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Free CFA Performance Measurement Practice Questions & Answers
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100% free · No login to startQuestion 1
What are the THREE components of performance evaluation and in what ORDER do they build upon each other?
Select an option first.
Correct answer: B — Performance measurement (calculates return and risk) → Performance attribution (explains HOW the return was achieved given risk taken) → Performance appraisal (determines whether results reflect skill, market conditions, or luck). Each component builds on the previous.
Explanation: B is correct: The three components are sequential: (1) Measurement is the foundation — you must first quantify what the return and risk were before explaining them. (2) Attribution uses the measurement results to identify which active decisions drove the performance. (3) Appraisal uses both measurement and attribution outputs to render a judgment on whether the performance reflects skill or luck. Performance evaluation answers three questions in sequence: What did the fund achieve? How did it achieve it? Was it skill or luck?
Question 2
What is the DIFFERENCE between performance attribution and performance appraisal?
Select an option first.
Correct answer: B — Performance attribution EXPLAINS the sources of return — which specific active decisions (allocation, security selection, timing) generated positive or negative active return. Performance appraisal EVALUATES the quality of the performance — specifically, whether the excess return achieved is statistically likely to reflect genuine investment skill (reproducible in the future) or merely market luck (not reproducible). Attribution asks 'how'; appraisal asks 'was it skill?'
Explanation: B is correct: Attribution and appraisal are distinct stages of performance evaluation. Attribution decomposes realized returns into sources: allocation effect (did the manager over/underweight the right sectors?), selection effect (did the manager pick better-than-benchmark securities within sectors?), and interaction effect (did these combine well?). Appraisal uses the attribution output plus statistical analysis to determine whether results can be expected to persist — a manager with high allocation effect in one period may have gotten lucky (the sector happened to outperform) or may have genuine skill (able to consistently identify outperforming sectors).
Question 3
What is the DIFFERENCE between MACRO attribution and MICRO attribution?
Select an option first.
Correct answer: B — Macro attribution analyzes investment decisions at the FUND SPONSOR level — evaluating the sponsor's decisions to allocate across asset classes, investment styles, and external managers versus the strategic asset allocation. Micro attribution analyzes decisions at the INDIVIDUAL PORTFOLIO MANAGER level — evaluating the manager's sector allocation and security selection decisions relative to their specific mandate/benchmark.
Explanation: B is correct: The distinction reflects different levels in the investment decision hierarchy. A pension fund sponsor makes decisions about: how much to allocate to equities vs. bonds (SAA), whether to use growth or value managers, and which specific managers to hire. Macro attribution evaluates these high-level decisions. Individual growth or value managers then make their own sector/stock decisions. Micro attribution evaluates these manager-level decisions. The Brinson models (BHB and BF) can be applied at either level: at the macro level, the 'segments' are asset classes or manager styles; at the micro level, the 'segments' are sectors or industries.
Question 4
What are the ADVANTAGES and DISADVANTAGES of RETURNS-BASED attribution?
Select an option first.
Correct answer: B — Returns-based attribution advantages: minimal data requirements (only need the manager's historical return stream); easy to implement; works even when holdings are not disclosed (e.g., for opaque hedge funds). Disadvantages: relies on regression against historical data — backward-looking and assumes the current strategy matches historical behavior; cannot detect mid-period changes in strategy; results depend heavily on the factors and historical period chosen.
Explanation: B is correct: The reading lists advantages and disadvantages for all three attribution methods. Returns-based: the key advantage is simplicity and low data requirements — just regress the manager's return against risk factors. The key disadvantage is that regression-based inference about the manager's strategy is backward-looking and may not reflect current exposures, especially if the strategy has recently changed. This is particularly problematic for momentum or tactical managers who shift exposures frequently. The method also has difficulty identifying exactly which securities or sectors drove performance.
Question 5
What is the PRIMARY DISADVANTAGE of HOLDINGS-BASED attribution compared to TRANSACTIONS-BASED attribution?
