The first picture shows the question, part (iii) what are the mean return and variance of the portfolios if they are 50% finananced by borrowing?

I dont know how to solve this one

The second picture shows the answer

I am confused by the answer, from where did they get Xp=2 Xf= -1 and so on

Kindly show me the working out of part iii with maybe an explanation so I understand and get how to solve it

Thanks!

Tuses Exercise Sheet 7 Exercise 1 Assume thereare two stocks A and B, with -1.4 and -0.8. Asume also that the CAPM model applics. (i) If the mean return on the market portfolio is 10% and the risk-free rate of return is 5%, calculate the mean return of the portfolios coasisting of: a, 75% of stock A and 25% of stock D. b. 50% of stock A and 50% of stock B, 25% of stock A and 75% of stock B. (ii) If the idiosyncratic variations of the stocks are .A-4, .a-2 and the variance of the market portfolio is 11-12, calculate the variance of the portfolios in (a), (b), (c). (iii) What are the mean return and variance of the portfolio Solution 1 (1) The security market line can be used to write if they are 50% finanoed by borrowing? -5+14(105) and fa 5+08(10-5) - For the portfolios 0.75 x 12 + 0.25 x 9 11.25, b, 0.5x12 + 0.5 x 9 10.5, f, = c. rp 0.25 12 + 0.75 x 9 9.75. = (u) The beta of a portfolio is found using and the variance Nou S Applying these results a a, 0.75 x 1.4 + 0.25 0.8 1.25 1.25212+(0.75216+0.2524) 28 b, , -0.5x 1.4 + 0.5 x 0.8 ; -1.1212 + (0.5216 + 0.524) 19.52. 0.25 x 1.4+0.75 x 0.8 -0.95 c. = , -0.952 12 + (0.25216+0.7524) 14.08 (iii) If 50% financed by borrowing the portfolio proportions are X-2 and X--1. So the exxpected return and variance are Evaluating for the individual portfolios a. f.-2x 11.25-1 x 5 17.5, : 22 x 28-112. b. f.. MM-1 x 5 = 16,22 x 19.52-78.08. C. f.-2x 9.75-1x 5 14.5, :-22 x 14.08-56.32. Exercise 2 Assume there are just two risky securities in the market portiolio. Security A, which constitutes 40% of this portfolio, has an expected return of 10% and a standard deviation of 20%. Security B has an expected return of 15% and a standard deviation of 28%. If the correlation between the assets is 0.3 and the risk free rate 5%, calculate the capital market line. Solution 2 The expected return on the market is 0.4 x 10+0.6 x 15-13