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CFA Level III Performance Measurement Practice Questions

Official outline
CFA Institute Level III exam topics and pathways
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6
Updated
Nov 3, 2026

  1. Question 1, hard

    A consultant runs returns-based style analysis on a fund using 36 monthly returns regressed on style indexes, with weights constrained to be non-negative and to sum to 100%. The fitted weights are 70% value, 25% small-cap and 5% cash, with an R-squared of 0.96. Which statement about this approach is accurate?

    • A.It reveals security-level holdings, so it replaces holdings-based style analysis, and it works equally well with any number of monthly returns
    • B.An R-squared of 0.96 means 96% of the fund's return came from manager skill
    • C.It can infer effective style without holdings data, but results depend on the chosen indexes and window and may lag style changes
    • D.The 5% cash weight proves the fund actually held that amount of cash during the period
    Show answer and explanationHide answer

    Correct answer: C. It can infer effective style without holdings data, but results depend on the chosen indexes and window and may lag style changes

    Returns-based style analysis regresses fund returns on style indexes to estimate effective exposures. It needs only returns, but the weights are statistical estimates sensitive to index choice and window length.

    • A. It uses returns only and cannot identify individual securities.
    • B. R-squared shows how much return variation the style indexes explain, which is the opposite of skill.
    • C. Correct: effective style is inferred from returns and depends on inputs.
    • D. A fitted cash weight is an estimate of exposure, not a verified holding.

  2. Question 2, hard

    In a Brinson-Fachler analysis, a portfolio holds 25% in Energy versus a benchmark weight of 35%. The portfolio's Energy holdings returned 12.0%, and the benchmark's Energy sector returned 9.0%. If interaction is reported as a separate term, what is the selection effect for Energy?

    • A.0.75%
    • B.1.05%
    • C.-0.30%
    • D.3.00%
    Show answer and explanationHide answer

    Correct answer: B. 1.05%

    Selection effect = benchmark weight x (portfolio sector return - benchmark sector return) = 0.35 x (12.0 - 9.0) = 1.05%. Interaction is (0.25 - 0.35) x 3.0 = -0.30%, reported separately.

    • A. Uses the portfolio weight, which combines selection and interaction.
    • B. Correct: 0.35 x 3.0% = 1.05%.
    • C. This is the interaction term, not selection.
    • D. Omits the weight and reports the raw return difference.

  3. Question 3, hard

    A multifactor attribution of an equity portfolio shows active return of 0.90%. The portfolio has an active exposure of +0.40 to value (factor return 3.0%) and -0.20 to momentum (factor return 5.0%). What portion of active return is not explained by these two factors?

    • A.0.70%
    • B.0.20%
    • C.1.10%
    • D.1.20%
    Show answer and explanationHide answer

    Correct answer: A. 0.70%

    Factor-explained active return = 0.40 x 3.0 + (-0.20 x 5.0) = 1.20 - 1.00 = 0.20%. The unexplained (specific) return is 0.90 - 0.20 = 0.70%.

    • A. Correct: 0.90% - 0.20% = 0.70%.
    • B. This is the factor-explained portion, not the residual.
    • C. Adds the factor return to active return instead of subtracting it.
    • D. This is the value-factor contribution alone, ignoring momentum and the total.

  4. Question 4, medium

    Fund Q returned 9.0% with a standard deviation of 14.0%. Its benchmark returned 8.0% with a standard deviation of 10.0%. The risk-free rate is 2.0%. What is Fund Q's M-squared relative to the benchmark?

    • A.+1.00%
    • B.-1.00%
    • C.7.00%
    • D.-0.10%
    Show answer and explanationHide answer

    Correct answer: B. -1.00%

    Fund Q's Sharpe ratio is (9 - 2) / 14 = 0.50. Scaled to the benchmark's 10% risk, its return is 2 + 0.50 x 10 = 7.0%. M-squared = 7.0 - 8.0 = -1.00%.

    • A. Reverses the sign of the difference.
    • B. Correct: 7.0% risk-matched return minus 8.0% benchmark return.
    • C. Stops at the risk-matched return and does not compare it with the benchmark.
    • D. Reports the Sharpe ratio difference (0.50 - 0.60) without scaling by risk.

  5. Question 5, medium

    A fund's month-end values for each 100 invested were 100, 120, 90, 108, 81 and 117. What is the fund's maximum drawdown, measured from peak to the subsequent trough?

    • A.25.0%
    • B.19.0%
    • C.32.5%
    • D.10.0%
    Show answer and explanationHide answer

    Correct answer: C. 32.5%

    The highest peak before the lowest trough is 120, and the lowest trough after it is 81. Maximum drawdown = (120 - 81) / 120 = 32.5%.

    • A. This is the drop from 120 to 90 (or from 108 to 81), a smaller decline than the full peak-to-trough.
    • B. Measures from the starting value of 100 to the trough, ignoring the higher peak.
    • C. Correct: (120 - 81) / 120 = 32.5%.
    • D. This is only the drop from 120 to 108.

  6. Question 6, hard

    A sponsor reviews a manager with an active return of 2.0% a year and an annual tracking error of 4.0% over three years. The sponsor wants to know whether the outperformance is statistically distinguishable from zero. What is the approximate t-statistic?

    • A.0.50
    • B.0.87
    • C.1.50
    • D.1.73
    Show answer and explanationHide answer

    Correct answer: B. 0.87

    t = mean active return / (tracking error / square root of number of years) = 2.0 / (4.0 / 1.732) = 0.87. This is well below typical critical values, so three years of data cannot confirm skill.

    • A. Divides the active return by tracking error without adjusting for sample length.
    • B. Correct: 2.0 / 2.31 = 0.87.
    • C. Multiplies active return by the number of years before dividing by tracking error.
    • D. Reports the square root of the number of years, not the t-statistic.

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