The probability the economy will boom is 10 percent while the probability of a recession is 20 percent.Stock A is expected to return 15 percent in a boom,9 percent in a normal economy,and lose 14 percent in a recession.Stock B should return 10 percent in a boom,6 percent in a normal economy,and 2 percent in a recession.Stock C is expected to return 5 percent in a boom,7 percent in a normal economy,and 8 percent in a recession.What is the standard deviation of a portfolio invested 20 percent in Stock A,30 percent in Stock B,and 50 percent in Stock C?
A).6 percent
B).9 percent
C)1.8 percent
D)2.2 percent
E)4.9 percent

Question

Quizplus · Accepted Answer

To find the standard deviation of the portfolio, calculate the expected return and variance using the given probabilities and returns for each stock. Then, compute the portfolio variance considering the weights of each stock and their covariances. Finally, take the square root of the variance to get the standard deviation. The calculations lead to a standard deviation of approximately 2.2 percent.

The Probability the Economy Will Boom Is 10 Percent While