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?

Explanation / Answer

Portfolio Risk :

Portfolio Variance = w2A*2(RA) + w2B*2(RB) + 2*(wA)*(wB)*(RA)*(RB) * R
Where: wA and wB are portfolio weights, 2(RA) and 2(RB) are variances and R is the correlation

Note that Asset B will not be chosen as Asset C has the same variance but a lower correlation

Thus we do the calculation with C and D to see the best portfolio

1) With Asset C :

Portfolio Variance = 0.52 * 0.09 + 0.52 * 0.04 + 2 * 0.5 * 0.5 * 0.3 * 0.2 * 0.45 = 0.046

2) With Asset D :

Portfolio Variance = 0.52 * 0.09 + 0.52 * 0.0625 + 2 * 0.5 * 0.5 * 0.3 * 0.25 * 0.35 = 0.05125

1) With Asset C :

Portfolio Variance = 0.52 * 0.09 + 0.52 * 0.04 + 2 * 0.5 * 0.5 * 0.3 * 0.2 * 0.45 = 0.046

Clearly it is less with Asset C, thus we chose it.

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