6.1 Risk-Adjusted Performance Measures

Risk-adjusted performance measures are essential tools for evaluating investment performance, accounting for the level of risk taken to achieve returns.

The Sharpe Ratio:

  • Definition: Measures excess return per unit of total risk (standard deviation)

  • Formula: Sharpe Ratio = (Rp – Rf) / σp

  • Interpretation: Higher indicates better risk-adjusted performance

  • Applications: Performance evaluation of diversified portfolios, manager selection

  • Limitations: Assumes normally distributed returns, uses standard deviation

The Treynor Ratio:

  • Definition: Measures excess return per unit of systematic risk (beta)

  • Formula: Treynor Ratio = (Rp – Rf) / βp

  • Interpretation: Higher indicates better risk-adjusted performance

  • Applications: Evaluating well-diversified portfolios

  • Limitations: Requires accurate beta estimation, limited to diversified portfolios

Jensen’s Alpha:

  • Definition: Measures excess return compared to CAPM expectations

  • Formula: αp = Rp – [Rf + βp × (Rm – Rf)]

  • Interpretation: Positive alpha indicates outperformance

  • Applications: Manager performance evaluation, assessment of investment skill

  • Limitations: Benchmark and model dependency

Information Ratio:

  • Definition: Measures excess return relative to benchmark divided by tracking error

  • Formula: IR = (Rp – Rb) / TE

  • Interpretation: Higher indicates better risk-adjusted performance

  • Applications: Evaluating active managers

6.2 Performance Attribution

Performance attribution decomposes portfolio returns into component parts to identify sources of value added or value lost.

The Attribution Framework:

  • Allocation Effect:

    • Contribution from asset allocation decisions

    • Calculation: Σ (wpj – wbj) × (Rbj – Rb)

    • Positive when overweighting outperforming asset classes

  • Selection Effect:

    • Contribution from security selection within asset classes

    • Calculation: Σ wbj × (Rpj – Rbj)

    • Positive when selected securities outperform benchmarks

  • Interaction Effect:

    • Contribution from the combination of allocation and selection

    • Calculation: Σ (wpj – wbj) × (Rpj – Rbj)

Practical Application:

  • Attribution Levels:

    • Top-level: Asset class allocation decisions

    • Mid-level: Sector or industry allocation decisions

    • Bottom-level: Individual security selection decisions

  • Frequency of Attribution:

    • Quarterly for most institutional portfolios

    • Monthly for more active management

    • Annual for strategic assessment

  • Reporting:

    • Clear and understandable presentation

    • Identification of sources of value added

    • Actionable insights for improvement

6.3 Performance Evaluation in Practice

Performance evaluation in practice involves multiple considerations beyond simple return measurement.

Benchmark Selection:

  • Appropriate Benchmarks:

    • Match the portfolio’s investment style and strategy

    • Consider the asset allocation and objectives

    • Use recognized and established indices

  • Custom Benchmarks:

    • Blended benchmarks for multi-asset portfolios

    • Reflect the portfolio’s strategic allocation

    • Appropriate for specific investment mandates

Consideration of Fees:

  • Performance should be evaluated net of fees

  • Fees impact net returns to clients

  • Comparison to benchmarks should be on a net basis

Time Period Considerations:

  • Multiple time periods should be evaluated

  • Rolling periods provide insight into consistency

  • Longer-term performance is more meaningful

Peer Group Comparison:

  • Compare to appropriate peer groups

  • Use consistent classification and methodology

  • Provide context for peer group performance

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