
Ultimate access to all questions.
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:
g(A, B) = 0.6A + 0.4B
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, E[g(A,B)], of the function?
A
2.30%
B
5.12%
C
6.53%
D
9.35%