The two-factor model for Security A is -4% + 6%(IP) + 2%(M) and for Security B is 1.5% + 3%(IP) + 2.5%(M). An analyst forecasts IP at 1.5% and M at 3% with respective variances at 3% and 2%. The Covariance of Securities A and B is 80.8. Covariance (IP, M) is
A) .1.
B) 1.4.
C) .8.
D) .6.

Question

Quizplus · Accepted Answer

The two-factor model for security is given by:
Ri = ai + biIP + ei
where Ri represents the return on security i, ai is the constant term, bi is the sensitivity of the security to changes in the market factor IP, and ei is the error term. The covariance of securities can be calculated as:
Cov (Ri, Rj) = bi,bjCov (IP, IP) + ei, ej
Here, we are given Cov (IP, M) and we need to find its value. Since we do not have any information on the sensitivities of the securities, we cannot calculate the covariance directly. However, we can use the fact that Cov (IP, M) = Var (IP) = 1.5% to eliminate some of the answer choices. Only option C satisfies this requirement. Therefore, the correct answer is C.

The Two-Factor Model for Security a Is -4% + 6%(IP)