Learning Module 1: Portfolio Performance Evaluation

1. Components of Portfolio Evaluation

LOS: Explain performance measurement, attribution, and appraisal and their interrelationships.

  • Performance Measurement: “What was the performance?”
    • Calculates rate of return (absolute) and risk (ex post or ex ante).
    • Foundational step.
  • Performance Attribution: “How was the performance achieved?”
    • Explains sources of return (e.g., selection vs. allocation) and risk.
    • Distinguishes active decisions from market exposures.
  • Performance Appraisal: “Was it skill or luck?”
    • Assesses quality of performance.
    • Determines if results are due to manager skill or randomness.

2. Effective Attribution Process

LOS: Describe attributes of an effective attribution process.

An effective process must: 1. Account for all return/risk: Explain 100% of the portfolio’s excess return/risk. 2. Reflect the investment process: Align with how the manager makes decisions (e.g., bottom-up vs. top-down). 3. Quantify active decisions: Isolate the impact of the manager’s bets. 4. Provide a complete understanding: Clarify the “why” behind the excess return.

3. Types of Attribution

LOS: Contrast return vs. risk attribution; macro vs. micro attribution. Returns-based vs. holdings-based vs. transactions-based.

Return vs. Risk Attribution

  • Return Attribution: Analyzes impact of active decisions on returns (excess return).
  • Risk Attribution: Analyzes impact of active decisions on risk (volatility or tracking error).

Macro vs. Micro Attribution

  • Macro Attribution: Evaluates the Fund Sponsor’s decisions.
    • Decisions: Strategic Asset Allocation (SAA), deviations from SAA, manager selection.
  • Micro Attribution: Evaluates the Portfolio Manager’s decisions.
    • Decisions: Security selection, sector allocation within their mandate.

Attribution Methodologies (Inputs)

Method Inputs Pros Cons Best For
Returns-based Total portfolio returns only Easy, requires least data Least accurate, vulnerable to data manipulation Hedge funds (limited transparency)
Holdings-based Beginning-of-period holdings More accurate than returns-based Ignores transactions during period (timing effect errors) Passive strategies / Low turnover
Transactions-based Holdings + all trades Most accurate, reconciles exactly Difficult, data-intensive, costly Active strategies, rigorous analysis

4. Return Attribution Models (Equity)

LOS: Interpret sources of portfolio returns using specified attribution (BHB, BF, Factor-based).

Arithmetic vs. Geometric

  • Arithmetic: \(R_P - R_B\). Amounts sum to excess return. Preferred for marketing/clients. Requires smoothing for multi-period.
  • Geometric: \((1+R_P)/(1+R_B) - 1\). Effects compound. Preferred for internal/mathematical accuracy.

Brinson-Hood-Beebower (BHB) Model

  • Allocation Effect (\(A_i\)): Value added by overweighting/underweighting sectors.
    • \[A_i = (w_i - W_i) \times B_i\]
    • \(w_i\): Portfolio weight, \(W_i\): Benchmark weight, \(B_i\): Benchmark sector return.
  • Selection Effect (\(S_i\)): Value added by selecting stocks within a sector.
    • \[S_i = W_i \times (R_i - B_i)\]
  • Interaction Effect (\(I_i\)): Joint effect of allocation and selection.
    • \[I_i = (w_i - W_i) \times (R_i - B_i)\]

Brinson-Fachler (BF) Model

  • Key Difference: Adjusts Allocation Effect to account for the overall market performance.
  • Allocation Effect (BF):
    • \[A_i = (w_i - W_i) \times (B_i - B)\]
    • \(B\): Total Benchmark Return.
    • Benefit: Correctly penalizes being overweight in a sector that underperforms the overall market (even if the sector return is positive), or rewards being underweight a sector that underperforms the overall market.

Factor-Based Attribution (e.g., Carhart 4-Factor)

  • Decomposes excess return into systematic factor exposures (tilts) and specific selection (alpha).
  • Carhart Model:
    • \[R_p - R_f = a_p + b_{p1}RMRF + b_{p2}SMB + b_{p3}HML + b_{p4}WML + E_p\]
    • Factors: Market (RMRF), Size (SMB), Value (HML), Momentum (WML).
    • Interpretation: Did the manager generate return from a “Value” tilt or from stock picking (\(a_p\))?

5. Fixed-Income Attribution

LOS: Interpret output from fixed-income attribution.

Fixed income is driven by interest rates, yield curve shape, and credit spreads.

Approaches

  1. Exposure Decomposition (Duration-based): Top-down. Groups bonds by duration buckets. Good for marketing.
  2. Yield Curve Decomposition (Duration-based): Uses duration and YTM changes. Breaks return into:
    • Yield/Income: Coupon.
    • Roll: Price change sliding down the curve.
    • Shift: Change in level of yield curve.
    • Slope: Change in yield curve slope (flattening/steepening).
    • Curvature: Reshaping of curve (butterfly).
    • Spread: Change in credit spreads.
    • Specific: Selection of individual bonds.
  3. Full Repricing: Most accurate, prices every security based on zero-coupon curves. Complex.

Example Interpretation: If “Shift” contribution is negative and “Duration” contribution is negative, the manager likely had a long duration duration posture while rates rose.

6. Risk Attribution

LOS: Considerations in selecting risk attribution approach.

Align risk attribution with the investment process: * Relative (Benchmark-aware) Mandates: Measure Tracking Risk (Active Risk). * Bottom-up: Marginal contribution to tracking risk per security. * Top-down: Contribution from allocation vs. selection. * Absolute Mandates: Measure Total Risk (Volatility/VaR). * Bottom-up: Marginal contribution to total portfolio variance.

