Equity Valuation and Portfolio Management

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:

where F^IND is the industry factor and F^SIZE is the size factor return, β and l are the security loadings to these two factors respectively and is 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 ...