$12\mathrm{.}7$ CAPM versus AP$.$ What is the relationship between the one$-$factor model and the CAPM?

Questions and Problems

Factor Models A researcher has determined that a two$-$factor model is appropriate to determine

the return on a stock. The factors are the percentage change in GNP and an interest rate. GNP is

expected to grow by $3\mathrm{.}6$ percent, and the interest rate is expected to be $3\mathrm{.}1$ percent. A stock has a

beta of $1\mathrm{.}3$ on the percentage change in GNP and a beta of $2\mathrm{.}75$ on the interest rate. If the

expected rate of return on the stock is $12$ percent, what is the revised expected return on the

stock if GNP actually grows by $3\mathrm{.}2$ percent and the interest rate is $3\mathrm{.}4$ percent?

Factor Models. Suppose a three$-$factor model is appropriate to describe the returns of a stock.

Information about those three factors is presented in the following chart:

a$.$ What is the systematic risk of the stock return?

b$.$ Suppose unexpected bad news about the firm was announced that causes the stock price to drop

by $1\mathrm{.}1$ percent. If the expected return on the stock is $12\mathrm{.}8$ percent, what is the total return on this

stock?

Factor Models. Suppose a factor model is appropriate to describe the returns on a stock. The

current expected return on the stock is $10\mathrm{.}5$ percent. Information about those factors is presented

in the following chart:

a$.$ What is the systematic risk of the stock return?

b$.$ The firm announced that its market share had unexpectedly increased from $23$ percent to $27$

percent. Investors know from past experience that the stock return will increase by $\mathrm{.}45$

percent for every $1$ percent increase in its market share. What is the unsystematic risk of the

stock?

c$.$ What is the total return on this stock?

Multifactor Models. Suppose stock returns can be explained by a two$-$factor model. The firm$-$

specific risks for all stocks are independent. The following table shows the information for two

diversified portfolios:

If the risk$-$free rate is $4$ percent, what are the risk premiums for each factor in this model?