CHAPTER EIGHTEENMEASURES OF RETURNSlide 3Slide 4Slide 5MAKING RELEVANT COMPARISONSTHE USE OF MARKET INDICESSlide 8Slide 9Slide 10ARITHMETIC V. GEOMETRIC AVERAGESSlide 12Slide 13RISK-ADJUSTED MEASURES OF PERFORMANCETREYNOR MEASURESlide 16Slide 17Slide 18THE SHARPE RATIOSlide 20Slide 21Slide 22THE JENSEN MEASURE OF PORTFOLIO PERFORMANCESlide 24Slide 25Slide 26Slide 27COMPARING MEASURES OF PERFORMANCESlide 29CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURESCRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES1CHAPTER EIGHTEENPORTFOLIO PERFORMANCE EVALUATION2MEASURES OF RETURN•MEASURES OF RETURN–complicated by addition or withdrawal of money by the investor–percentage change is not reliable when the base amount may be changing–timing of additions or withdrawals is important to measurement3MEASURES OF RETURN•TWO MEASURES OF RETURN–Dollar-Weighted Returns•uses discounted cash flow approach•weighted because the period with the greater number of shares has a greater influence on the overall average4MEASURES OF RETURN•TWO MEASURES OF RETURN–Time-Weighted Returns•used when cash flows occur between beginning and ending of investment horizon•ignores number of shares held in each period5MEASURES OF RETURN•TWO MEASURES OF RETURN–Comparison of Time-Weighted to Dollar-Weighted Returns•Time-weighted useful in pension fund management where manager cannot control the deposits or withdrawals to the fund6MAKING RELEVANT COMPARISONS•PERFORMANCE–should be evaluated on the basis of a relative and not an absolute basis•this is done by use of a benchmark portfolio–BENCHMARK PORTFOLIO•should be relevant and feasible•reflects objectives of the fund•reflects return as well as risk7THE USE OF MARKET INDICES•INDICES–are used to indicate performance but depend upon•the securities used to calculate them•the calculation weighting measures8THE USE OF MARKET INDICES•INDICES–Three Calculation Weighting Methods:•price weighting–sum prices and divided by a constant to determine average price–EXAMPLE: THE DOW JONES INDICES9THE USE OF MARKET INDICES•INDICES–Three Calculation Weighting Methods:•value weighting (capitalization method)–price times number of shares outstanding is summed–divide by beginning value of index–EXAMPLE:»S&P500»WILSHIRE 5000»RUSSELL 100010THE USE OF MARKET INDICES•INDICES–Three Calculation Weighting Methods:•equal weighting–multiply the level of the index on the previous day by the arithmetic mean of the daily price relatives–EXAMPLE:»VALUE LINE COMPOSITE11ARITHMETIC V. GEOMETRIC AVERAGES•GEOMETRIC MEAN FRAMEWORKGM = ( HPR)1/N - 1where = the summation of the product of HPR= the holding period returns n= the number of periods12ARITHMETIC V. GEOMETRIC AVERAGES•GEOMETRIC MEAN FRAMEWORK–measures past performance well–represents exactly the constant rate of return needed to earn in each year to match some historical performance13ARITHMETIC V. GEOMETRIC AVERAGES•ARITHMETIC MEAN FRAMEWORK–provides a good indication of the expected rate of return for an investment during a future individual year–it is biased upward if you attempt to measure an asset’s long-run performance14RISK-ADJUSTED MEASURES OF PERFORMANCE•THE REWARD TO VOLATILITY RATIO (TREYNOR MEASURE)–There are two components of risk•risk associated with market fluctuations•risk associated with the stock–Characteristic Line (ex post security line)•defines the relationship between historical portfolio returns and the market portfolio15TREYNOR MEASURE•TREYNOR MEASURE–Formulawhere arp = the average portfolio returnarf = the average risk free ratep= the slope of the characteristicline during the time periodpfppararRVOL16TREYNOR MEASURETHE CHARACTERISTIC LINEarppSML17TREYNOR MEASURE•CHARACTERISTIC LINE–slope of CL•measures the relative volatility of portfolio returns in relation to returns for the aggregate market, i.e. the portfolio’s beta•the higher the slope, the more sensitive is the portfolio to the market18TREYNOR MEASURETHE CHARACTERISTIC LINEarppSML19THE SHARPE RATIO•THE REWARD TO VARIABILITY (SHARPE RATIO)–measure of risk-adjusted performance that uses a benchmark based on the ex-post security market line–total risk is measured by p20THE SHARPE RATIO•SHARPE RATIO–formula:where SR = the Sharpe ratiop = the total riskpfppararSR21THE SHARPE RATIO•SHARPE RATIO–indicates the risk premium per unit of total risk –uses the Capital Market Line in its analysis22THE SHARPE RATIOarppCML23THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE•BASED ON THE CAPM EQUATION–measures the average return on the portfolio over and above that predicted by the CAPM–given the portfolio’s beta and the average market return])([)( R FRrER FRrEmi24THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE•THE JENSEN MEASURE–known as the portfolio’s alpha value•recall the linear regression equation y =  + x + e•alpha is the intercept25THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE•DERIVATION OF ALPHA–Let the expectations formula in terms of realized rates of return be written–subtracting RFR from both sides jttmtjtjtuRFRRRFRR  jttmtjtjtuRFRRRFRR 26THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE•DERIVATION OF ALPHA–in this form an intercept value for the regression is not expected if all assets are in equilibrium–in words, the risk premium earned on the jth portfolio is equal to j times a market risk premium plus a random error term27THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE•DERIVATION OF ALPHA–to measure superior portfolio performance, you must allow for an intercept –a superior manager has a significant and positive alpha because of constant positive random errors28COMPARING MEASURES OF PERFORMANCE•TREYNOR V. SHARPE –SR measures uses as a measure of risk while Treynor uses –SR evaluates the manager on the basis of both rate of return performance as well as diversification29COMPARING MEASURES OF PERFORMANCE–for a completely diversified portfolio•SR and Treynor give identical rankings because total risk is really systematic variance•any difference in ranking comes directly from a difference in diversification30CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES•Use of a market surrogate•Roll: criticized any measure that attempted to model the market portfolio with a surrogate such as