Suppose that portfolios I and II in Problem 58 are unchanged and portfolio III consists of 2 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. A customer wants 12 blocks of common stock, 6 municipal bonds, and 6 blocks of preferred stock. How many units of each portfolio should be offered?
To determine how many units of each portfolio should be offered, we need to compare the customer's desired allocation to the current allocation of the portfolios.
Let's start by listing the current allocation of each portfolio:
Portfolio I: 3 blocks of common stock, 4 municipal bonds, 2 blocks of preferred stock
Portfolio II: 4 blocks of common stock, 2 municipal bonds, 3 blocks of preferred stock
Portfolio III: 2 blocks of common stock, 2 municipal bonds, 3 blocks of preferred stock
Now, let's consider the customer's desired allocation:
Desired allocation: 12 blocks of common stock, 6 municipal bonds, 6 blocks of preferred stock
To find out how many units of each portfolio should be offered, we can follow these steps:
1. Determine the total number of blocks of each asset in the desired allocation and the current allocation.
Current allocation:
- Common stock: Portfolio I: 3 blocks, Portfolio II: 4 blocks, Portfolio III: 2 blocks
- Municipal bonds: Portfolio I: 4 bonds, Portfolio II: 2 bonds, Portfolio III: 2 bonds
- Preferred stock: Portfolio I: 2 blocks, Portfolio II: 3 blocks, Portfolio III: 3 blocks
Desired allocation:
- Common stock: 12 blocks
- Municipal bonds: 6 bonds
- Preferred stock: 6 blocks
2. Calculate the difference between the desired allocation and the current allocation for each asset.
Current allocation - Desired allocation:
- Common stock: Portfolio I: 3 - 12 = -9 blocks, Portfolio II: 4 - 12 = -8 blocks, Portfolio III: 2 - 12 = -10 blocks
- Municipal bonds: Portfolio I: 4 - 6 = -2 bonds, Portfolio II: 2 - 6 = -4 bonds, Portfolio III: 2 - 6 = -4 bonds
- Preferred stock: Portfolio I: 2 - 6 = -4 blocks, Portfolio II: 3 - 6 = -3 blocks, Portfolio III: 3 - 6 = -3 blocks
3. Offer the units with the largest negative difference for sale.
In this case, the portfolio with the largest negative difference in each asset is Portfolio III. Thus, the number of units of each portfolio to be offered would be:
- Portfolio I: 0 units
- Portfolio II: 0 units
- Portfolio III: 10 units
Therefore, you should offer 10 units of Portfolio III to the customer to satisfy their desired allocation.