PORTFOLIO PERFORMANCE MEASUREMENT

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PORTFOLIO PERFORMANCE MEASUREMENT

• If we are paying an active manager to provide
  superior performance, how can we be sure we are
  getting what we pay for?
• Techniques
• Risk-adjusted measures
• Market-timing measures
• Performance attribution and style analysis

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RISK-ADJUSTED MEASURES

• What return should we have expected, for the same
  level of risk, from a manager with no particular
  skill?
• Did our manager do better than this?
• Whats the relevant measure of risk?
• Whats the relevant benchmark portfolio?

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SHARPE MEASURE

• Compare portfolio risk premium to total risk
• Equal to slope of Capital Allocation Line
• Need a benchmark market portfolio?

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MODIGLIANI MEASURE

• Portfolio risk may be different from benchmark
  risk
• What would managed portfolio risk premium have
  been if we had levered or unlevered to benchmark
  risk?

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ADJUSTING TO MARKET RISK
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TREYNOR MEASURE

• Compare portfolio risk premium to systematic risk
• Potentially misleading for a portfolio with
  substantial unsystematic risk

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JENSENS ALPHA

• Alpha is a measure of excess return relative to
  CAPM standard
• Again, watch for unsystematic risk
• Ease of regression application

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APPRAISAL RATIO

• Compare alpha to residual risk
• Watch out for differences in systematic risk
• Could be useful for comparing active portfolios

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BEFORE- OR AFTER-THE-FACT MEASUREMENT?

• The theory behind risk-adjusted performance
  measures calls for before-the-fact measurement
• What are the data-gathering problems in
  before-the-fact measurement?
• In practice, were stuck with after-the fact data
• Luck vs. skill problem of statistical power

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A PROBLEM WITH AFTER-THE-FACT MEASUREMENT

• According to our estimate of alpha, the manager
  in the example looks good. But why?
• Good stock picker?
• Good market timer?
• Market-timing ability is hard to detect with
  Jensens alpha

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SUCCESSFUL MARKET TIMINGAND MISLEADING ALPHA
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TESTING FOR MARKET TIMINGTREYNOR-MAZUY
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TESTING FOR MARKET TIMINGHENRIKSSON-MERTON
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PERFORMANCE ATTRIBUTIONANALYSIS

• For each asset class i
• Benchmark weights
• Benchmark returns
• Portfolio weights
• Portfolio weights

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DECOMPOSING PERFORMANCE
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PERFORMANCE ATTRIBUTIONCOMPONENTS

• Asset allocation contribution
• Security selection contribution
• Interaction

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STYLE ANALYSIS

• Define the managers style in terms of
  benchmark portfolios (e.g., asset classes)
• Regress managed portfolio returns against
  benchmark returns
• Fitted values from the regression are the
  managers style-adjusted expected returns
• Residual (tracking error) is the measure of
  superior performance

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EXAMPLE OF STYLE ANALYSIS
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THE PORTFOLIO MANAGEMENT PROCESS