Question

Consider a stock that is sensitive to three risk factors. The risk premiums of this stock for these three factors are 3%, 7% and 1%. In terms of sensitivity to these three risk factors, the values are 1.2, 1.8 and 0.6, respectively. The return on a zero beta stock is 3%. Calculate the expected return of this stock using the APT model assuming the numerical value of the error term is 0.

17.8%

19.8%

21.8%

12.8%

Answer 1

Factors	Risk Premium	Sensitivity( Beta)
Factor 1	3%	1.2
Factor 2	7%	1.8
Factor 3	1%	0.6
Risk Free Return= 3%
Calculation of Expected Return
Using APT model,
Expected Return=	Rf+ Factor 1 Risk Premium x Factor 1 Beta + Factor 2 Risk Premium x Factor 2 Beta + Factor 3 Risk Premium x Factor 3 Beta
Expected Return=	3% + 3%x 1.2+ 7% x 1.8+ 1% x 0.6
Expected Return=	3% + 3.6% + 12.6%+ 0.6%
Expected Return=	19.80%