Select an option first.
Correct answer: B — Holdings-based attribution uses beginning-of-period portfolio weights to assess active bets and their returns. It does NOT account for portfolio changes made DURING the evaluation period. For a manager with high turnover who makes significant trades intra-period, the beginning weights no longer represent the actual exposures during the period. This creates a 'timing' or 'trading' effect — the difference between holdings-based and actual returns — that is not explained by the attribution model.
Explanation: B is correct: The reading explicitly notes this limitation: holdings-based 'does not adjust for portfolio changes made during the evaluation period; hence, the output may not fully reconcile to overall portfolio returns for a manager with high turnover. This mismatch is referred to as a 'timing' or 'trading' effect.' For a buy-and-hold manager with minimal turnover, holdings-based attribution is adequate. For a high-turnover manager making multiple trades daily, only transactions-based attribution captures the full impact of the trading activity on performance.
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Question 6
In the BHB model, what does the ALLOCATION EFFECT measure, and what is its formula?
Select an option first.
Correct answer: B — Allocation effect measures the value added/subtracted by the decision to OVERWEIGHT or UNDERWEIGHT a segment relative to the benchmark. Formula: Ai = (wi − Wi) × Bi, where wi = portfolio weight in segment i, Wi = benchmark weight in segment i, Bi = benchmark return in segment i. Positive allocation effect: overweighted (wi > Wi) a segment that earned a positive benchmark return, OR underweighted a segment with negative benchmark return.
Explanation: B is correct: The BHB allocation effect specifically multiplies the ACTIVE WEIGHT (wi − Wi) by the BENCHMARK SEGMENT RETURN (Bi, not the portfolio return). This measures: did the manager weight this segment more/less than benchmark, and did the segment return positively or negatively? The formula assigns credit for overweighting a segment if its benchmark return is positive, and penalizes for overweighting if its benchmark return is negative. The BF model addresses a drawback of BHB by using (Bi − B) instead of just Bi — making the sign of the allocation effect directly indicate whether the allocation decision was correct.
Question 7
What is the SELECTION EFFECT in the Brinson models (BHB and BF) and what is its formula?
Select an option first.
Correct answer: B — Selection effect = Wi × (Ri − Bi), where Wi = benchmark weight in segment i, Ri = portfolio return in segment i, Bi = benchmark return in segment i. It measures the value added from PICKING BETTER-THAN-BENCHMARK SECURITIES within each segment, weighted by the benchmark weight. Positive selection: the manager's actual holdings in a segment outperformed the segment's benchmark return.
Explanation: B is correct: The selection effect captures whether the manager's specific security choices within each segment outperformed the segment's passive return. Formula: Wi × (Ri − Bi). Using benchmark weight Wi (not portfolio weight wi) isolates the selection decision from the allocation decision. If Ri > Bi, the manager selected better-than-benchmark securities in segment i — positive selection. If Ri < Bi, the manager's picks underperformed within the segment. The total selection effect across all segments measures the manager's overall stock-picking ability.
Question 8
What is the INTERACTION EFFECT in the BHB model and what does it capture?
Select an option first.
Correct answer: B — Interaction effect = (wi − Wi) × (Ri − Bi). It captures the joint effect of simultaneously making both an active allocation decision (wi ≠ Wi) AND an active selection decision (Ri ≠ Bi). Positive interaction: over-weighting a segment (wi > Wi) AND having better-than-benchmark selection within it (Ri > Bi). Negative: over-weighting a segment but having worse selection within it. It represents the additional value (or loss) from combining these two active decisions.
Explanation: B is correct: Formula: (wi − Wi) × (Ri − Bi). This captures the 'interaction' or joint effect of two active bets. Economically: if you overweight growth stocks (allocation bet) AND your specific growth stock picks outperform the growth benchmark (selection bet), you benefit from both effects plus an interaction benefit from having done both correctly together. If you overweight growth but your picks within growth underperform, the negative interaction offsets some of the positive allocation. In practice, interactions are often small but can be significant for concentrated active managers.
