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问一道题：NO.PZ2019103001000026

问题如下：

Mowery informs Compton that DFC has a single $500 million liability due in nine years, and she wants SD&R to construct a bond portfolio that earns a rate of return sufficient to pay off the obligation.

Compton provides the four US dollar–denominated bond portfolios in Exhibit 1 for consideration. Compton explains that the portfolios consist of non-callable, investment-grade corporate and government bonds of various maturities because zero-coupon bonds are unavailable.

Based on Exhibit 1, which of the portfolios will best immunize SD&R’s single liability?

选项：

Portfolio 1

Portfolio 2

Portfolio 3

解释：

B is correct.

In the case of a single liability, immunization is achieved by matching the bond portfolio’s Macaulay duration with the horizon date. DFC has a single liability of $500 million due in nine years. Portfolio 2 has a Macaulay duration of 8.9, which is closer to 9 than that of either Portfolio 1 or 3. Therefore, Portfolio 2 will best immunize the portfolio against the liability.

A的MD比9更高，不选择的原因是convexity更大么？

嗨，从没放弃的小努力你好：

由题干：DFC has a single $500 million liability due in nine years

我们可以知道，这是一笔单期负债，负债9年后到期，所以负债的Maturity = 9 years。

因为是单期负债，只有一笔现金流发生在第9年年末，所以衡量现金流发生时间的Macaulay duration也等于9 years，所以我们知道负债的Macaulay duration = 9 years。

要匹配单期负债，需要满足以下三个条件：

1、PV of assets ≥ PV of liability；

2、Asset Macaulay duration = Liability Macaulay duration (单期负债Liability Maturity)

3、Minimize Asset convexity；

A的资产，其Macaulay duration是9.8，离负债的Macaulay duration 9差距太大，所以不选。

这道题只有Portfolio 2和Portfolio 4的Macaulay duration满足匹配单期负债的要求，因为离9很近。

所以，合适的Portfolio只能在2和4里面选，下面就是进一步通过Convexity和PV的要求来判断了。因为表格里没给PV所以可以不考虑，通过Convexity筛选发现Portfolio 4是匹配最合适的资产组合。

但是这道题是让在1、2、3里面选，只有Portfolio 2了。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

问一道题：NO.PZ2019103001000026

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