Question

You are considering investing $2900 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 75% and 25% respectively. X has an expected rate of return of 16.0%, and Y has an expected rate of return of 13%. To form a complete portfolio with an expected rate of return of 10%, you should invest approximately ________ in the risky portfolio. This will mean you will also invest approximately ________ and ________ of your complete portfolio in security X and Y, respectively.

50%; 38%; 13%

53%; 40%; 13%

0%; 75%; 25%

29%; 59%; 12%

Answer 1

a). E(R_risky) = [Pi x Ri]

    = [0.75 x 16%] + [0.25 x 13%] = 12% + 3.25% = 15.25%

Let Investment in Risky Portfolio be X, then Investment in Risk-Free is (1 - X)

E(R_p) = [Pi x Ri]

10% = [15.25% * X] + [4% * (1 - X)]

10% = X(15.25%) + 4% - X(4%)

6% = X(11.25%)

X = 6% / 11.25% = 0.5333, or 53.33%

b). Investment in security X = Investment in Risky Portfolio x 75%

= 53.33% x 0.75 = 40%

Investment in security Y = Investment in Risky Portfolio x 25%

= 53.33% x 0.25 = 13.33%

Hence, Option "B" is correct.