Question

A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 35%, while stock B has a standard deviation of return of 15%. The correlation coefficient between the returns on A and B is .45. Stock A comprises 40% of the portfolio, while stock B comprises 60% of the portfolio. The standard deviation of the return on this portfolio is _________.

Please show all work.

Answer 1

Oportfolio = wig+wo3 + 2wW2P1,20102 Where: W W 04 02 P12 = = = = = Proportion of the portfolio invested in Asset 1 Proportion of the portfolio invested in Asset 2 Asset 1 standard deviation of returns Asset 2 standard deviation of returns Correlation coefficient between the returns of Asset 1 and Asset 2

$\sigma = \sqrt{(0.40 * 0.35)^2 + (0.60 * 0.15)^2 + (2 * 0.40 * 0.60 * 0.35 * 0.15 * 0.45)}$

$\sigma = \sqrt{0.0196 + 0.0081 + 0.01134}$

$\sigma = \sqrt{0.03904}$

$\sigma = 0.1976$

Standard deviation = 19.76%