PORTFOLIO PERFORMANCE MEASUREMENT èIf we are paying an active manager to provide superior performance, how can we be sure we are getting what we pay for? èTechniques: èRisk-adjusted measures èMarket-timing measures èPerformance attribution and “style” analysis

RISK-ADJUSTED MEASURES èWhat return should we have expected, for the same level of risk, from a manager with no particular skill? èDid our manager do better than this? èWhat’s the relevant measure of risk? èWhat’s the relevant benchmark portfolio?

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

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?

ADJUSTING TO MARKET RISK

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

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

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

BEFORE- OR AFTER-THE-FACT MEASUREMENT? èThe theory behind risk-adjusted performance measures calls for before-the- fact measurement èWhat are the data-gathering problems in before- the-fact measurement? èIn practice, we’re stuck with after-the fact data èLuck vs. skill: problem of statistical power

A PROBLEM WITH AFTER-THE-FACT MEASUREMENT èAccording to our estimate of alpha, the manager in the example looks good. But why? èGood stock picker? èGood market timer? èMarket-timing ability is hard to detect with Jensen’s alpha

SUCCESSFUL MARKET TIMING AND MISLEADING ALPHA

TESTING FOR MARKET TIMING: TREYNOR-MAZUY

TESTING FOR MARKET TIMING: HENRIKSSON-MERTON

PERFORMANCE ATTRIBUTION ANALYSIS For each asset class i: –Benchmark weights –Benchmark returns –Portfolio weights

DECOMPOSING PERFORMANCE

PERFORMANCE ATTRIBUTION COMPONENTS Asset allocation contribution Security selection contribution Interaction

“STYLE” ANALYSIS èDefine the manager’s “style” in terms of benchmark portfolios (e.g., asset classes) èRegress managed portfolio returns against benchmark returns èFitted values from the regression are the manager’s style-adjusted expected returns èResidual (“tracking error”) is the measure of superior performance

EXAMPLE OF STYLE ANALYSIS

THE PORTFOLIO MANAGEMENT PROCESS