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 0.45. 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 _________.
A) 23.00%
B) 19.76%
C) 18.45%
D) 17.67%

Question

Quizplus · Accepted Answer

The formula for the standard deviation of a portfolio composed of two stocks with weights W1 and W2 is: 
Portfolio SD = √((W1^2 × SD1^2) + (W2^2 × SD2^2) + 2 × W1 × W2 × SD1 × SD2 × p)
where SD1 and SD2 are the standard deviations of returns of stocks 1 and 2, respectively, and p is the correlation coefficient between their returns.

Plugging in the given values, we get: 
Portfolio SD = √((0.4^2 × 0.35^2) + (0.6^2 × 0.15^2) + 2 × 0.4 × 0.6 × 0.35 × 0.15 × 0.45) = 0.1976 or 19.76%.

Therefore, the best choice is B.

A Portfolio Is Composed of Two Stocks,A and B