Lecture10 Portfolio Performance Evaluation

# Lecture10 Portfolio Performance Evaluation - Portfolio...

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Portfolio Performance Evaluation Tyler R. Henry 1 FINA 4310 Outline Contents 1 Performance Measures 1 2 Attribution Analysis 7 1 Performance Measures Performance Evaluation Why do we need it? To evaluate actively managed portfolios Pension funds Mutual funds To compare performance of portfolios with different risks Absolute measures not sufﬁcient (simple returns) Relative measures control for risk ("risk-adjusted returns") To determine where to allocate our funds Which managers have skill? Different Performance Measures There are many to choose from, and different measures are appropriate in differ- ent situations. Sharpe ratio Treynor measure Jensen’s alpha 1

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M 2 measure T 2 measure Benchmark returns Appraisal Ratio These are risk-adjusted measures , but they adjust for different types of risk. Sharpe Ratio S p = r p - r f σ p where: r p = average portfolio return r f = average risk-free rate σ p = standard deviation of portfolio return What is the relevant type of risk for the Sharpe ratio? In what type of situation would the Sharpe ratio be appropriate? Treynor Measure T p = r p - r f β p where: r p = average portfolio return r f = average risk-free rate β p = weighted average portfolio beta What is the relevant type of risk for the Treynor measure? In what type of situation would the Treynor measure be appropriate? Jensens Alpha α p = r p - [ r f + β p ( r M - r f )] where: α p = portfolio alpha r p = average portfolio return r M = average return on market portfolio r f = average risk-free rate β p = weighted average portfolio beta What is the relevant type of risk for the Jensens alpha? In what type of situation would the Jensens alpha be appropriate? 2
Jensen’s Alpha Jensen’s Alpha Use sample averages [() ] pp f p Mf rr α β =− + CAPM controls for portfolio risk 11/07/07 FINA 4310 7 Calculating Risk-Adjusted Measures Example: Consider the following risk and return measures for an actively man- aged portfolio and a market index portfolio: Calculating risk adjusted measure Calculating risk-adjusted measures Example : Consider the following risk and return measures for an actively managed portfolio and a market index portfolio: managed portfolio and a market index portfolio: Active Portfolio Market Portfolio Average return 24% 19% Standard deviation 35% 22% Beta 1.4 1.0 If the risk-free rate is 6%, evaluate the relative performance of the actively managed portfolio. What is the economic interpretation of these measures? Are the measures easy to interpret? 11/07/07 FINA 4310 8 If the risk-free rate is 6%, evaluate the relative performance of the actively man- aged portfolio. What is the economic interpretation of these measures?

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Lecture10 Portfolio Performance Evaluation - Portfolio...

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