Question 9
How does the Brinson-Fachler (BF) model DIFFER from the BHB model, and why is BF considered superior for interpreting individual segment allocation decisions?
Select an option first.
Correct answer: B — The BF model changes the allocation formula from Ai = (wi − Wi) × Bi (BHB) to Ai = (wi − Wi) × (Bi − B), where B is the TOTAL benchmark return. By comparing the segment return to the total benchmark return (not zero), BF ensures the sign of the allocation effect directly indicates whether the allocation decision was CORRECT. BHB can show a positive allocation effect for overweighting a sector that underperformed the total benchmark — misleading. BF makes the allocation effect interpretively transparent.
Explanation: B is correct: The reading provides a clear example. Using BHB: growth allocation effect = (0.75 − 0.60) × 10% = +1.5% (positive, though overweighting growth when growth underperformed the 14% total benchmark was actually a bad decision). Using BF: growth allocation effect = (0.75 − 0.60) × (10% − 14%) = −0.60% (negative, correctly showing the growth overweight was a bad decision when growth returned 10% vs. 14% benchmark). BF's allocation effect sign reliably indicates whether the allocation was a good or bad decision — BHB's doesn't for individual segments.
Question 10
In a Brinson model attribution: portfolio weight in Technology = 30%, benchmark weight = 20%. Technology portfolio return = 15%, technology benchmark return = 12%, total benchmark return = 10%. Calculate the BF allocation effect and selection effect for technology.
Select an option first.
Correct answer: B — BF Allocation = (wi − Wi) × (Bi − B) = (0.30 − 0.20) × (12% − 10%) = 0.10 × 2% = +0.20%. Selection = Wi × (Ri − Bi) = 0.20 × (15% − 12%) = 0.20 × 3% = +0.60%.
Explanation: B is correct: BF Allocation = (30% − 20%) × (12% − 10%) = 10% × 2% = 0.20%. Technology returned 12% benchmark vs. 10% overall benchmark — overweighting technology was a good decision (+). Selection = 20% × (15% − 12%) = 20% × 3% = 0.60%. Within technology, the manager's specific picks returned 15% vs. the 12% technology benchmark — positive stock selection (+). Both effects are positive: good allocation (overweighted an outperforming sector) AND good selection (picked better stocks within the sector).
Question 11
Total active return reconciliation: Using BHB model with the following sector contributions — Allocation total = +0.5%, Selection total = −0.3%, Interaction total = +0.1%. Portfolio return = 12%, Benchmark return = 11.3%. Does the model reconcile?
Select an option first.
Correct answer: A — No — the attribution total (0.3%) does not match active return (0.7%)
Explanation: A is correct: Active return = 12% − 11.3% = 0.7%. Attribution total = 0.5% − 0.3% + 0.1% = 0.3%. Gap = 0.7% − 0.3% = 0.4% unexplained. This residual violates the effective attribution requirement of explaining 100% of excess return. Common causes: cash holdings not captured in the model, transactions during the period (use transactions-based attribution), currency effects not modeled, or data errors. When a residual exists, the attribution analysis is incomplete and potentially misleading — reported allocation and selection effects may absorb some of the unexplained return.
Question 12
What is 'micro attribution' and how would it be applied to a GROWTH equity manager who underperformed their growth benchmark?
Select an option first.
Correct answer: B — Micro attribution is applied at the individual portfolio manager level. For a growth manager underperforming their growth benchmark, micro attribution would decompose the underperformance into: sector allocation within growth (did they over/underweight technology vs. healthcare within growth?), stock selection within each growth sector (did their specific technology picks underperform the technology segment of the growth benchmark?), and interaction effects. This identifies whether the underperformance came from sector bets or stock picking.
