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 _________.

Answer 1

19.76%

Step-by-step explanation:

the standard deviation of the portfolio return (σ) = √{(weight of stock A² x standard deviation of stock A²) + (weight of stock B² x standard deviation of stock B²) + (2 x weight of stock A x weight of stock B x standard deviation stock A + standard deviation of stock B x correlation coefficient)}

σ = √{(0.4² x 0.35²) + (0.6² x 0.15²) + (2 x 0.4 x 0.6 x 0.35 + 0.15 x 0.45)}

σ = √{(0.16 x 0.1225) + (0.36 x 0.0225) + 0.01134}

σ = √{0.0196 + 0.0081 + 0.01134} = √0.03904

σ = 0.19758 or 19.76%