APT Assume that the returns on individual securities are generated by the following two-factor model:

R it 5 E ( R it ) 1 b ij F 1 t 1 b i 2 F 2 t Here:

R it is the return on Security i at Time t.

F 1 t and F 2 t are market factors with zero expectation and zero covariance.

In addition, assume that there is a capital market for four securities, and the capital market for these four assets is perfect in the sense that there are no transaction costs and short sales (i.e., negative positions) are permitted. The characteristics of the four securities follow:

Security b1 b2 E(R)

1 1.0 1.5 20%

2 .5 2.0 20 3 1.0 .5 10 4 1.5 .75 10

a. Construct a portfolio containing (long or short) Securities 1 and 2, with a return that does not depend on the market factor, F 1 t , in any way. ( Hint: Such a portfolio will have b 1 5 0.) Compute the expected return and b 2 coefficient for this portfolio.

b. Following the procedure in (a), construct a portfolio containing Securities 3 and 4 with a return that does not depend on the market factor, F 1 t . Compute the expected return and b 2 coefficient for this portfolio.

c. There is a risk-free asset with an expected return equal to 5 percent, b 1 5 0, and b 2 50.

Describe a possible arbitrage opportunity in such detail that an investor could implement it.

d. What effect would the existence of these kinds of arbitrage opportunities have on the capital markets for these securities in the short run and long run? Graph your analysis.