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## Chapter 4

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**Chapter 4**Evaluating Portfolio Performance**Why Evaluating Portfolio Performance Is Not Simple**• Cash inflows and outflows mean that different, legitimate methods of computing returns will provide different performance results. • Time-weighted vs. dollar weighted**Interim Cash Flows**• Additions of cash to or removals of cash from a portfolio • – dividends or interest payments left in portfolio are not interim cash flows • –charges in a margin account added to the debit balance, or offset against a cash position are not interim cash flows**Two Tools to Measure Actual Return Over a Period**• Geometric Mean Return • Time-weighted rate of return measure • Internal Rate of Return • Dollar-weighted rate of return measure**Which Rate Should Be Used?**• Depends on conditions governing cash flows • If portfolio manager controls timing of cash flows, use IRR • If he or she does not, use GMR • Return to an investor is always IRR • Performance by portfolio manager is usually GMR**Two Components to Benchmarking**• Selection of market index • Selection of comparison method • Should be risk-adjusted comparison • Can adjust risk based on: • Beta • Variance (or standard deviation)**Choices for a Market Index**• Dow Jones Industrial Average • Standard & Poor’s 500 • Other Domestic Indexes • Foreign Indexes • Bond Indexes**Dow Jones Industrial Average**• Oldest, started in 1884 • Most commonly quoted • Flaws: • Small number of stocks (30) • Industries not proportionally represented • Focuses only on large, mature companies • Ignores dividends • Price-weighted index**Price Weighted Index**• Add up all prices and divide by number of securities in index • Unless there have been: • Stock splits • Stock dividends • Changes in composition of index • Adjustments made via denominator • Stock with highest price has most impact**Standard & Poor’s 500**• Advantages: • Large percentage of total market capitalization • Includes stocks from multiple markets • Industry representation more typical of economy • Value weighted (as are most indexes)**Value Weighted Index**• Capitalizations of all companies in index added together • Capitalization = price x number of shares • Sum divided by sum of capitalizations on start date • Neutral with regard to splits and dividends • Minor adjustment with regard to changes in components**Other Indexes**• NASDAQ 100 • NYSE Composite • Russell 3000, 1000, and 2000 • Dow Jones Wilshire 5000 • Closest to a Total Market Index**Other Indexes (continued)**• Value Line Index • Only equally weighted index Foreign Indexes • FTSE 100 • MSCI EAFE • Bond Indexes • Lehman Brothers Aggregate Bond Index • Lehman Brothers Corporate Bond Index • Lehman Brothers Government Bond Index • Lehman Brothers Mortgage-Backed Securities Index**Computing Risk Adjusted Performance Using Standard Deviation**• Sharpe ratio – also called reward-to-variability ratio (RVAR)**Also called the reward-to-volatility ratio (RVOL)**Treynor ratio**Other Beta-Based Measures ofPerformanceEvaluation**• Jensen’s alpha • Information Ratio • A portfolio’s alpha divided by the standard deviation of the error term from the estimation of a portfolio’s characteristic line • The larger the value of the ratio, the more attractive the performance of the portfolio**Choosing a Performance Measure**• Use the Sharpe ratio when it is important to consider total variability and not just exposure to systematic risk • Use the Information ratio when a portfolio is divided into two components and only one is actively managed • Use the Treynor ratio when an overall portfolio has been allocated to multiple active managers