Explanation: B is correct: At the micro attribution level, the benchmark is the manager's specific mandate benchmark (e.g., the Russell 1000 Growth Index for a large-cap growth manager). The 'segments' are sectors or industries within growth (technology, healthcare, consumer discretionary, etc.). The allocation effect captures whether the manager overweighted the right sectors within growth; the selection effect captures whether they picked better individual stocks within each sector. This micro-level analysis enables the fund sponsor to evaluate whether the manager is adding value through sector bets, stock picking, or neither.
Question 13
What is ARITHMETIC attribution vs. GEOMETRIC attribution, and which does the reading indicate is most commonly used in practice?
Select an option first.
Correct answer: B — Arithmetic attribution: defines active return as the DIFFERENCE between portfolio and benchmark returns (R − B) — additive across segments but does not compound correctly across multiple periods (2% + 2% ≠ the true multi-period active return of 4.16%). Geometric attribution: defines active return as a RATIO (R/B − 1) — compounds correctly across multiple periods. Despite geometric attribution's theoretical superiority for multi-period analysis, the reading notes that 'a vast majority of performance appraisal practitioners use arithmetic attribution.'
Explanation: B is correct: The reading demonstrates the arithmetic vs. geometric distinction clearly with the example: two periods of 5% portfolio and 3% benchmark. Arithmetic active return = 2% each period; over two periods = 4.04% compounded but not 4%. Geometric: each period = 1.05/1.03 − 1 = 1.94%; two periods = (1.0194)² − 1 = 3.92%. Geometric compounds exactly. Despite this theoretical advantage, arithmetic attribution dominates practice due to its intuitive additive decomposition (allocation + selection + interaction = total) and ease of communication. The reading explicitly confirms 'a vast majority of performance appraisal practitioners use arithmetic attribution.'
Question 14
In fixed-income attribution using EXPOSURE DECOMPOSITION, what are the FOUR active bets a fixed-income manager could take?
Select an option first.
Correct answer: B — Duration — extending or shortening portfolio duration relative to benchmark (expressing a view on yield level changes); Curve shape — positioning the yield curve exposure differently from benchmark (expressing a view on yield curve steepening/flattening); Sector selection — overweighting government vs. corporate vs. securitized segments (expressing a view on credit spread changes); Bond selection — overweighting specific bonds expected to outperform within their sector.
Explanation: B is correct: The reading specifically identifies these four active bets that an exposure decomposition attribution captures: (1) Duration bet — are you more/less rate-sensitive than the benchmark?; (2) Curve shape bet — are you positioned for flattening, steepening, or specific maturity outperformance?; (3) Sector bet — do you overweight corporate vs. government (credit spread exposure)?; (4) Bond selection bet — within each sector, do you hold bonds that outperform the sector average? Each bet corresponds to an attribution component that explains whether the manager added or lost value through that specific active decision.
Question 15
In a YIELD CURVE DECOMPOSITION attribution, what are the SIX sources of fixed-income return?
Select an option first.
Correct answer: A — Yield (coupon income), Roll (rolldown return), Shift (parallel yield curve change), Shape (curve shape change), Spread (credit spread change), Residual (unexplained)
Explanation: A is correct: The reading lists these specific six components: (1) Yield — return from collecting coupon income; (2) Roll — return from the bond rolling down a stable yield curve (rolldown); (3) Shift — return from a parallel shift in the yield curve, estimated through duration and convexity; (4) Shape — return from changes in yield curve shape (steepening, flattening, butterflying); (5) Spread — return from changes in credit spread (sector or security-specific); (6) Residual — unexplained component from estimation error in duration and convexity approximations. The first three (yield, roll, shift) correspond to the fixed-income return decomposition from Reading 7.
Question 16
A fixed-income attribution shows: Duration contribution = +33bps, Curve shape = −39bps, Sector allocation = −8bps, Bond selection = +22bps, Residual = +6bps. Total attribution = +14bps. Benchmark return = 2.56%. Portfolio return = 2.70%. What is the unexplained residual if attribution is complete?
Select an option first.
Correct answer: D — Active return = 2.70% − 2.56% = 0.14% = 14bps. Attribution: 33 − 39 − 8 + 22 + 6 = +14bps. The attribution reconciles fully.
