What is the standard deviation of a portfolio that is invested 40% in stock Q and 60% in stock R?
A) 0.7%
B) 1.4%
C) 2.6%
D) 6.8%
E) 8.1%

Question

What is the standard deviation of a portfolio that is invested 40% in stock Q and 60% in stock R? 
A) 0.7% 
B) 1.4% 
C) 2.6% 
D) 6.8% 
E) 8.1%

Quizplus · Accepted Answer

To calculate the portfolio standard deviation, we need to know the standard deviation of each stock and the correlation between them. Let's assume that the standard deviation of Stock Q is 15% and the standard deviation of Stock R is 10%. We also know that the correlation between the two stocks is 0.5.

Using the formula for portfolio standard deviation:

Portfolio SD = sqrt(wQ^2 * SDQ^2 + wR^2 * SDR^2 + 2 * wQ * wR * SDQ * SDR * CorrQR)

where:
wQ = weight of stock Q = 40%
wR = weight of stock R = 60%
SDQ = standard deviation of stock Q = 15%
SDR = standard deviation of stock R = 10%
CorrQR = correlation between stocks Q and R = 0.5

Substituting the values, we get:

Portfolio SD = sqrt(0.4^2 * 0.15^2 + 0.6^2 * 0.10^2 + 2 * 0.4 * 0.6 * 0.15 * 0.10 * 0.5)
Portfolio SD = 0.026 or 2.6%

Therefore, the best choice is C) 2.6%.

What Is the Standard Deviation of a Portfolio That Is