Question

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

Factor	Factor Beta	Factor Risk Premium
Inflation	1.1	8	%
Industrial production	0.6	9
Oil prices	0.3	7

a. If T-bills currently offer a 7% 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	8	%	8	%
Industrial production	5		9
Oil prices	2		0

Answer 1

Solution 1:

The APT formula is

E(ri) = rf + Beta i1 * RP1 + Beta i2 * RP2 + ......... + Beta kn * RPn

Where

rf = Risk free rate of return

Betai = Beta of the specified factor

RP = Risk Premium of specified factor

kn = n th factor

Treasury bill or T-Bill is a Risk Free Investment that's why its yield will be the Risk free rate of return

E(ri) = 7 + 1.1*8 + 0.6*9 + 0.3*7

E(ri) = 7 + 8.8 + 5.4 + 2.1

E(ri) = 23.3%

Solution 2 :

Surprises in the macro factors will result in surprises in the return of the stock

Unexpected return from the macro factors :

1.1 * (8-8) + 0.6 * (9 -5) + 0.3 * (0-2)

= 1.8%

E(ri) = 23.3 + 1.8

E(ri) = 25.1 %