Explanation: D is correct: Active return = portfolio return − benchmark = 2.70% − 2.56% = 0.14% = 14bps. Attribution total = +33 − 39 − 8 + 22 + 6 = +14bps. The attribution reconciles exactly — 100% of active return is explained. The residual of +6bps is explicitly included as a component of the attribution (from estimation error in duration/convexity approximations), not an unaccounted gap. The effective attribution attribute #1 (reflects 100% of return) is satisfied. The manager added value mainly through duration positioning (+33bps) and bond selection (+22bps) but lost value through yield curve shape positioning (−39bps) and sector allocation (−8bps).
Question 17
What is the PRIMARY ADVANTAGE of FULL REPRICING yield curve decomposition over DURATION-BASED yield curve decomposition?
Select an option first.
Correct answer: B — Full repricing uses individual SPOT RATES for each cash flow at specific maturities rather than aggregate duration and yield-to-maturity estimates. It is the MOST PRECISE method because: it avoids the approximation errors inherent in using a single YTM and duration; it can accommodate non-parallel yield curve changes at each specific maturity point; and it handles the broadest range of instruments (including callable bonds, amortizing securities). The drawback is highest computational complexity.
Explanation: B is correct: The three methods form a precision spectrum: Exposure decomposition (simplest, lowest data requirements, used for marketing/client reporting) → Duration-based yield curve decomposition (moderate complexity, used by analysts) → Full repricing (most complex, most precise, broadest instrument coverage, used by quantitative risk managers). Full repricing breaks down each bond's total return by the specific spot rates that determine each individual cash flow's discounting — capturing non-parallel yield curve movements at the sub-maturity level. The tradeoff is implementation complexity making it 'least likely to be easily understood by the recipient.'
Question 18
When should RELATIVE risk attribution be used versus ABSOLUTE risk attribution?
Select an option first.
Correct answer: B — Relative risk attribution is appropriate when the portfolio is managed against a benchmark — active risk (tracking error) is the relevant risk metric, and attribution measures how each active bet contributed to tracking error. Absolute risk attribution is appropriate for absolute return strategies with no benchmark (e.g., hedge funds targeting a fixed return regardless of market direction) — total volatility or VaR is the relevant risk metric, not tracking error relative to an arbitrary index.
Explanation: B is correct: The reading states: 'a relative-based risk attribution analysis would not be appropriate for a portfolio manager who has predetermined an absolute target return investment goal.' The choice of risk metric must match the manager's objective. Benchmark-relative manager → tracking error → relative risk attribution (how much did each sector bet contribute to tracking error?). Absolute return manager → total volatility or VaR → absolute risk attribution (how much did each position contribute to total portfolio risk?). Using the wrong risk measure leads to misleading attribution — e.g., a market-neutral hedge fund might have zero tracking error vs. S&P 500 but high absolute volatility.
Question 19
What are the SEVEN types of benchmarks identified in the reading, and which type is used as the denominator in the Sortino ratio?
Select an option first.
Correct answer: B — Absolute, Broad market indexes, Style indexes, Factor-model-based, Returns-based, Custom security universe, and Median manager (peer group). The ABSOLUTE benchmark (minimum acceptable return, MAR) is the target return in the Sortino ratio — it is the denominator's reference point, not the risk-free rate.
Explanation: B is correct: The reading lists all seven benchmark types. The absolute benchmark is unique: 'an absolute benchmark is a return objective that aims to exceed a minimum target return (an example would be the minimum acceptable return (MAR) that is used in computing the Sortino ratio).' The Sortino ratio = (portfolio return − MAR) / semi-deviation of returns below MAR. The MAR is the reference in both the numerator (as the minimum required return) and the denominator (returns below MAR constitute the downside semi-deviation). Note: MAR is NOT the risk-free rate — it can be any target return the investor specifies.
