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# Investment Analysis and Portfolio Management First Canadian Edition

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1. 18 Investment Analysis and Portfolio Management First Canadian Edition By Reilly, Brown, Hedges, Chang

2. 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

3. 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

4. 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

5. 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.

6. 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%

7. 1. Treynor Portfolio Performance Measure

8. 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

9. - R RFR i = S i s i 2. Sharpe Performance Measure • where: • σi= the standard deviation of the rate of return for Portfolio i

10. - 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

11. 2. Sharpe Performance Measure

12. 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

13. 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

14. 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:

15. - 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

16. Comparing Performance Measures

17. 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.

18. 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!

19. 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!