Suppose that your client decides to invest in your portfolio a proportion y of the total investment
budget so that the overall portfolio will have an expected rate of return of 16%.
a. What is the proportion y?
To determine the proportion y, we need to understand how the expected rate of return is calculated for a portfolio.
In a portfolio, the expected rate of return is the weighted average of the individual investments' rates of return. The weights are determined based on the proportions of the total investment budget allocated to each investment.
Let's assume the client has a total investment budget of B. The proportion y represents the portion of the budget allocated to the portfolio. Therefore, the remaining portion (1 - y) will be invested elsewhere, but for simplicity, we won't consider it in this calculation.
Now, let's assume the portfolio's rate of return is denoted as R. The expected rate of return (E) for the overall portfolio, to achieve the target of 16%, can be found using the following formula:
E = y * R
Given that E = 16%, the equation becomes:
16% = y * R
To find y, we need the value of R, the rate of return for the portfolio. Without that information, we cannot determine the exact value of y.