Question Solved1 Answer Assume that the returns on individual securities are generated by the following two-factor model: R2 = E(R)+B:Fi + PizF, where R, is the return on security i, and E(R) is the expected return on security i. Fi and F2 are market factors. In addition, assume that there is a capital market for four securities, and the capital market for these four assets is perfect. The characteristics of the four securities follow: Security 1 2 3 4 B1 1.0 0.5 1.0 1.5 B2 1.5 2.0 0.5 0.75 E(R) 20% 20% 10% 10% (a) Construct a portfolio containing (long or short) securities 1 and 2, with a return that does not depend on the market factor, F1, in any way. Compute the expected return and B2 coefficient for this portfolio. (1 pt.) (b) Construct a portfolio containing (long or short) securities 3 and 4 with a return that does not depend on the market factor, F1. Compute the expected return and B2 coefficient for this portfolio. (1 pt.)

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Transcribed Image Text: Assume that the returns on individual securities are generated by the following two-factor model: R2 = E(R)+B:Fi + PizF, where R, is the return on security i, and E(R) is the expected return on security i. Fi and F2 are market factors. In addition, assume that there is a capital market for four securities, and the capital market for these four assets is perfect. The characteristics of the four securities follow: Security 1 2 3 4 B1 1.0 0.5 1.0 1.5 B2 1.5 2.0 0.5 0.75 E(R) 20% 20% 10% 10% (a) Construct a portfolio containing (long or short) securities 1 and 2, with a return that does not depend on the market factor, F1, in any way. Compute the expected return and B2 coefficient for this portfolio. (1 pt.) (b) Construct a portfolio containing (long or short) securities 3 and 4 with a return that does not depend on the market factor, F1. Compute the expected return and B2 coefficient for this portfolio. (1 pt.)
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Transcribed Image Text: Assume that the returns on individual securities are generated by the following two-factor model: R2 = E(R)+B:Fi + PizF, where R, is the return on security i, and E(R) is the expected return on security i. Fi and F2 are market factors. In addition, assume that there is a capital market for four securities, and the capital market for these four assets is perfect. The characteristics of the four securities follow: Security 1 2 3 4 B1 1.0 0.5 1.0 1.5 B2 1.5 2.0 0.5 0.75 E(R) 20% 20% 10% 10% (a) Construct a portfolio containing (long or short) securities 1 and 2, with a return that does not depend on the market factor, F1, in any way. Compute the expected return and B2 coefficient for this portfolio. (1 pt.) (b) Construct a portfolio containing (long or short) securities 3 and 4 with a return that does not depend on the market factor, F1. Compute the expected return and B2 coefficient for this portfolio. (1 pt.)
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First of all I am sorry  , The sum has a lot of sub parts , and I can answer only 4 as per Chegg Guidelines. I will try my best. PLEASE GV A RATING IF U LIKE MY EFFORTS, IT WILL KEEP US MOTIVATED. THANK YOU  IN ADVANCE. In case u need further clarification, use Comment box. Thank U Ans: a) Since the return does not depend on F1, so Beta 1 = 0 Let the weight of security 1 = X1 So, the weight of security 2 = 1- X1......................(1) Wt beta of security 1 and 2 = 0 (Wt 1 *Beta 1 ) + (Wt2 * Beta 2) = 0 (X1*1.0) + (0.5*(1-X1)) = 0 X1 + 0.5 - 0.5X1 = 0 0.5X1 = - 0.5 X1 = -1   So substituting in eq (1) Wt of X 2 = 1 - X1 = 1 - (-1) = 1+ 1 Wt of X2 =  2   a-1 Expected return = (Wts * Individual Returns) =  (-1 * 20% ) + (2*20%) = -20% + 40% = 20% (Wt 1 *Beta 1 ) ... See the full answer