A fund that beats the S&P 500 by 3% in a year of rising small-cap and value premia has told you nothing about manager skill — the excess return may be fully explained by systematic exposures any passive index fund could replicate at near-zero cost. Risk-adjusted performance measurement is the set of tools that separate what the manager earned above what she owed in systematic compensation. The wrong choice of measure leads to systematic hiring of leveraged beta-chasers and dismissal of genuine alpha generators.
This note covers the classical single-benchmark measures (Sharpe, Treynor, Jensen), their correct domain of application, and the multi-index generalizations required when fund style deviates from the broad market. The evidence on average fund performance — positive alpha before fees, negative after — is developed alongside the measures.
In this lesson
- Return measurement before performance evaluation
- The risk decomposition
- Sharpe ratio
- Treynor measure
- Jensen's alpha
- Appraisal ratio and information ratio
- Multi-index alpha
- What the evidence says
- Manipulation-proof performance measure
Before you start
- CAPM: The Security Market Line and Beta Pricing
- The Arbitrage Pricing Theory: Factor Structure and Pricing
The full lesson, with worked examples and exercise solutions, is for members.
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