Question

Assume that the returns on individual securities are generated by the following two-factor model: E(Rit)Bj Fıt + BgFu Rit Here: Rr is the return on Security i at Time t F and F 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., negative positions) are permitted. The characteristics of the four securities follow: Security 31 E(R) 1 2 3 4 1.00 50 1.00 1.50 1.50 2.00 50 .75 20% 15 20 20 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 B, 0.) (Do not round intermediate calculations. A negative answer should be indicated by a minus sign.) X1 X2 a-1. Compute the expected return and B2 coefficient for this portfolio. (Do not round intermediate calculations and enter your expected return answer as a percent. Leave no cells blank be certain to enter "0" wherever required.) 9% Expected return b. Construct a portfolio containing Securities 3 and 4, with a return that does not depend on the market factor, Ft in any way. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) X3 X4 b-1. Compute the expected return and B2 coefficient for this portfolio. (Do not round intermediate calculations and enter your expected return answer as a percent. Round your answers to the nearest whole number. Leave no cells blank be certain to enter "0" wherever required.) 96 Expected return

Answer 1

a. 1*X1 + (1-X1)*0.50 = 0

X1 = -1

X2 = 1 - (-1) = 2

a-1 Expected return = -20% + 2*15% = 10%

beta 2 = -1.5 + 2*2 = 2.5

b. X3*1 + (1-X3)*1.5 = 0

X3 = 3

X4 = 1 - 3 = -2

expected return = 20%

beta 2 = 3*0.5 - 2*075 = 0