
Explanation:
First, we find the expected portfolio return and standard deviation. The weights of the portfolio are:
The expected return of the portfolio is:
The variance of the portfolio since Fund X and Fund Y are independent (correlation is 0):
The standard deviation of the portfolio is:
The z-score to find the probability that returns are greater than 30 (assumed 30%):
According to standard normal distribution tables, the cumulative probability up to is approximately $0.9678P(Z > 1.85) = 1 - 0.9678 = 0.0322$
Ultimate access to all questions.
No comments yet.
Q.66 Suppose that the returns on Fund X follow a normal distribution with a mean of 4% and a standard deviation of 8%. In comparison, the returns on Fund Y also follow a normal distribution with a mean of 9% and a standard deviation of 20%. Suppose further that Fund X comprises USD 40 million in assets while Fund Y comprises USD 60 Million in assets. Assuming that Fund X and Fund Y are independent, what is the probability that the returns on the portfolio made up of the two funds will be greater than 30?
A
0.7224.
B
0.0322.
C
0.9678.
D
0.2776.