1. Emily, an analyst at Fantastique Computers (FC), models the company’s stock a

Question

1. 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%

Explanation / Answer

APT Model

Risk free rate (RF) = 8%

Required rate of return of inflation (Ri) = 13%

Required rate of return of industrial Production (Rip) = 10%

Required rate of return of Risk Bearing Portfolio (Rr) = 8%

bi = 0.9

bip = 1.2

br = 0.7

Required rate of return using multi Factor APT Model is calculated below using following formula:

Required rate of return = RF + (Ri – RF)× bi + (Rip – RF)× bip + (Rr – RF)× br

                                      = 8% + (13% – 8%) × 0.9 + (10% – 8%) × 1.2+ (6% – 8%) × 0.7

                                      = 8% + 4.5% + 2.4% - 1.4%

                                      =13.5%

Required rate of return for Fantastique Computers using APT model is 13.5%.

Hence, Option (A) is correct answer.

Again

CAPM Model

Risk free rate = 8%

Market return = 15%

Beta = 1.1

Expected rate of return is calculated below using CAPM formula:

Expected rate of return = Risk free rate + (Market Return - Risk free rate) × Beta

                                      = 8% + (15% - 8%) × 1.1

                                      = 8% + 7% × 1.1

                                      = 8% + 7.70%

                                      = 15.70%

Expected rate of return of company stock is 15.70%.

Hence, Option (A) is correct answer.

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