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%

Option (B) 5.5%

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%