Question

Emily, an analyst at Fantastique Computers (FC), models the company’s stock assuming that the return earned on all stocks depends on only three risk factors: inflation, industrial production, and the market's aggregate degree of risk aversion. In today's economy, the risk-free rate ( ) is 8%, while the return on the market portfolio ( ) is 15%. Any remaining relevant data is given in the following table:

Variable :

The required rate of return on an inflation portfolio, 13%

The required return on an industrial production portfolio, 10%

The required return on a risk-bearing portfolio, 6%

Factor sensitivity to the inflation portfolio, 0.9

Factor sensitivity to the industrial production portfolio, 1.2 Factor sensitivity to the risk-bearing portfolio, 0.7

FantastiqueComputers’s beta, 1.1

Using an APT model, Emily calculates that FC’s required rate of return is:

a) 13.50%

b) 13.00%

c) 15.70%

d) 5.50%

If Emily used the Capital Asset Pricing Model, she would have calculated that FC’s required rate of return is:

a) 15.70%

b) 0.30%

c) 13.50%

d) -7.70%

Answer 1

The APT model:

The required return in the APT model can be calculated as :

E(R) = Rf + risk premium of inflation*factor sensitivity + risk premium of industrial production* factor sensitivity + risk premium of risk bearing*factor sensitivity

= 8 + (0.9)(13 - 8) + 1.2(10 - 8) + 0.7( 6 - 8)

= 8 + 4.5 + 2.4 - 1.4

=13.5%.

The correct option is option a.

The required return by the CAPM model is :

Re = Rf + (Rm- Rf) beta

= 8 + (15 - 8)1.1

= 15.7%.

The correct option is option a.

the required return by FC is 15.7%.