18 Investment Analysis and Portfolio Management First Canadian Edition By Reilly, Brown, Hedges, Chang
Chapter 18Evaluation of Portfolio Performance You are only responsible for pages 569 to the top of 580 • Peer Group Comparison • Risk-Adjusted Composite Performance Measures • Other Performance Measures
Evaluation of Portfolio Performance A. Peer Group Comparisons • Collects the returns produced by a representative universe of investors over a specific period of time Potential problems • No explicit adjustment for risk!! • Difficult to form comparable peer group
Evaluation of Portfolio Performance B. Risk-Adjusted Performance Measures 1. Treynor Portfolio Performance Measure • Builds on capital markets theory (incl. CAPM) • Assumes a completely diversified portfolio leaving systematic risk as the relevant risk • Focuses on the portfolio’s undiversifiable risk: market or systematic risk
1. Treynor Portfolio Performance Measure • The Formula • Numerator is the risk premium • Denominator is a measure of risk • Ti is the slope of the characteristic line • All risk averse investors prefer to maximize Ti . • If a Ti > Tm (the value of the market portfolio), the security(portfolio) plots above the SML , indicating superior risk-adjusted performance.
1. Treynor Portfolio Performance Measure Example: Assume the market return is 14% and risk-free rate is 8%. The average annual returns for Managers W, X, and Y are 12%, 16%, and 18% respectively. The corresponding betas are 0.9, 1.05, and 1.20. What are the T values for the market and managers? • TM = (14%-8%) / 1 =6% • TW = (12%-8%) / 0.9 =4.4% • TX = (16%-8%) / 1.05 =7.6% • TY = (18%-8%) / 1.20 =8.3%
B. Risk-Adjusted Performance Measures 2. Sharpe Portfolio Performance Measure • Seeks to measure the total risk of a portfolio, not just the level of systematic risk. • Shows the risk premium earned over the risk free rate per unit of standard deviation (or total risk). • Sharpe ratios greater than the ratio for the market portfolio indicate superior performance • Linked to the CML
- R RFR i = S i s i 2. Sharpe Performance Measure • where: • σi= the standard deviation of the rate of return for Portfolio i
- R RFR i = S i s i 2. Sharpe Performance Measure Assume the market return is 14% with a standard deviation of 20%, and risk-free rate is 8%. The average annual returns for Managers D, E, and F are 13%, 17%, and 16% respectively. The corresponding standard deviations are 18%, 22%, and 23%. What are the Sharpe measures for the market and the managers? • SM = (14%-8%) / 20% =0.300 • SD = (13%-8%) / 18% =0.278 • SE = (17%-8%) / 22% =0.409 • SF = (16%-8%) / 23% =0.348
Treynor’s versus Sharpe’s Measure Treynor versus Sharpe Measure • Sharpe uses standard deviation of returns as the measure of risk • Treynor measure uses beta (systematic risk) • Methods agree on rankings of completely diversified portfolios. • A poorly diversified portfolio could have a high Treynor ratio (ignores unsystematic risk) but a lower Sharpe ratio. • Produce relative not absolute rankings of performance
B. Risk-Adjusted Performance Measures 3. Jensen Portfolio Performance Measure Rjt- RFRt = αj + βj[Rmt– RFRt ] + ejt where: αj = Jensen measure ejt = random error term (assume on average it is zero) • αjrepresents the average excess return of the portfolio above that predicted by CAPM • Superior managers will generate a significantly positive alpha; inferior managers will generate a significantly negative alpha
B. Risk-Adjusted Performance Measures 3. Applying the Jensen Measure • Requires using a different RFR for each time interval during the sample period • Does not directly consider portfolio manager’s ability to diversify because it calculates risk premiums in term of systematic risk (similar to the Treynor measure) • Flexible enough to allow for alternative models of risk and expected return than the CAPM. Risk-adjusted performance can be computed relative to any of the multifactor models:
- R R ER j b j = = IR j s s ER ER B. Risk-Adjusted Performance Measures 4. Information Ratio Performance Measure • Widely-used measure • Measures average return in excess of a benchmark portfolio, divided by the standard deviation of this excess return where: Rb= the average return for the benchmark portfolio σER = the standard deviation of the excess return • σERcan be called the tracking errorof the investor’s portfolio and it is a “cost” of active management
Comparing Performance Measures Implications of High Positive Correlations • Although the measures provide a generally consistent assessment of portfolio performance when taken as a whole, they remain distinct at an individual level. • Best to consider these composites collectively. • User must understand what each measure means.
Other Performance Measures Performance Attribution Analysis • Attempts to distinguish the source of portfolio’s overall performance • Selecting superior securities • Demonstrating superior timing skills You do not need to know this section for the final exam!
Reporting Investment Performance Fundamental Principles of PPS • Total return must be used • Time-weighted rates of return must be used • Portfolios must be valued at least monthly and periodic returns must be geometrically linked • Composite return performance (if presented) must contain all actual fee-paying accounts • Performance must be calculated after deduction of trading expenses • Taxes must be recognized when incurred • Annual returns for all years must be presented • Disclosure requirements must be met Note: You do not need to know this for the final exam either!