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 8.2% on factor 1 and 12.2% on factor 2. Treasury bills obviously offer zero risk premium.

1. According to the APT, what is the risk premium on each of the three stocks?

1b Suppose you buy $540 of X and $135 of Y and sell $405 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium?

2. Suppose you buy $216 of X and $162 of Y and sell $108 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium?

2b Finally, suppose you buy $432 of X and $54 of Y and sell $216 of Z. What is your portfolio's sensitivity now to each of the two factors? And what is the expected risk premium?