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

R_it = E (R_it) + b β_ij F_1t + β_t2 F_2t

Here:

R_it is the return on Security i at Time t.

F_1t and F_2t 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:

a. Construct a portfolio containing (long or short) Securities 1 and 2, with a return that does not depend on the market factor, F_1t, in any way. 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, F_1t. Compute the expected return and β₂ coefficient for this portfolio.

c. There is a risk-free asset with an expected return equal to 5 percent, β₁ = 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 run and long run? Graph your analysis.

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E(R) 20% 20 10 10 Security β2 1.0 .5 1.5 2.0 1.5 .75