1 Arbitrage Pricing Theory 1. Consider the APT for a finance economy with T = 1 and only three equally likely states, i.e. S = 3 with probabilities 7 (s) 1/3 for s = 1,2,3. Suppose there are two factors, which are given, in their raw form, by 0 -- and F2 2 1 (1) De-mean and orthogonalize the factors to obtain fi and f2. What is the factor span? (Hint: It may help to know that the following matrix decomposition holds: (11) -0() where the columns of the rightmost matrix are the two right eigenvectors of the matrix on the left hand side. (2) Write out the APT assumptions and determine what these hypotheses imply about the residuals for any security. (3) Calculate the two betas for any security return vector. (4) What can be said about market in completeness in this economy? 1 Arbitrage Pricing Theory 1. Consider the APT for a finance economy with T = 1 and only three equally likely states, i.e. S = 3 with probabilities 7 (s) 1/3 for s = 1,2,3. Suppose there are two factors, which are given, in their raw form, by 0 -- and F2 2 1 (1) De-mean and orthogonalize the factors to obtain fi and f2. What is the factor span? (Hint: It may help to know that the following matrix decomposition holds: (11) -0() where the columns of the rightmost matrix are the two right eigenvectors of the matrix on the left hand side. (2) Write out the APT assumptions and determine what these hypotheses imply about the residuals for any security. (3) Calculate the two betas for any security return vector. (4) What can be said about market in completeness in this economy