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Villanova SMF Chapter 9 Elton, Gruber, Brown & Goetzmann

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Formation of Optimal Portfolios The Single Index Model is Superior As shown in chapter 7 Stocks are analyzed and ranked based on excess return and beta. The portfolio weighting of the individual asset is based on the following:

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Table 9-1 Data Required to Determine Optimal Portfolio R F = 5% Elton, Gruber, Brown, and Goetzman: Modern Portfolio Theory and Investment Analysis, Sixth Edition © John Wiley & Sons, Inc. Security Ranking

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Table 9-2 Calculations for Determining Cut-off Rate with s 2 m = 10 Elton, Gruber, Brown, and Goetzman: Modern Portfolio Theory and Investment Analysis, Sixth Edition © John Wiley & Sons, Inc. Cut-off Rates

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Table 9-5 Optimum Percentages Elton, Gruber, Brown, and Goetzman: Modern Portfolio Theory and Investment Analysis, Sixth Edition © John Wiley & Sons, Inc. Short Sales

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Security Selection with a Purchasable Index This equation measures the excess returns as functions of risk (m designates the index) We compare assets with betas identical to the index If a passive combination of a riskless asset and an index have a higher return than Ri, the individual asset should not be purchased (in fact it should be shorted.)

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The Constant Correlation Model This model assumes that all securites share the same correlation, therefore standard deviation replaces Beta as the key measure of risk Securities can be ranked by their excess return as a portion of standard deviation (risk)

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Table 9-6 Data to Determine Ranking R F = 5% Elton, Gruber, Brown, and Goetzman: Modern Portfolio Theory and Investment Analysis, Sixth Edition © John Wiley & Sons, Inc. Determine Ranking

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Finding the Cut-off Rate The method is similar to the single-index model We find the cutoff rate Ci and choose based on that. Similar to previous discussions if short sales are allowed all stocks that do not make the cutoff are held in the short portfolio Note that the assumed correlation between all securities is.5 Also notice that the rate drops after the third security

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Table 9-7 Determining the Cut-off Rate r = 0.5 Elton, Gruber, Brown, and Goetzman: Modern Portfolio Theory and Investment Analysis, Sixth Edition © John Wiley & Sons, Inc. Determining Cut-Off

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Other Return Structures When Multi-group models are employed ranking is based on both excess return and standard deviation. There may be many different cut off rates from group to group. Beta is important in single index models because it measures the risk of the asset on the portfolio as a whole.

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