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Transcript

Portfolio Performance Evaluation Chapter 24 McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. 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 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 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 $54 per share 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: 51 112 50 1 (1 r ) (1 r ) 2 r 7.117% 24-5 Time-Weighted Return 53 50 2 r1 10% 50 54 53 2 r2 5.66% 53 Simple Average Return: (10% + 5.66%) / 2 = 7.83% 24-6 Averaging Returns Arithmetic Mean: Text Example Average: n rt r t 1 n (.10 + .0566) / 2 = 7.83% Geometric Mean: Text Example Average: 1/ n r (1 rt ) 1 t 1 n [ (1.1) (1.0566) ]1/2 - 1 = 7.81% 24-7 Geometric & Arithmetic Means Compared Past Performance - generally the geometric mean is preferable to arithmetic mean because it represents a constant rate of return we would have needed to earn in each year to match actual performance over past period. Predicting Future Returns from historical returns arithmetic is preferable to geometric mean, because it is an unbiased estimate of the portfolio’s expected return. In contrast while the geometric mean is always less than the arithmetic mean, it constitutes a downward- biased estimator of the stock’s expected return. 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 24-9 Factors Leading to Abnormal Performance Market timing Superior selection Sectors or industries Individual companies 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 p return 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 24-12 M2 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 24-13 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 24-14 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. 24-15 Appraisal Ratio (Information Ratio) 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 24-16 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 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. 24-18 Market Timing Adjusting portfolio for up and down movements in the market Low Market Return - low ßeta High Market Return - high ßeta 24-19 Example of Market Timing rp - rf * * * * * * * * * ** * * * * * ** * * * * * rm - rf Steadily Increasing the Beta 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 24-21 Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure 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, Summarize the performance differences into appropriate categories. 24-23 Formula for Attribution n n i 1 i 1 rB wBi rBi & rp w pi rpi n n i 1 i 1 rp rB w pi rpi wBi rBi n (w i 1 r wBi rBi ) pi pi Where B is the bogey portfolio and p is the managed portfolio 24-24 Contributions for Performance Contribution for asset allocation + Contribution for security selection (wpi - wBi) rBi wpi (rpi - rBi) = Total Contribution from asset class wpirpi -wBirBi 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 24-26 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 24-27