Question

2. You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 2% 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 0.10 and variance of 0.0081, and Y has an expected rate of return of 0.06 and a variance of 0.0036. The coefficient of correlation, rho, between X and Y is 0.45. If you decide to hold a complete portfolio that has a standard deviation of expected returns, i.e., the risk or sigma, of 10% (35%) Phey =9S 60% tyo% 1800'

Answer 1

The formula for standard deviation is:

Under root (W1²SD1² + W2²SD2² + 2W1SD1*W2SD2*rho)

Under root (0.4² * 0.0081 + 0.6² * 0.0036 + 2*0.4*0.09*0.6*0.06*0.45)

=0.086

Assuming 35% in question is weight mentioned:

1000 * 35% = 350 in portfolio P

2% TRSY = 1000-350 = 650

In portfolio P:

X = 40% * 350 = 140

Y = 60% * 350 = 210

SR for risky portfolio :

0.076-0.02 / 0.086 = 0.651

Expected Ret for portfolio: Wi * Ri

0.14*0.1 + 0.6*0.06 + 0.65*0.02 = 0.063