Question 20
What are the ADVANTAGES of STYLE INDEX benchmarks versus broad market index benchmarks?
Select an option first.
Correct answer: B — Style index advantages: they are widely available, understood by clients, and widely accepted; if the index reflects the manager's investment style (e.g., Russell 2000 Growth for a small-cap growth manager), it is a more appropriate benchmark than a broad index (e.g., S&P 500 or total market). Disadvantages: some style indexes have large weightings in specific securities creating concentration; different providers define 'style' differently, producing different benchmark returns for the same manager description.
Explanation: B is correct: The reading lists style indexes' advantages (widely available, understood, accepted; appropriate if reflecting manager's style) and disadvantages (potentially inappropriate sector/security concentrations; different definitions across providers). For example, a small-cap growth manager should use a small-cap growth index (like Russell 2000 Growth), not the S&P 500. But if Morningstar and Russell classify 'growth' differently, the manager's attribution will differ depending on which style index is used — creating comparability problems across managers and measurement periods.
Question 21
What is the 'MISFIT ACTIVE RETURN' and the 'TRUE ACTIVE RETURN' in the context of misspecified benchmarks?
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Correct answer: B — When the investor's stated benchmark (investor benchmark) differs from the manager's true benchmark (normal portfolio/appropriate benchmark): Misfit active return = normal portfolio return − investor benchmark return (reflects the style difference between what the manager does and what the investor benchmark measures). True active return = portfolio return − normal portfolio return (reflects only the manager's genuine active decisions within their true benchmark). Total = misfit + true active return.
Explanation: B is correct: The reading gives a specific example: a manager of large, liquid French stocks evaluated against Euronext 100 (which includes non-French stocks). Portfolio = 10%, Euronext 100 = 9%, CAC 40 (proper benchmark) = 12%. Misfit active return = CAC 40 − Euronext 100 = 12% − 9% = +3% (the style difference between managing French-only vs. the European index). True active return = Portfolio − CAC 40 = 10% − 12% = −2% (the manager actually underperformed their appropriate benchmark). Total: 10% − 9% = +1% (appears to outperform the investor benchmark but actually underperforms the true one). Benchmark misspecification distorts performance evaluation significantly.
Question 22
What is the SHARPE RATIO and what is its PRIMARY LIMITATION?
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Correct answer: B — Sharpe ratio = (portfolio return − risk-free rate) / standard deviation of portfolio returns. The primary limitation is that the denominator (standard deviation) penalizes ALL volatility equally — both upside volatility (favorable surprises) and downside volatility (adverse surprises) count against the ratio. A fund with highly skewed positive returns (many small gains, occasional large gains) is penalized for its 'good' volatility in the same way as a fund with negatively skewed returns (many small gains, occasional large losses).
Explanation: B is correct: The reading explicitly states this limitation: 'a key drawback with the ratio is that the denominator does not differentiate between volatility that is upside versus downside. Therefore, with the Sharpe ratio, there is a penalty for all volatility, even if it is 'good' volatility.' This makes the Sharpe ratio potentially misleading for strategies with positive skewness (where higher standard deviation partly reflects large positive outcomes) or negative skewness (where it understates the true downside risk). The Sortino ratio was developed specifically to address this limitation.
Question 23
What is the INFORMATION RATIO and how does it differ from the Sharpe ratio?
Select an option first.
Correct answer: B — Information ratio = (portfolio active return) / tracking risk = (Rp − Rb) / σ(Rp − Rb). It measures active return (vs. benchmark, not risk-free) per unit of ACTIVE risk (tracking error vs. benchmark, not total portfolio risk). The Sharpe ratio uses total portfolio risk in the denominator; the IR uses only the active risk component. The IR specifically evaluates ACTIVE management skill; the Sharpe ratio evaluates total portfolio risk-adjusted return.
