Portfolio Performance Evaluation Chapter 24 Mc GrawHillIrwin Copyright

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Portfolio Performance Evaluation Chapter 24 Mc. Graw-Hill/Irwin Copyright © 2005 by The Mc. Graw-Hill

Portfolio Performance Evaluation Chapter 24 Mc. Graw-Hill/Irwin Copyright © 2005 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Introduction Complicated subject Theoretically correct measures are difficult to construct Different statistics or measures

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 24 -2

Dollar- and Time-Weighted Returns Dollar-weighted returns Internal rate of return considering the cash flow

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 24 -3

Text Example of Multiperiod Returns Period Action 0 Purchase 1 share at $50 1

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 24 -4

Dollar-Weighted Return Period Cash Flow 0 -50 share purchase 1 +2 dividend -53 share

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: 24 -5

Time-Weighted Return Simple Average Return: (10% + 5. 66%) / 2 = 7. 83%

Time-Weighted Return Simple Average Return: (10% + 5. 66%) / 2 = 7. 83% 24 -6

Averaging Returns Arithmetic Mean: Text Example Average: (. 10 +. 0566) / 2 =

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% 24 -7

Geometric & Arithmetic Means Compared Past Performance - generally the geometric mean is preferable

Geometric & 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 if the forecast and estimation period are equal 24 -8

Abnormal Performance What is abnormal? Abnormal performance is measured: Benchmark portfolio Market adjusted Market

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 Factors of abnormal performance Market timing Superior selection Sectors or industries Individual companies 24 -9

Risk Adjusted Performance: Sharpe 1) Sharpe Index rp - rf p rp = Average

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 p return 24 -10

M 2 Measure Developed by Modigliani and Modigliani Equates the volatility of the managed

M 2 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 24 -11

M 2 Measure: Example Managed Portfolio: return = 35% standard deviation = 42% Market

M 2 Measure: Example Managed Portfolio: return = 35% standard deviation = 42% Market Portfolio: return = 28% T-bill return = 6% standard deviation = 30% 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 24 -12

Risk Adjusted Performance: Treynor 2) Treynor Measure rp - rf ßp rp = Average

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� 24 -13

Risk Adjusted Performance: Jensen 3) Jensen’s Measure p= rp - [ rf + ßp

Risk Adjusted Performance: Jensen 3) Jensen’s Measure p= rp - [ rf + ßp ( rm - rf) ] p = Alpha for the portfolio rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Avg. return on market index port. 24 -14

Appraisal Ratio = p / (ep) Appraisal Ratio divides the alpha of the portfolio

Appraisal Ratio = p / (ep) Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk Nonsystematic risk could, in theory, be eliminated by diversification 24 -15

Which Measure is Appropriate? It depends on investment assumptions 1) If the portfolio represents

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 24 -16

Limitations Assumptions underlying measures limit their usefulness When the portfolio is being actively managed,

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 24 -17

Market Timing Adjusting portfolio for up and down movements in the market Low Market

Market Timing Adjusting portfolio for up and down movements in the market Low Market Return - low ßeta High Market Return - high ßeta 24 -18

Example of Market Timing rp - rf * * * * ** * *

Example of Market Timing rp - rf * * * * ** * * rm - rf Steadily Increasing the Beta 24 -19

Performance Attribution Decomposing overall performance into components Components are related to specific elements of

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 24 -20

Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for

Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure Calculate the return on the ‘Bogey’ and on the managed portfolio Explain the difference in return based on component weights or selection Summarize the performance differences into appropriate categories 24 -21

Formula for Attribution Where B is the bogey portfolio and p is the managed

Formula for Attribution Where B is the bogey portfolio and p is the managed portfolio 24 -22

Contributions for Performance Contribution for asset allocation + Contribution for security selection (wpi -

Contributions for Performance Contribution for asset allocation + Contribution for security selection (wpi - w. Bi) r. Bi wpi (rpi - r. Bi) = Total Contribution from asset class wpirpi -w. Bir. Bi 24 -23

Complications to Measuring Performance Two major problems Need many observations even when portfolio mean

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 24 -24

Style Analysis Based on regression analysis Examines asset allocation for broad groups of stocks

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 24 -25