How can we evaluate the performance of a portfolio manager? It turns out that even average portfolio return is not as straightforward to measure as it might seem. In addition, adjusting average returns for risk presents a host of other problems. In this chapter, we begin with the measurement of portfolio returns. From there we move on to conventional approaches to risk adjustment. We identify the problems with these approaches when applied in various situations. | Chapter 24 Portfolio Performance Evaluation 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 Introduction 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 Dollar- and Time-Weighted Returns 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 Period Cash Flow 0 -50 share purchase 1 +2 dividend -53 share purchase 2 +4 dividend + 108 shares sold Internal Rate of Return: Dollar-Weighted Return Time-Weighted Return . | Chapter 24 Portfolio Performance Evaluation 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 Introduction 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 Dollar- and Time-Weighted Returns 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 Period Cash Flow 0 -50 share purchase 1 +2 dividend -53 share purchase 2 +4 dividend + 108 shares sold Internal Rate of Return: Dollar-Weighted Return Time-Weighted Return Simple Average Return: (10% + ) / 2 = Averaging Returns Arithmetic Mean: Geometric Mean: Text Example Average: (.10 + .0566) / 2 = [ () () ]1/2 - 1 = Text Example Average: 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 Geometric & Arithmetic Means Compared 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 Abnormal Performance Market timing Superior selection Sectors or industries Individual companies Factors Leading to Abnormal Performance 1) Sharpe Index rp - rf p rp = Average return on the portfolio rf = Average risk free rate p = .
