Question

4. Howie, a security analyst, has used the concept of multiple regression to determine the sensitivity of a certain stock to various factors. He has found that the following factors are the most indicative of his stock’s returns:

Factor	Factor Beta	Factor risk premium
Inflation	1.2	3%
unemployment	0.8	5%
Industrial production	0.7	6%

If the rate on 90-day T-bills is 3%,

a. what is the expected return for this stock?

b. What is the Jensen Alpha if the portfolio return is 12%

Answer 1

a. Calcualting expected return for this stock

Generally under CAPM model we use to take only beta for calculating expected return but as per Arbitrage Pricing Theory (APT) the expected return varies due to several factors.

So according to APT method the formula to find the expected return for this stock=

=Risk free rate of return+ (Beta *risk premium) of each factor

= Risk free rate of return+(inflation beta* inflation risk premium)+(unemployement beta*unemployement risk premium)+(Industrial production beta*Industrial production risk premium)

considering t bill interest rate as risk free interest rate Rf= 3%

=3%+(1.2*3%)+(0.8*5%)+(0.7*6%)

=expected return for this stock=14.8%

b. Jensen Alpha = given return of the portfolio -return calculated as above

if Jensen Alpha is positive it means portfolio has out performed when compared to the market and if Jensen Alpha is negative it means the portfolio has under performed when compared to the market.

so given portfolio return = 12%

Jensen Alpha = 12%-14.8%= -2.8%

this means portfolio has under performed when compared to the market.