7. Benchmarks

LOS: Liability-based vs. Asset-based benchmarks; Benchmark quality; Misspecification.

Liability-Based Benchmarks

Used when assets must fund specific liabilities (e.g., Defined Benefit Pension). * Focus: Funded status (Assets vs. Liabilities). * Metrics: Correlation of assets to liabilities. * Note: Broad market indexes are usually inappropriate (different duration/risk).

Asset-Based Benchmarks

  1. Absolute Return: Minimum target (e.g., 5% or Cash + 4%).
  2. Broad Market Indexes: e.g., S&P 500. Well-known, investable.
  3. Style Indexes: e.g., Russell 1000 Value. Better fit for specific styles.
  4. Factor-Model-Based: Set of factor exposures (beta, size, value).
  5. Returns-Based: Constructed via regression of manager returns against style indices (Sharpe Style Analysis).
  6. Manager Universes (Peer Groups): Median return of similar managers.
    • Flaw: Survivorship bias, not investable, “herding” incentive.
  7. Custom Security-Based: Comparison portfolio built specifically to reflect manager’s universe/constraints.

Tests of Benchmark Quality (Bailey & Tierney)

  • SAMURAI:
    • Specified in advance.
    • Appropriate (consistent with style).
    • Measurable (frequent calculation).
    • Unambiguous (clearly defined identities/weights).
    • Reflective of current investment opinions (manager knows/can trade components).
    • Accountable (manager accepts it).
    • Investable (passive option available).

Benchmark Misspecification

Decomposition of Return: \[P = M + S + A\] * M: Market Return. * S: Style Return (\(B - M\)). * A: Active Management (\(P - B\)). * Impact: If the benchmark (\(B\)) doesn’t match the manager’s style (\(S\)), the “True Active Return” (\(A\)) is distorted by the “Misfit Return” (difference between Investor Benchmark and Manager’s Normal Portfolio). * Correlation Test: \(P-B\) (Active) should have low correlation with \(B-M\) (Style). If correlation is high, the benchmark is likely bad (systematic bias).

8. Benchmarking Alternative Investments

LOS: Problems with benchmarking alternatives.

  • Hedge Funds: Diverse strategies, use of leverage/shorting. Broad indexes don’t work. Peer groups suffer backfill/survivorship bias.
  • Private Equity: Illiquid, infrequent pricing. IRR based. Benchmarks (Cambridge/Preqin) rely on voluntary reporting. Public Market Equivalent (PME) is a common solution (simulates public index cash flows into PE timing).
  • Real Estate: Appraisal-based valuations smooth volatility (understate risk). Highly specific to property type/geography.
  • Commodities: Futures-based. Weighting schemes vary significantly (e.g., production vs. liquidity).
  • Distressed Securities: Stale pricing, illiquidity.

9. Performance Appraisal Measures

LOS: Calculate and interpret appraisal ratios.

Risk-Adjusted Ratios

  1. Sharpe Ratio (\(S_A\)): Excess return per unit of Total Risk (Std Dev).
    • \[S_A = \frac{\bar{R}_p - \bar{R}_f}{\sigma_p}\]
    • Drawback: Penalizes upside volatility; assumes normality.
  2. Treynor Ratio (\(T_A\)): Excess return per unit of Systematic Risk (Beta).
    • \[T_A = \frac{\bar{R}_p - \bar{R}_f}{\beta_p}\]
    • Use: When portfolio is part of a diversified whole.
  3. Information Ratio (IR): Active return per unit of Active Risk (Tracking Error).
    • \[IR = \frac{\bar{R}_p - \bar{R}_B}{\sigma(R_p - R_B)}\]
    • Use: Evaluates consistency of outperformance against benchmark.
  4. Appraisal Ratio (AR): Alpha per unit of Unsystematic Risk (Residual Risk).
    • \[AR = \frac{\alpha}{\sigma_\epsilon}\]
    • Use: Factor regression context.
  5. Sortino Ratio: Excess return (over MAR) per unit of Downside Risk.
    • \[Sortino = \frac{\bar{R}_p - \text{MAR}}{\text{Target Semideviation}}\]
    • MAR: Minimum Acceptable Return.
    • Semideviation: Uses only returns below MAR.
    • Use: For asymmetric return distributions (e.g., hedge funds, options) or capital preservation goals.

Capture Ratios

  • Upside Capture (UC): Portfolio Return / Benchmark Return (when Benchmark > 0). > 100% is good.
  • Downside Capture (DC): Portfolio Return / Benchmark Return (when Benchmark < 0). < 100% is good.
  • Capture Ratio (CR): \(UC / DC\).
    • \(CR > 1\): Convex profile (good).
    • \(CR < 1\): Concave profile (bad).

Drawdown

  • Maximum Drawdown: Largest peak-to-trough decline in value.
  • Drawdown Duration: Time from start of drawdown to full recovery (trough-to-zero).
  • Relevance: Assesses “pain” of holding the strategy; recovery requires geometrically higher returns (e.g., 50% loss requires 100% gain).

10. Evaluating Manager Skill

LOS: Evaluate skill.

  • Distinguishing Luck vs. Skill:
    • Short records are often noise.
    • “Paradox of Skill”: As aggregate skill rises, luck determines the winner (narrower dispersion).
  • Hypothesis Testing:
    • \(t\)-stat for Alpha. Need long time series for statistical significance.
  • Synthesis:
    • Combine attribution (did they stick to their style?) with appraisal (was the risk-adjusted return good?).
    • Check for consistency: Does the attribution match the stated philosophy?