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 _________. A. 23% B. 19.76% C. 18.45% D. 17.67%

Answer 1

Answer:

B. 19.76%

Explanation:

The standard deviation of the rate of return of an investment portfolio refers to the standard deviation of the portfolio investment which is employed to gauge the volatility that is inherent in the portfolio investment.

In order to calculate this, we first estimate the variance of the of the return on this portfolio using the following formula:

Portfolio return variance = (WA^2 * SDA^2) + (WB^2 * SDB^2) + (2 * WA * SDA * WB * SDB * CFab) ......................... (1)

Where;

WA = Weight of Stock A = 40%

WB = Weight of Stock B = 60%

SDA = Standard deviation of stock A return = 35%

SDB = Standard deviation of stock B return = 15%

CFab = The correlation between stock A and stock B = 0.45

Substituting all the values into equation (1), we have:

Portfolio return variance = (40%^2 * 35%^2) + (60%^2 * 15%^2) + (2 * 40% * 35% * 60% * 15% * 0.45)

Portfolio return variance = 3.904%, or 0.03904

The standard deviation of the return on this portfolio can now be calculated as follows:

$PRSD = \sqrt{PRV}$ ........................... (2)

Where;

PRSD = Portfolio return standard deviation = ?

PRV = Portfolio return variance = 3.904%

Substituting the values into equation (2), we have:

$PRSD = \sqrt{0.03904}$

PRSD = 0.1976, or 19.76%

Therefore, the standard deviation of the return on this portfolio is 19.76%, and the correct option is B. 19.76%.