Question

Consider the following multifactor (APT) model of security returns for a particular stock.

Factor	Factor Beta	Factor Risk Premium
Inflation	1.7	5	%
Industrial production	1.3	8
Oil prices	0.8	2

a. If T-bills currently offer a 8% yield, find the expected rate of return on this stock if the market views the stock as fairly priced. (Do not round intermediate calculations. Round your answer to 1 decimal place.)

b. Suppose that the market expects the values for the three macro factors given in column 1 below, but that the actual values turn out as given in column 2. Calculate the revised expectations for the rate of return on the stock once the “surprises” become known. (Do not round intermediate calculations. Round your answer to 1 decimal place.)

Factor	Expected Value		Actual Value
Inflation	5	%	3	%
Industrial production	3		5
Oil prices	1		0

Answer 1

a. The expected rate of return is computed as follows:

= Risk free rate + Beta₁ x Factor risk premium₁ + Beta₂ x Factor risk premium₂ + Beta₃ x Factor risk premium₃

Risk free rate = 8% or 0.08

Beta₁ = 1.7

Factor risk premium₁ = 5% or 0.05

Beta₂ = 1.3

Factor risk premium₂ = 8% or 0.08

Beta₃ = 0.8

Factor risk premium₃ = 2% or 0.02

Now by plugging these values in the above mentioned formula we shall get:

= 0.08 + 1.7 ( 0.05 ) + 1.3 ( 0.08 ) + 0.8 ( 0.02 )

= 28.5%

b. Revised Expectations on rate of return is computed as follows:

= Beta₁ x ( Actual value₁ - Expected Value₁ ) + Beta₂ x ( Actual value₂ - Expected Value₂ ) + Beta₃ x ( Actual value₃ - Expected Value₃ )

= 1.7 ( 3% - 5% ) + 1.3 ( 5% - 3% ) + 0.8 ( 0% - 1% )

= - 1.6%

So the revised expectations on rate of return will be

= 28.5% - 1.6%

= 26.9%

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