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Equity Valuation and Portfolio Management by Harry M. Markowitz, Frank J. Fabozzi

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QUESTIONS

Questions 1 through 5 pertain to the following information:

Assume that a portfolio managers constructs an equally-weighted portfolio of two stocks from different industries and wants to analyze the risk of this portfolio using a two-factor model in the following form:

image

where FIND is the industry factor and FSIZE is the size factor return, β and l are the security loadings to these two factors respectively and imageis the idiosyncratic return.

Using statistical techniques, the portfolio manager finds that the first stock has an industry beta of β1 = 1.4 and the second stock has an industry beta of β2 = 0.8. This means that the first stock moves more than average when its industry moves in a certain direction and the opposite is true for the second stock. The loading to the size factor (l) is a function of the market value of the company and is standardized such that it has a mean of 0 and a standard deviation of 1. Using this formulation, the portfolio manager finds that the first stock has a size loading of l1= −1. This means that the market value of this stock is 1 standard deviation smaller than the market average. The second stock has a size loading of l2 = 2, which tells us that it belongs to a large-cap company.

The industry factor corresponding to the first stock has a ...

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