Question

Exercise 5 Your financially unsophisticated friend has invested all of his $10,000 savings into Apple stocks. He recently heard of a concept called diversification that might help him reduce the risk of his investment. He is considering selling $2,000 of Apple stocks and investing this amount into stocks of Allstate. As he is unsure about the risk implications of this move, he asks you to determine the fraction by which he could reduce his total return volatility if he indeed rearranged his investments. To answer your friend's question, you pull return data from Yahoo Finance and find that Apple exhibits a (monthly) return volatility of 0.076, that Allstate exhibits a (monthly) return volatility of 0.047, and that the return covariance between Apple and Allstate is 0.0016.

Answer 1

Standard Deviation of Apple = 0.076

Standard Deviation of AllState = 0.047

Covariance = 0.0016

If all $10000 invested in Apple., Volatility of Investment = standard deviation of apple = 0.076

If $8000 invested in Apple and $2000 in Allstate

Proportion invested in Apple = $8000/ $10000 = 0.8

Proportion invested in Allstate = $2000/ $10000 = 0.2

The standard deviation of a portfolio is given by

Op = W;*W, *0; * 0;* Pij

Where Wi is the weight of the security i,

is the standard deviation of returns of security i.

and is the correlation coefficient between returns of security i and security j

So, standard deviation of portfolio =sqrt (0.8²*0.076²+0.2²*0.047²+2*0.8*0.2*0.0016)

=sqrt(0.004297)

=0.065552

So, reduction in volatility = (0.076-0.065552) = 0.010448

Fraction by which total return volatility could be reduced by investing in Allstate = 0.010448/0.076 = 0.13748