Explanation:
Correct Answer: C
C is correct. The goal is to calculate the expected value of to assess the anticipated portfolio performance. The expectation of a function of a bivariate random variable is a probability weighted average of the function of the outcomes. The expectation is simply the sum of each possible outcome across dimensions A and B weighted by its probability of occurrence. There are 4 possible outcomes, each weighted by their probability. The expected value (or expectation) of is denoted as and is therefore computed as follows:
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Q-26. A senior investment advisor at a wealth management firm manages an investment portfolio consisting of two main assets, fund A and fund B, for a group of clients. The annual returns of these assets can be represented as random variables, denoted as A and B, respectively. The advisor wants to estimate future portfolio performance by calculating the expectation of a specific function that is based on the anticipated returns of both funds A and B. The function is given by:
where the coefficients reflect the portfolio allocation of 60% to fund A and 40% to fund B.
In the analysis, the advisor assumes that the returns of both fund A and fund B can take on only two possible year-end values, and constructs the joint probability mass function (PMF) as follows:
| A | |||
|---|---|---|---|
| 8% | 11% | ||
| B | 1% | 0.15 | 0.20 |
| 3% | 0.40 | 0.25 |
What is the correct expectation, , of the function?
A
A. 2.30%
B
B. 5.12%
C
C. 6.53%
D
D. 9.35%
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