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

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, where each one has the following characteristics:

The capital market for these four assets is perfect in the sense that there are no transactions costs and short sales can take place.

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 1 0.) Compute the expected return and 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, F1t. Compute the expected return and 2 coefficient for this portfolio.

c. Consider a risk-free asset with expected return equal to 5 percent, 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.

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=== it R = E(R) + BiFi + BizF21