# Chapter 9 Elton, Gruber, Brown & Goetzmann

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Chapter 9 Elton, Gruber, Brown & Goetzmann
Villanova SMF Chapter 9 Elton, Gruber, Brown & Goetzmann

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:

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

Table 9-2 Calculations for Determining Cut-off Rate with s2m = 10
Cut-off Rates Table 9-2 Calculations for Determining Cut-off Rate with s2m = 10 Elton, Gruber, Brown, and Goetzman: Modern Portfolio Theory and Investment Analysis, Sixth Edition © John Wiley & Sons, Inc.

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

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.)

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)

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

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

Table 9-7 Determining the Cut-off Rate r = 0.5
Determining Cut-Off 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.

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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