Question

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed

of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and

Y. The optimal weights of X and Y in P are 40% and 60%, respectively. X has an expected rate of

return of 0.12 and variance of 0.0081, and Y has an expected rate of return of 0.09 and a variance

of 0.0016. The coefficient of correlation, rho, between X and Y is 0.45. If you decide to hold a

complete portfolio that has an expected outcome of $1,180

a. What will be the dollar values of your positions in X, Y, and Treasury bills,

respectively? (10%)

b. What is the risk for the risky portfolio P (10%)?

c. What is the SR for the risky portfolio P (5%)?

d. What is the risk for this complete portfolio C (5%)?

(Hint: risk in complete portfolio C is the product of y (the weight in P) and the risk of P.

e. What is the SR for this complete portfolio C (5%)?

Answer 1

a Expected outcome of Complete porttalio=1180 Expected setup of Complete portfolio = 1180-1oooloo a 1000 Hence, if 18= w x E(Rp) + W X Elhy 18 = (W x [ 0.4x12 +06+ 9] + (1-Wp ) x 5 & L ar24.5 = /5 we know that p Comprises of two Stocks X and Y E W = 40% of 2.5=ORGI Wy = 60 % of 2.5= 1.5 We l.Sevd alt al 25 Dollar value of x= x 1000 = $ 1000 Dollar value of Y= 1.5x1000 = $ 1500 Dollar value of Treasury = - 15x1000 - $1.500 1 of Risk or million s.D of risky Paltolio P. euro twy o y + 2 w W X TX Goreet on & 81 t o.f2 x 16+ 2x0.480 6X9X4 X45 © = 5.15 % SRis, Shape ratio of P = E(Rp) - ht =- [6-4X12+ 06 - 5- lool Teachers Teacher (Ronde comment 5.15 places