Explanation: B is correct: The key distinction is what constitutes 'return' and 'risk' in each measure. Sharpe: excess return over risk-free / total standard deviation — measures efficiency of total portfolio risk-taking. IR: active return (above benchmark) / tracking error (standard deviation of active return) — measures efficiency of ACTIVE risk-taking. For evaluating active managers, the IR is more appropriate because it directly measures whether the manager's active decisions (deviations from benchmark) created value per unit of risk taken. A manager with high IR is a superior active manager; high Sharpe could reflect simply taking more market risk passively.
Question 24
What is the APPRAISAL RATIO and how is it calculated?
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Correct answer: B — Appraisal ratio = alpha (α) / standard error of the regression (σε), where both are derived from a factor-based regression (typically CAPM). Alpha = portfolio return − CAPM fair return. σε = residual standard deviation of the regression = sqrt(total portfolio variance − systematic variance). The appraisal ratio measures active return per unit of RESIDUAL (non-systematic) risk — analogous to the information ratio but derived from a factor model regression.
Explanation: B is correct: The reading states: 'The appraisal ratio measures the ratio of active return, α, to the volatility of the residual term, σε, both derived from a factor-based regression.' Under CAPM: α = portfolio return − [Rf + β(Rm − Rf)]. σε = sqrt(σp² − β²σm²). The AR measures how much alpha the manager generates per unit of residual (idiosyncratic, non-market-explained) risk. A higher AR indicates better use of active risk. The reading notes: 'The AR is analogous to the information ratio — it looks at active return per unit of active risk. The only difference to the information ratio is that the AR uses a factor-based regression to estimate active return and active risk.'
Question 25
What is the TREYNOR RATIO and when is it most appropriate?
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Correct answer: B — Treynor ratio = (portfolio return − risk-free rate) / beta (systematic risk). It measures excess return per unit of SYSTEMATIC (market) risk rather than total risk. It is most appropriate for evaluating WELL-DIVERSIFIED portfolios where unsystematic (idiosyncratic) risk has been effectively eliminated — the remaining risk is primarily market risk (beta). For undiversified or concentrated portfolios, total risk (Sharpe) or residual risk (Appraisal ratio) are more appropriate.
Explanation: B is correct: The reading states: 'The Treynor ratio is only useful in evaluating portfolios that have systematic risk and do not have unsystematic risk; in other words, such portfolios are well diversified.' The key distinction from Sharpe: Treynor uses beta (systematic risk) while Sharpe uses standard deviation (total risk = systematic + unsystematic). For a well-diversified portfolio, most of the risk IS systematic, so Treynor and Sharpe lead to similar conclusions. For a concentrated portfolio with significant idiosyncratic risk, Treynor overstates performance by excluding unsystematic risk from the denominator.
Question 26
What is the SORTINO RATIO and why is it more appropriate than the Sharpe ratio for investments with NON-NORMAL return distributions?
Select an option first.
Correct answer: B — Sortino ratio = (portfolio return − MAR) / semi-standard deviation of returns below MAR. It is more appropriate for non-normal distributions because: (1) It penalizes ONLY downside volatility (returns below MAR) — 'good' upside volatility doesn't count against the manager; (2) Positively skewed strategies (hedge funds with favorable asymmetry) get credit for their asymmetry; (3) Negatively skewed strategies (short volatility) are appropriately penalized more than Sharpe indicates. Clients care more about downside risk than upside volatility.
Explanation: B is correct: The reading states: 'The Sortino ratio is more appropriate for investments with non-normal (nonsymmetrical) return distributions. Positively skewed and negatively skewed investment strategies would both result in lower Sharpe ratios (higher standard deviation), but only the negatively skewed investment strategy would result in a lower Sortino ratio (higher semi-standard deviation).' A positively skewed fund has high standard deviation partly from large positive outcomes — Sortino correctly recognizes this doesn't represent true downside risk. The MAR is the investor's specified minimum acceptable return, making the Sortino ratio subjective (different MARs give different ratios).
Question 27
What are CAPTURE RATIOS and how do they measure asymmetric performance?
Select an option first.
