You are a portfolio investor and, for simplicity, are investing in only two asse

Question

You are a portfolio investor and, for simplicity, are investing in only two assets. You must invest in one asset(called Asset A) and then choose one additional asset from a choice of 3 assets. The asset you must invest in has a variance of 0.09. Now, you must choose 1 asset from the following 3.

i) asset B has a variance of 0.04 and a correlation of 0.90 with Asset A.

ii) Asset C has a variance of 0.04 and a correlation of 0.45 with Asset A.

iii) Asset D has a standard deviation of 0.25 and a correlation of 0.35 with Asset A.

Assume equal weights in Asset A and the 2nd asset you choose. You are to choose the asset that provides you the lowest portfolio risk. Which asset do you choose? (please show all work for i, ii and iii.)

Explanation / Answer

Let,

v1 = variance of first asset

v2 = variance of second asset

o = correlation between two assets

w1 = weight of first asset

w2 = weight of second asset

Variance of the portfolio

= v1*(w1)^2 + v2*(w2)^2 + 2*w1*w2*(v1v2)^0.5

Now,

1. Varianc of A and B:

= 0.09*(0.5)^2 + 0.04*(0.5)^2 + 2*0.9*0.5*0.5*(0.09*0.04)^0.5

= 0.0225 + 0.01 + 0.027 = 0.0595

2. Variance of A and C:

= 0.09*(0.5)^2 + 0.04*(0.5)^2 + 2*0.45*0.5*0.5*(0.09*0.04)^0.5

= 0.0225 + 0.01 + 0.0135

= 0.046

3. Variance of D = (Standard Deviation of D)^2 = (0.25)^2 = 0.0625

Variance of A and D:

= 0.09*(0.5)^2 + 0.0625*(0.5)^2 + 2*0.35*0.5*0.5*(0.09*0.0625)^0.5

= 0.0225 + 0.015625 + 0.013125

= 0.05125

From the above calculations, we can see that portfolio with A and C has the lowest portfoilio variance of 0.046.

Thus, we choose asset C.

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