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

R it = E ( R it )  +  β ij F 1t  +  β i2 F 2t Here:

Rit is the return for security i at time t F1t and F2t 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 β1 β2 E(R)(%)
1 1.0 1.50 20 2 0.5 2.00 20 3 1.0 0.50 10 4 1.5 0.75 10

(a) Construct a portfolio containing (long or short) securities 1 and 2, with a return that does not depend on the market factor, F1t, in any way. (Hint: Such a portfolio will have βl = 0.) Compute the expected return and β2 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 F1t. Compute the expected return and β2 coefficient for this portfolio.

(c) There is a risk-free asset with expected return equal to 5 per cent, βl = 0, and β2 = 0. 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 and long run? Graph your analysis.