Question

# You are considering investing \$2,300 in a complete portfolio. The complete portfolio is composed of Treasury...

 You are considering investing \$2,300 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 60% and 40% respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 12%. To form a complete portfolio with an expected rate of return of 8%, 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.

 Amount invested 2300 Risk-free rate 4% Optmial weight of X in P 60% Optmial weight of Y in P 40% expected return of X 14% expected return of Y 12% Expected return of Risky portfolio = (Weight of X * Exp. Return) + (weight of Y * exp. Return) (0.60*14)+(0.40*12) 13.200% Expected return of complete portfolio = 8% Assume weight of P = x, weight of risk free = 1-x 8 = (x * 13.2) + (1-x)*4) 8 =13.2x + 4 - 4x 4 = 9.2x x = 0.434782609 Amount to be invested in Risky portfolio = 2300*0.4348 = \$1000 Amount invested in x = 1000*60% = \$600 Amount invested in y = 1000*40% = \$400