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1. Suppose a three-factor model is appropriate to describe the returns of a stock. Information about those three factors is presented in the following chart:
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 β1 = 0.)
b. Compute the expected return and β2 coefficient for this portfolio.
c. 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.
d. Compute the expected return and β2 coefficient for this portfolio.
e. 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.
f. 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.