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CHAPTER TWENTY-FOUR PORTFOLIO PERFORMANCE EVALUATION

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MEASURES OF RETURN n 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 measurement

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MEASURES OF RETURN n TWO MEASURES OF RETURN Dollar-Weighted Returns 3 uses discounted cash flow approach 3 weighted because the period with the greater number of shares has a greater influence on the overall average

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MEASURES OF RETURN n TWO MEASURES OF RETURN Time-Weighted Returns 3 used when cash flows occur between beginning and ending of investment horizon 3 ignores number of shares held in each period

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MEASURES OF RETURN n TWO MEASURES OF RETURN Comparison of Time-Weighted to Dollar- Weighted Returns 3 Time-weighted useful in pension fund management where manager cannot control the deposits or withdrawals to the fund

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MAKING RELEVANT COMPARISONS n PERFORMANCE should be evaluated on the basis of a relative and not an absolute basis 3 this is done by use of a benchmark portfolio BENCHMARK PORTFOLIO 3 should be relevant and feasible 3 reflects objectives of the fund 3 reflects return as well as risk

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THE USE OF MARKET INDICES n INDICES are used to indicate performance but depend upon 3 the securities used to calculate them 3 the calculation weighting measures

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THE USE OF MARKET INDICES n INDICES Three Calculation Weighting Methods: 3 price weighting – sum prices and divided by a constant to determine average price – EXAMPLE: THE DOW JONES INDICES

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THE USE OF MARKET INDICES n INDICES Three Calculation Weighting Methods: 3 value weighting (capitalization method) – price times number of shares outstanding is summed – divide by beginning value of index – EXAMPLE: S&P500 WILSHIRE 5000 RUSSELL 1000

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THE USE OF MARKET INDICES n INDICES Three Calculation Weighting Methods: 3 equal weighting – multiply the level of the index on the previous day by the arithmetic mean of the daily price relatives – EXAMPLE: VALUE LINE COMPOSITE

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ARITHMETIC V. GEOMETRIC AVERAGES n GEOMETRIC MEAN FRAMEWORK GM = ( HPR) 1/N - 1 where = the summation of the product of HPR= the holding period returns n= the number of periods

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ARITHMETIC V. GEOMETRIC AVERAGES n GEOMETRIC MEAN FRAMEWORK measures past performance well represents exactly the constant rate of return needed to earn in each year to match some historical performance

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ARITHMETIC V. GEOMETRIC AVERAGES n 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 performance

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RISK-ADJUSTED MEASURES OF PERFORMANCE n THE REWARD TO VOLATILITLY RATIO (TREYNOR MEASURE) There are two components of risk 3 risk associated with market fluctuations 3 risk associated with the stock Characteristic Line (ex post security line) 3 defines the relationship between historical portfolio returns and the market portfolio

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TREYNOR MEASURE n TREYNOR MEASURE Formula wherear p = the average portfolio return ar f = the average risk free rate p = the slope of the characteristic line during the time period

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TREYNOR MEASURE THE CHARACTERISTIC LINE ar p pp SML

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TREYNOR MEASURE n CHARACTERISTIC LINE slope of CL 3 measures the relative volatility of portfolio returns in relation to returns for the aggregate market, i.e. the portfolio’s beta 3 the higher the slope, the more sensitive is the portfolio to the market

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TREYNOR MEASURE THE CHARACTERISTIC LINE ar p pp SML

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THE SHARPE RATIO n 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 p

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THE SHARPE RATIO n SHARPE RATIO formula: whereSR = the Sharpe ratio p = the total risk

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THE SHARPE RATIO n SHARPE RATIO indicates the risk premium per unit of total risk uses the Capital Market Line in its analysis

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THE SHARPE RATIO ar p pp CML

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THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE n 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

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THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE n THE JENSEN MEASURE known as the portfolio’s alpha value 3 recall the linear regression equation y = + x + e 3 alpha is the intercept

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THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE n DERIVATION OF ALPHA Let the expectations formula in terms of realized rates of return be written subtracting RFR from both sides

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THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE n 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 term

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THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE n 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 errors

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COMPARING MEASURES OF PERFORMANCE n 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 diversification

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COMPARING MEASURES OF PERFORMANCE for a completely diversified portfolio 3 SR and Treynor give identical rankings because total risk is really systematic variance 3 any difference in ranking comes directly from a difference in diversification

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CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES n Use of a market surrogate 3 Roll: criticized any measure that attempted to model the market portfolio with a surrogate such as the S&P500 – it is almost impossible to form a portfolio whose returns replicate those over time – making slight changes in the surrogate may completely change performance rankings

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CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES n measuring the risk free rate 3 using T-bills gives too low of a return making it easier for a portfolio to show superior performance 3 borrowing a T-bill rate is unrealistically low and produces too high a rate of return making it more difficult to show superior performance

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END OF CHAPTER 24

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