Question

Consider a portfolio consisting of the following two risky assets. Asset i Hi, Return on Asset i 7% 7% 0, Risk in Asset i 18% 14% The coefficient of correlation between the returns is p = -100%. (a) State the expected return and associated risk (as measured by the standard deviation) in terms of w if w is the weight allocation of Asset 1 in the portfolio. Hry (w) = 0.07 Or, (w) = sqrt(0.0632w^2-0.C (b) Suppose that the portfolio was constructed so that it's risk (as measured by the standard deviation) was minimized. Determine the following: (1) The percentage of the portfolio's initial value invested in: Asset 1, w = w1 = 43.75 % to 2 decimal places Asset 2, W2 = 56.25 % to 2 decimal places (ii) The expected rate of return on the portfolio.

Answer 1

a. urv(w) = 0.07 (w) + 0.07 (1 - w) = 0.07

Std.dev(w) = ((w^2)*(0.18)^2) + ((1-w)^2)*(0.14)^2) + 2*w*(1-w)*0.14*0.18*(-1)

b. Weight of asset A for minimum variance(risk) = (σb²-ρabσaσb) / (σa² + σb² – 2ρabσaσb)

Putting the values and solving the equation gives => w(1) = 43.75%

w(2) = 100 - 43.75 = 56.25%

Portfolio return = 0.4375*0.07 + 0.5625 *0.07 = 0.07 or 7%

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