Question

The following question illustrates the APT. Imagine that there are only two pervasive macroeconomic factors. Investments X, Y, and Z have the following sensitivities to these two factors:

Investment	b1	b2
X	1.75	0
Y	−1.00	2.00
Z	2.00	1.00

We assume that the expected risk premium is 6.2% on factor 1 and 10.2% on factor 2. Treasury bills obviously offer zero risk premium.

a. According to the APT, what is the risk premium on each of the three stocks? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Stocks	Risk Premiums
X	%
Y	%
Z	%

b-1. Suppose you buy $380 of X and $95 of Y and sell $285 of Z. What is the sensitivity of your portfolio to each of the two factors? (Leave no cells blank, enter "0" wherever required. A negative answer should be indicated by a minus sign. Round your answers to 2 decimal places.)

	Sensitivity
Factor 1
Factor 2

b-2. What is the expected risk premium? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Expected risk premium             %

c-1. Suppose you buy $152 of X and $114 of Y and sell $76 of Z. What is the sensitivity of your portfolio to each of the two factors? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Sensitivity
Factor 1
Factor 2

c-2. What is the expected risk premium? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Expected risk premium             %

d-1. Finally, suppose you buy $304 of X and $38 of Y and sell $152 of Z. What is your portfolio's sensitivity now to each of the two factors? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 1 decimal place.)

	Sensitivity
Factor 1
Factor 2

d-2. What is the expected risk premium? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Expected risk premium             %

Answer 1

1.
=1.75*6.2%+0*10.2%=10.85%

2.
=-1*6.2%+2*10.2%=14.20%

3.
=2*6.2%+1*10.2%=0.226

4.
=(1.75*380-1*95-2*285)/(380+95-285)=0

5.
=(0*380+2*95-1*285)/(380+95-285)=-0.5

6.
=(1.75*380-1*95-2*285)/(380+95-285)*6.2%+(0*380+2*95-1*285)/(380+95-285)*10.2%=-5.1%

7.
=(1.75*152-1*114-2*76)/(152+114-76)=0

8.
=(0*152+2*114-1*76)/(152+114-76)=0.8

9.
=(1.75*152-1*114-2*76)/(152+114-76)*6.2%+(0*152+2*114-1*76)/(152+114-76)*10.2%=8.16%

10.
=(1.75*304-1*38-2*152)/(304+38-152)=1

11.
=(0*304+2*38-1*152)/(304+38-152)=-0.4

12.
=(1.75*304-1*38-2*152)/(304+38-152)*6.2%+(0*304+2*38-1*152)/(304+38-152)*10.2%=2.12%