NO.PZ2023032703000026
问题如下：
Poquessing Zerbe is a fixed-income portfolio manager. One of her institutional clients, Mahanoy Oswayo, needs to immunize a single 10-year liability of USD 120,000,000. Zerbe calculates the present value of this future liability to be USD 92,221,521.
Zerbe decides not to use zero-coupon bonds to immunize the liability and considers three possible immunization portfolios using non-callable, fixed-rate US Treasury bonds. Zerbe prepares a comparative analysis of the three portfolios in Exhibit 1. Zerbe explains to Oswayo that, once chosen, the immunization portfolio will need to be rebalanced over time.
A. Determine which portfolio in Exhibit 1 would best immunize the future liability. Justify your response. (2018 Q7)
选项：
解释：
Determine which portfolio in Exhibit 1 would best immunize the future liability. (circle one)
Portfolio A Portfolio B Portfolio C
Justify your response.
The characteristics of a bond portfolio structured to immunize a single liability are that it (1) has an initial market value that equals or exceeds the present value of the liability; (2) has a portfolio Macaulay duration that matches the liability’s due date; and (3) minimizes the portfolio convexity statistic. Portfolio A is the most appropriate portfolio to immunize the future liability. Since all three portfolios have approximately equal cash flow yields, we can use the following three criteria to select the best portfolio for the immunization:
1. Market Value: The immunizing portfolio’s initial market value must equal or exceed the present value of the liability. Portfolio A’s initial market value of USD 92,339,315 exceeds the outflow’s present value of USD 92,221,521. Portfolio B is not appropriate because its market value of USD 92,101,324 is less than the present value of the future outflow.
2. Macaulay Duration: The immunizing portfolio’s Macaulay duration must closely match the due date of the single liability outflow. Portfolio A’s Macaulay duration of 9.998 closely matches the ten-year horizon of the outflow. Portfolio C is not appropriate because its Macaulay duration of 9.537 is furthest away from the investment horizon of ten years.
3. Convexity: For given levels of Macaulay duration and cash flow yield, smaller convexity is preferable to minimize structural risk. Minimizing convexity is the same as minimizing dispersion when considering portfolios with similar Macaulay durations and cash flow yields. Reducing a portfolio’s dispersion reduces its structural risk—the risk that yield curve twists and non-parallel shifts create duration gaps between the immunization portfolio and the liability outflow. Although Portfolio C has the lowest convexity at 108.969, its Macaulay duration does not closely match the outflow time horizon. Of the remaining two portfolios, Portfolio A has the lower convexity at 119.079; this lower convexity will minimize structural risk.
老师，请问考试中这样回答可以吗，我是按每个条件排除法的形式来回答的？
还想问一下关于convexity那条，考试中需要像答案一样把convexity的定义全都写上吗？还是说只要提到minimize convexity to lower structural risk即可？谢谢！
To immunize a single 10-year liability of USD 120,000,000, the following criteria should be satisfied:
- Market value of the portfolio should equal to or exceed the present value of the future liability of USD 92,221,521. Portfolio B is inappropriate because its market value of USD 92,101,324 is lower than USD 92,221,521.
- Macaulay duration of the portfolio should closely match the time horizon of the liability, which is 10 year in this case. Therefore, Portfolio C fail to meet this criteria as it has Macaulay duration 9.537 that is well below 10.
- Convexity of the portfolio should be minimized in order to lower structural risk.
As a result, Portfolio A would best immunize the future liability. Portfolio A has market value of USD92,339,315 which exceeds the present value of future liability of USD 92,221,521. Its Macaulay duration of 9.998 closely matches the time horizon of the liability. For the given market value and macaulay duration, Portfolio A also has a lower convexity of 119.079.