Correct answer: B — Upside capture ratio = portfolio return during benchmark UP periods / benchmark return during UP periods. Downside capture ratio = portfolio return during benchmark DOWN periods / benchmark return during DOWN periods. An ideal active manager has: upside capture > 100% (outperforms when market rises) AND downside capture < 100% (loses less when market falls). This 'capture more on the upside, lose less on the downside' pattern demonstrates asymmetric skill.
Explanation: B is correct: Capture ratios measure the manager's performance asymmetry across market environments. Example: a portfolio with 120% upside capture and 80% downside capture means it gains 20% more than the benchmark in bull markets but only loses 80% as much in bear markets — highly attractive. A portfolio with 90% upside and 110% downside capture loses more in bear markets and gains less in bull markets — unattractive. These ratios are intuitive for client communication because they directly relate to actual market experiences (up periods and down periods) rather than statistical abstractions.
Question 28
What is DRAWDOWN DURATION and how does it differ from maximum drawdown?
Select an option first.
Correct answer: B — Maximum drawdown = the MAGNITUDE of the worst peak-to-trough decline (e.g., −30% from peak to trough). Drawdown duration = the TOTAL LENGTH OF TIME from the initial peak to the recovery to the same peak level — includes both the decline period (peak to trough) AND the recovery period (trough back to peak). A fund can have a small maximum drawdown but long duration (slow gradual decline with slow recovery), or large drawdown with short duration (sharp crash but rapid recovery).
Explanation: B is correct: The reading distinguishes both measures as separate risk metrics. A strategy could have a −10% maximum drawdown that takes 3 years to recover (long duration — psychologically difficult for investors who were in at the peak). Another strategy might have a −30% maximum drawdown that recovers in 6 months (short duration — severe but brief). Both dimensions matter for investor experience and strategy evaluation. Drawdown duration captures the 'how long was this painful?' question that maximum drawdown alone doesn't answer. Together, they give a more complete picture of downside risk experience.
Question 29
What are the LIMITATIONS of the Sortino ratio?
Select an option first.
Correct answer: B — Key limitations: (1) The MAR is SUBJECTIVE — different investors specify different target returns, making cross-manager comparisons problematic if they use different MARs; (2) Returns below MAR may be too few in a short evaluation period to estimate semi-deviation reliably; (3) Does not capture tail risk beyond the semi-deviation measure; (4) Like all single-period measures, may not reflect the true distribution if the evaluation period is too short.
Explanation: B is correct: The reading explicitly notes the comparability problem: 'a comparability problem exists with the Sortino ratio because the determination of MAR is subjective and specific to each investor.' If Manager A is evaluated using MAR = 5% and Manager B is evaluated using MAR = 3%, their Sortino ratios are not directly comparable — the denominator (semi-deviation relative to MAR) will be calculated differently. Additionally, for strategies with few losing periods (e.g., a short-volatility fund that rarely loses), the semi-deviation is estimated from very few observations, making the ratio statistically unreliable.
Question 30
What distinguishes a FACTOR-MODEL-BASED benchmark from a STYLE INDEX benchmark?
Select an option first.
Correct answer: B — Style indexes are constructed from actual securities grouped by style characteristics (e.g., large-cap value). Factor-model benchmarks are SYNTHETIC — they represent a portfolio with specified FACTOR EXPOSURES (market beta, size, value, momentum, etc.) that are typical for the manager, constructed from the manager's past portfolios. The factor model benchmark better captures the systematic risk exposures the manager regularly takes, and can accommodate strategies that don't neatly fit standard style categories.
Explanation: B is correct: The reading distinguishes these: style indexes are fixed, pre-defined collections of securities. Factor-model benchmarks are customized to the specific manager's historical risk exposures — they are portfolios constructed to match the manager's typical factor loadings. The advantage: better captures the specific risk profile of an unusual strategy that doesn't fit a standard style box. Disadvantage: requires estimation of factor exposures from historical data (backward-looking), and the normal portfolio is constructed from past behavior that may not persist.
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