Question

How much should you invest in Y so that your portfolio will have a risk of 13%, given the following:

	X	Y
E[r]	8%	18%
St.Dev	10%	20%

The correlation between the returns of the two assets is 0.

Answer in decimal form and, if you have two answers report the one that will produce the higher expected returns.

Answer 1

Given that

Standard deviation of asset X, SDx = 10%

Standard deviation of asset Y, SDy = 20%

required risk of portfolio = 13%

correlation between two asset = 0

let weight in asset Y be w, then weight in asset X is 1-w

So, portfolio standard deviation is calculated as (For correlation 0)

SD = ((Wx*SDx)^2 + (Wy*SDy)^2)^(1/2)

=> 13^2 = ((1-w)*10)^2 + (w*20)^2

=> 169 = 100 +100w^2 -200w + 400w^2

=> 500w^2 - 200w - 69 = 0

solving quadratic equation, we get

w = (-b +- (b^2 - 4ac)^0.5)/2a = (200 +- (200^2 + 4*69*500)^0.5)/1000 = 0.6219 or -0.2219

since return in 0.6219 is higher.

So, weight of asset Y, w = 62.19% or 0.6219