Question

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.

Answer 1

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