
Explanation:
We first find the combined mean and combined standard deviation.
The combined expected mean return of the two funds is given by:
The combined standard deviation of the two funds is given by:
The z-statistic is
Therefore,
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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.
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