The standard deviation of a portfolio that has 40% of its value invested in a risk-free asset and 60% of its value invested in a risky asset with a standard deviation of 30% is
A) 18%.
B) 14%.
C) 21%.
D) 24%.
E) 20%.

Question

Quizplus · Accepted Answer

The formula for the standard deviation of a portfolio that has a percentage w of its value invested in asset A with a standard deviation σA and a percentage (1 − w) of its value invested in asset B with a standard deviation σB is:

σportfolio = sqrt(w^2 * σA^2 + (1 − w)^2 * σB^2 + 2w(1 − w)ρABσAσB)

where ρAB is the correlation coefficient between the two assets (which we assume to be zero in this case since the risk-free asset has a standard deviation of zero).

Thus, the standard deviation of the portfolio is:

σportfolio = sqrt(0.4^2 * 0^2 + 0.6^2 * 0.3^2) = 0.18 or 18%

Therefore, the best choice is A) 18%.

The Standard Deviation of a Portfolio That Has 40% of Its