Question

You invest 45% of your money in Stock Y and the rest in Stock Z. The standard deviation of Stock Y's annual returns is 56% and the standard deviation of Stock Z's annual returns is 44%. The return correlation between the two stocks is -0.6. By how many percentage points did diversification reduce your risk in this case? Write your answer out to three decimals - for example, write 6.2% as .062.

Answer 1

Standard Deviation of Portfolio =   (( Weight of Y* Standard Deviation of Y)² + ( Weight of Z* Standard Deviation of Z)² +2 * Weight of Y* Weight of Z* Standard Deviation of Y* Standard Deviation of Z* Correlation coefficient)^0.5
=((45%*56%)^2+(55%*44%)^2+2*45%*55%*56%*44%*-0.6)^0.5 =22.11045%

Without diversification Standard Deviation of Portfolio =Weight of Y*Standard Deviation of Y+Weight of Z*Standard Deviation of Z =45%*56%+55%*44% =49.4%

Percentage point through which diversification would reduce your risk =49.40%-22.11045% =27.290% or 0.273