Evaluating Portfolio Performance

1. Evaluating Portfolio Performance

2. Introduction • Active vs. passive portfolio management • Active selection will mean some non-systematic risk  not holding a completely diversified portfolio • Portfolio performance tied to manager’s compensation (directly or indirectly) • For example, a hedge fund may charge “2 & 20” (2% management fee based on AUM, and 20% performance fee or carried interest) • Long-only equity managers charge only a management fee: Ad valorem (a % of AUM)

3. Benchmarking Performance • Benchmark is typically a stock index, bond index, or a weighted average of different indices • Depends on the portfolio mandate • The benchmark is the investor’s passive alternative • Simple performance measure against benchmark (using holding period returns): rP – rB • Called “active return”, “relative return“, or “value added”,

4. Tracking Error Measures deviations from benchmark • where rPt is the portfolio return, and rBt is the benchmark return • Most common performance measure for index fund / ETF managers • Measures “tracking risk”

6. Tracking Error • Many actively managed portfolios have a target tracking error. Maintaining this target is a part of portfolio risk management • Having cash in portfolio will increase tracking error • Cash does not always reduce “risk” if you are benchmarked! It increases your tracking risk

7. Example Target value added, rp-rB Target tracking error What is the relationship between target tracking error and target value added?

8. Tracking Error and Optimization • Three-dimensional application of the Markowitz Model • State Street Global Markets (currency strategy): “Maximizes: Expected Return - Risk Aversion x Standard Deviation2 -Tracking Error Aversion x Tracking Error2 ”

9. Risk-Adjusted Returns • Popular media reports mostly raw returns • If investors care about risk, then may want to consider return per unit of risk • Traditional risk-adjusted measures: • Sharpe ratio • Treynor measure • Appraisal or information ratio • Jensen’s alpha

10. Sharpe Ratio • A reward-to-variability ratio, using realized returns • Average excess returns per unit of total risk (standard deviation of portfolio returns) • The most popular risk-adjusted measure • Use it to compare different portfolios, or to evaluate portfolio against the benchmark

11. Treynor Measure • Average excess returns per unit of systematic risk • Need to first estimate the portfolio beta using the Single Index Model • Risk that cannot be diversified away

12. Jensen’s Alpha • A classic measure of “stock-picking ability” • Benchmark: the CAPM • Estimate using regression analysis • If p > 0 (and statistically significant), then there is “abnormal” portfolio return, over and above what is predicted by the CAPM • Same idea can be applied using the Fama-French model

13. Information Ratio • Also called the Appraisal ratio • Alpha per unit of diversifiable (or non-systematic) risk • Appropriate when considering a move from a passively managed to an actively managed portfolio • Potential benefit: alpha, but will also add diversifiable risk to the portfolio

14. Information Ratio • Industry Version: • Measures the efficiency with which a portfolio’s tracking risk delivers active return • Difference: Performance is benchmarked to a simple market index, rather than to the CAPM (or the Single Index Model)