INVESTMENTS | BODIE, KANE, MARCUSCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinCHAPTER 24Portfolio Performance EvaluationINVESTMENTS | BODIE, KANE, MARCUS Two common ways to measure average portfolio return:1. Time-weighted returns 2. Dollar-weighted returns Returns must be adjusted for risk.Introduction2INVESTMENTS | BODIE, KANE, MARCUSTime-weighted returns The geometric average is a time- weighted average. Each periods return has equal weight.Dollar- and Time-Weighted Returns3INVESTMENTS | BODIE, KANE, MARCUSDollar-weighted returns Internal rate of return considering the cash flow from or to investment Returns are weighted by the amount invested in each period:Dollar- and Time-Weighted Returns4INVESTMENTS | BODIE, KANE, MARCUSExample of Multiperiod Returns5INVESTMENTS | BODIE, KANE, MARCUSDollar-weighted Return (IRR):Dollar-Weighted Return-$50-$53$2$4+$1086INVESTMENTS | BODIE, KANE, MARCUSTime-Weighted ReturnThe dollar-weighted average is less than the time-weighted average in this example because more money is invested in year two, when the return was lower.rG = (1.1) (1.0566) 1/2 1 = 7.81%7INVESTMENTS | BODIE, KANE, MARCUS The simplest and most popular way to adjust returns for risk is to compare the portfolios return with the returns on a comparison universe. The comparison universe is a benchmark composed of a group of funds or portfolios with similar risk characteristics, such as growth stock funds or high-yield bond funds.Adjusting Returns for Risk8INVESTMENTS | BODIE, KANE, MARCUSFigure 24.1 Universe Comparison9INVESTMENTS | BODIE, KANE, MARCUS1) Sharpe IndexRisk Adjusted Performance: Sharperp = Average return on the portfolio rf = Average risk free ratep= Standard deviation of portfolio return10INVESTMENTS | BODIE, KANE, MARCUS2) Treynor MeasureRisk Adjusted Performance: Treynorrp = Average return on the portfolio rf = Average risk free ratep = Weighted average beta for portfolio11INVESTMENTS | BODIE, KANE, MARCUSRisk Adjusted Performance: Jensen3) Jensens Measurep= Alpha for the portfolio rp = Average return on the portfoliop = Weighted average Betarf = Average risk free raterm = Average return on market index portfolio12INVESTMENTS | BODIE, KANE, MARCUSInformation RatioInformation Ratio = ap / s(ep)The information ratio divides the alpha of the portfolio by the nonsystematic risk.Nonsystematic risk could, in theory, be eliminated by diversification.13INVESTMENTS | BODIE, KANE, MARCUSM2 Measure Developed by Modigliani and Modigliani Create an adjusted portfolio (P*)that has the same standard deviation as the market index. Because the market index and P* have the same standard deviation, their returns are comparable:14INVESTMENTS | BODIE, KANE, MARCUSM2 Measure: ExampleManaged Portfolio: return = 35% standard deviation = 42%Market Portfolio: return = 28%standard deviation = 30% T-bill return = 6%P* Portfolio:30/42 = .714 in P and (1-.714) or .286 in T-billsThe return on P* is (.714) (.35) + (.286) (.06) = 26.7%Since this return is less than the market, the managed portfolio underperformed.15INVESTMENTS | BODIE, KANE, MARCUSFigure 24.2 M2 of Portfolio P16INVESTMENTS | BODIE, KANE, MARCUSIt depends on investment assumptions 1) If the portfolio represents the entire risky investment , then use the Sharpe measure. 2) If the portfolio is one of many combined into a larger investment fund, use the Jensen or the Treynor measure. The Treynor measure is appealing because it weighs excess returns against systematic risk.Which Measure is Appropriate?17INVESTMENTS | BODIE, KANE, MARCUSTable 24.1 Portfolio PerformanceIs Q better than P?18INVESTMENTS | BODIE, KANE, MARCUSFigure 24.3 Treynors Measure19INVESTMENTS | BODIE, KANE, MARCUSTable 24.3 Performance Statistics20INVESTMENTS | BODIE, KANE, MARCUSInterpretation of Table 24.3 If P or Q represents the entire investment, Q is better because of its higher Sharpe measure and better M2. If P and Q are competing for a role as one of a number of subportfolios, Q also dominates because its Treynor measure is higher. If we seek an active portfolio to mix with an index portfolio, P is better due to its higher information ratio.21INVESTMENTS | BODIE, KANE, MARCUSPerformance Measurement for Hedge Funds When the hedge fund is optimally combined with the baseline portfolio, the improvement in the Sharpe measure will be determined by its information ratio:22INVESTMENTS | BODIE, KANE, MARCUSPerformance Measurement with Changing Portfolio Composition We need a very long observation period to measure performance with any precision, even if the return distribution is stable with a constant mean and variance. What if the mean and variance are not constant? We need to keep track of portfolio changes.23INVESTMENTS | BODIE, KANE, MARCUSFigure 24.4 Portfolio Returns24INVESTMENTS | BODIE, KANE, MARCUSMarket Timing In its pure form,