Portfolio Performance Evaluation Chapter 24 Portfolio Performance Evaluation Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-1

Introduction Complicated subject Theoretically correct measures are difficult to construct Different statistics or measures are appropriate for different types of investment decisions or portfolios Many industry and academic measures are different The nature of active management leads to measurement problems Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-2

Dollar- and Time-Weighted Returns Dollar-weighted returns: Internal rate of return considering the cash flow from or to investment Returns are weighted by the amount invested in each stock Time-weighted returns: Not weighted by investment amount Equal weighting Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-3

Text Example of Multiperiod Returns Period Action 0 Purchase 1 share at $50 1 Purchase 1 share at $53 Stock pays a dividend of $2 per share 2 Stock pays a dividend of $2 per share Stock is sold at $108 per share Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-4

Dollar-Weighted Return Period Cash Flow 0 -50 share purchase 1 +2 dividend -53 share purchase 2 +4 dividend + 108 shares sold Internal Rate of Return: Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-5

Time-Weighted Return Simple Average Return: (10% + 5.66%) / 2 = 7.83% Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-6

Averaging Returns Arithmetic Mean: Text Example Average: (.10 + .0566) / 2 = 7.81% Geometric Mean: Text Example Average: [ (1.1) (1.0566) ]1/2 - 1 = 7.83% Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-7

Geometric and Arithmetic Means Compared Past Performance Generally the geometric mean is preferable to arithmetic Predicting Future Returns from historical returns Use a weighted average of arithmetic and geometric averages of historical returns if the forecast period is less than the estimation period Use geometric is the forecast and estimation period are equal Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-8

Abnormal Performance What is abnormal? Abnormal performance is measured: Benchmark portfolio Market adjusted Market model / index model adjusted Reward to risk measures such as the Sharpe Measure: E (rp-rf) / p Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-9

Factors Leading to Abnormal Performance Market timing Superior selection Sectors or industries Individual companies Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-10

Risk Adjusted Performance: Sharpe 1) Sharpe Index rp - rf  p rp = Average return on the portfolio rf = Average risk free rate  = Standard deviation of portfolio return p Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-11

M2 Measure Developed by Modigliani and Modigliani Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-12

M2 Measure: Example Managed Portfolio: return = 35% standard deviation = 42% Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6% Hypothetical Portfolio: 30/42 = .714 in P (1-.714) or .286 in T-bills (.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-13

Risk Adjusted Performance: Treynor 2) Treynor Measure rp - rf ßp rp = Average return on the portfolio rf = Average risk free rate ßp = Weighted average for portfolio Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-14

Risk Adjusted Performance: Jensen 3) Jensen’s Measure = rp - [ rf + ßp ( rm - rf) ]  p  = Alpha for the portfolio p rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Average return on market index port Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-15

Appraisal Ratio Appraisal Ratio = ap / s(ep) Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk Nonsystematic risk could, in theory, be eliminated by diversification Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-16

Which Measure is Appropriate? It depends on investment assumptions: 1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market 2) If many alternatives are possible, use the Jensen or the Treynor measure The Treynor measure is more complete because it adjusts for risk Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-17

Limitations Assumptions underlying measures limit their usefulness When the portfolio is being actively managed, basic stability requirements are not met Practitioners often use benchmark portfolio comparisons to measure performance Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-18

Market Timing Adjusting portfolio for up and down movements in the market: Low Market Return low ßeta High Market Return high ßeta Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-19

Example of Market Timing rp - rf * * * * * * * * * * * * * * * * * * * * * rm - rf * * Steadily Increasing the Beta Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-20

Performance Attribution Decomposing overall performance into components Components are related to specific elements of performance Example components: Broad Allocation Industry Security Choice Up and Down Markets Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-21

Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio: Use indexes for each component Use target weight structure Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-22

Attributing Performance to Components Calculate the return on the ‘Bogey’ and on the managed portfolio Explain the difference in return based on component weights or selection Summarise the performance differences into appropriate categories Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-23

Formula for Attribution Where B is the bogey portfolio and p is the managed portfolio Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-24

Contributions for Performance Contribution for asset allocation (wpi - wBi) rBi + Contribution for security selection wpi (rpi - rBi) = Total Contribution from asset class wpirpi -wBirBi Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-25

Complications to Measuring Performance Two major problems: Need many observations even when portfolio mean and variance are constant Active management leads to shifts in parameters making measurement more difficult To measure well: You need a lot of short intervals For each period you need to specify the makeup of the portfolio Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-26

Evaluation in Practice Traditionally based on quarterly data Sample used to range 5-10 years Currently, managers need to disclose exact composition quarterly Some window dressing do take place Portfolio values are published on daily basis Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-27

Style Analysis Based on regression analysis Examines asset allocation for broad groups of stocks More precise than comparing to the broad market Sharpe’s analysis: 97.3% of returns attributed to style Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-28

Summary Appropriate performance measures: Noisy portfolio returns Sharpe Information ratio Treynor or Jenson Noisy portfolio returns Timing the market Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-29

Summary Measuring selection success Use of appropriate benchmark Style analysis Rating of funds Morningstar ratings Risk-adjusted ratings Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 24-30