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

Answer) The portfolio with the lowest risk is with C

St. deviation of stock = (Variance of stock)^1/2

Portfolio St. deviation = [(Weight of Stock A * St. deviation of Stock A)^2 + (Weight of Stock C * St. deviation of Stock C )^2 + 2* Weight of Stock A * St. deviation of Stock A * Weight of Stock C * St. deviation of Stock C*correlation coefficient) ]^1/2

Using the formulae for St, deviation I have calculated the st. deviation of A and C

St. deviation of A = 30%

St. deviation of C = 20%

Correlation of A & C = 0.45

Portfolio St. deviation A & C = [ ( 0.0225) + (0.01) + (0.0135) ] ^ 1/2

= [(0.046)]^1/2 = 21.45%

Similary I had applied the above formulaes and calculated Portfolio St. deviation of A with D and B

Portfolio st. deviation of A with B = 24.39%

Portfolio st. deviation of A with D = 33.35%

Hence the portfolio of A with C had the least risk.

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