Question

Consider the multi-factor APT with two factors. The risk premiums on the factor 1 and factor 2 portfolios are respectively 5% and 3%. Stock A has a beta of 1.4 on factor 1, and a beta of 0.5 on factor 2. The expected return on stock A is 14%. If no arbitrage opportunities exist, the risk-free rate of return is __________.

A) 5.0%
B) 5.5%
C) 6.0%
D) 6.5%

Answer 1

Option (B) 5.5%

Step-by-step explanation:

Data provided in the question :

Factor Risk premium

Factor 1 5%

Factor 2 3%

Beta of stock A on factor 1 = 1.4

Beta of stock A on factor 2 = 0.5

Expected return = 14%

Now,

Expected return

= Risk free rate + (Beta of factor 1 × Risk premium of factor 1) + (Beta of factor 2 × Risk premium of factor 2)

or

14% = Risk free rate + (1.4 × 5%) + (0.5 × 3%)

or

14% = Risk free rate + ( 7% + 1.5% )

or

Risk free rate = 5.5%

Hence,

Option (B) 5.5%