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🍀 · 2024年06月30日

Macaulay duration约等于投资期

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.

有的题目里说portfolio的Macaulay duration接近于投资期就可以,Portfolio C的Macaulay duration9.5距离10也不算特别远,并且convexity最小。

距离投资期的远近多远算远呢?

1 个答案
已采纳答案

发亮_品职助教 · 2024年07月01日

是的,理论上是要求investment horizon = macaulay duration,实际在选的时候,只需要近似相等即可。


但近似多少算近,这个没有一个标准的尺度去衡量,我们也没办法绝对地判断数据大小是否够远or够近。


但注意,这种题目总是会给3~4个待选的portfolio来挑选。这时候就注意看3个组合的数据,要比较着看,那种相对来说比较远的数据就可以直接排除。有了几个备选组合,就有了比较的参考系,排除掉数据相对离谱的即可。


比如,在这道题的3个组合里,Portfolio 1的macaulay duration = 9.998, Portfolio 2的macaulay duration=10.002,portfolio 3的macaulay duration = 9.537,而负债的time horizon=10


以负债的10为benchmark挑选的话,portfolio 1和portfolio 2的数据相对最接近,而portfolio 3的Macaulay duration数据差的有点太远,所以直接排除portfolio 3.


单期负债匹配、多期负债匹配里面,duration筛选是第一条件,先满足duration的背景下,再去找convexity是否满足条件。

做题的时候不用担心是否误判,因为题目设置的数据是一定能用这种相对的排除法找到最优的。

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2024-02-09 11:18 1 · 回答

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2024-02-08 17:57 1 · 回答

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