager universes suffer from survivorship bias — underperforming managers close, their histories are removed, and the median shifts upward, making a strategy of 'beating the median' harder retroactively than in real-time.
Explanation: B is correct: The reading explicitly notes that manager universes are 'not acceptable benchmarks' specifically because they cannot be identified or specified in advance (the median return is only known after the fact) and cannot be invested in (no passive replication possible). The survivorship bias compounds the problem: if 200 managers start the year and 20 close due to poor performance, their bad returns are removed from the universe — making the historical median return look better than what was actually achievable. A manager evaluated against this median faces a biased retroactive comparison.
Question 85
For HEDGE FUND benchmarking, why are all three common benchmark approaches (broad market index, risk-free rate, peer universe) inadequate?
Select an option first.
Correct answer: B — Broad market index: hedge funds use leverage, shorts, and derivatives with low correlation to markets — the benchmark doesn't reflect the strategy. Risk-free rate: while appropriate for pure arbitrage strategies, most hedge funds carry systematic risk and leverage that makes the risk-free rate an insufficient hurdle. Peer universe: individual hedge funds differ enormously in strategy; appraisal smoothing from illiquid assets reduces reported volatility, inflating measured Sharpe ratios and making peer comparison misleading.
Explanation: B is correct: The reading methodically dismisses all three options. Broad index: a long/short equity fund has near-zero net market exposure — comparing to S&P 500 makes no sense. Risk-free rate: if you add a spread to compensate for leverage, what spread is appropriate? This is subjective. Peer universe: survivorship bias inflates historical peer returns, and the appraisal smoothing effect (illiquid assets priced infrequently show artificially low volatility) makes Sharpe ratios misleadingly high, causing over-allocation to hedge funds. The honest conclusion: defining truly valid benchmarks for most hedge fund strategies is extremely difficult.
Question 86
What is 'appraisal smoothing' in alternative investment benchmarking, and what is its effect on measured risk and Sharpe ratios?
Select an option first.
Correct answer: B — Appraisal smoothing occurs when illiquid assets (real estate, PE, hedge fund illiquid positions) are valued infrequently using appraisals rather than market prices. Since appraised values don't fluctuate as often as market prices, reported returns show lower month-to-month variation than the true economic volatility. This understates standard deviation, which inflates the Sharpe ratio (return/σ — same return divided by smaller σ = higher ratio), potentially causing excessive capital allocation to these strategies.
Explanation: B is correct: Consider a real estate property valued quarterly by an appraiser vs. daily by the market. The quarterly valuation shows a smooth path while the true underlying value may fluctuate daily. Reported σ is artificially low because consecutive reported prices are correlated (both using stale appraisal values). Sharpe ratio = active return / σ — with an artificially low σ, the Sharpe ratio is artificially high. Investors seeing a high Sharpe ratio allocate more to these assets, potentially taking on more true risk than they realize. This is a key limitation of risk measures applied to illiquid alternative investments.
Question 87
What is the 'return to style' (S) component in the return decomposition formula P = M + S + A?
Select an option first.
Correct answer: B — S = benchmark return (B) − broad market return (M). It represents the incremental return attributable to the manager's particular investment style (e.g., small-cap growth) relative to the broad market. If S > 0, the manager's style was in favor during the period. If S < 0, the manager's style underperformed the broad market — this is not the manager's fault (it reflects style tilts, not active decisions).
Explanation: B is correct: The decomposition P = M + S + A cleanly separates return into three components: M = broad market return (passive return from being in the market); S = B − M = style tilt return (positive or negative based on whether the manager's style was in or out of favor); A = P − B = true active return (what the manager adds through security selection and active decisions). This decomposition allows proper evaluation — a manager with A > 0 is adding value through skill; a manager whose total return exceeds M only because S > 0 is benefiting from style without demonstrating skill.
Question 88
What is the key difference between the SHARPE RATIO and the TREYNOR RATIO, and when is each more appropriate?
Select an option first.
Correct answer: B — Sharpe ratio uses total risk (standard deviation) in the denominator — appropriate for evaluating the performance of a portfolio that represents an investor's entire wealth (standalone evaluation). Treynor ratio uses systematic risk (beta) — appropriate for evaluating a portfolio that is one of many in a diversified fund (the unsystematic risk has been diversified away at the fund level). For a well-diversified portfolio, both ratios produce the same ranking.
Explanation: B is correct: The choice depends on the portfolio's role. A pension fund's entire equity allocation = standalone → use Sharpe (total risk is relevant). A single equity manager within a multi-manager fund → use Treynor (the manager's idiosyncratic risk diversifies away; only systematic risk matters to the fund). The reading explicitly notes that Treynor 'is only useful for portfolios that have systematic risk and do not have unsystematic risk — well-diversified portfolios.' If comparing managers who hold concentrated portfolios, the Sharpe ratio (total risk) is more appropriate.
Question 89
What is the INFORMATION RATIO and what does it measure specifically?
Select an option first.
Correct answer: B — IR = (mean portfolio return − mean benchmark return) / tracking error = active return / tracking risk. It measures the consistency of active return generation per unit of active risk (tracking error). A high IR (> 0.5 is generally considered good) indicates the manager consistently outperforms their benchmark without excessive benchmark-relative risk. Unlike the Sharpe ratio (which evaluates absolute returns), the IR evaluates the value-added per unit of benchmark-relative risk.
Explanation: B is correct: IR = Active return / Tracking risk. This is the benchmark-relative equivalent of the Sharpe ratio. Tracking error (tracking risk) measures the standard deviation of the return differences (portfolio − benchmark) over time. A manager who consistently beats the benchmark by 1% per month with very low variance in that excess return has a high IR. A manager who beats by 5% one month but trails by 4% the next has high tracking error and a lower IR despite similar average active return. The IR penalizes inconsistency in benchmark-relative performance.
Question 90
What is the SORTINO RATIO and in what situations does it provide a better measure than the Sharpe ratio?
Select an option first.
Correct answer: B — Sortino ratio = (portfolio return − MAR) / downside deviation (semideviation below MAR). Unlike the Sharpe ratio, it only penalizes downside volatility — positive excess returns above the MAR are not counted against the manager. It is more appropriate for: (1) portfolios with non-normal return distributions (hedge funds, options strategies that are positively skewed — Sharpe penalizes upside skew unfairly); (2) investors primarily concerned with avoiding losses below a target return rather than minimizing all volatility.
Explanation: B is correct: Consider two managers: Manager A has a return distribution that is positively skewed (high upside volatility, low downside). Manager B has the same mean and standard deviation but symmetric distribution. Sharpe ratio treats both identically (uses total σ). Sortino ratio rewards Manager A because upside volatility above the MAR is ignored — only downside deviations count. For investors with capital preservation goals (minimum acceptable return is the critical threshold), the Sortino ratio better captures relevant risk. The key limitation: MAR is subjective — different MAR assumptions produce different Sortino ratios, making comparison across managers difficult.
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