Celestine · 2020年03月17日

问一道题：NO.PZ201812310200000109

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问题如下：

Ibarra wants to know the credit spread of bond B2 over a theoretical comparable-maturity government bond with the same coupon rate as this bond. The foregoing credit spread is closest to:

选项：

108 bps.

101 bps.

225 bps.

解释：

A is correct. The corporate bond’s fair value is computed in the solution to Question 8 as €1,101.24 The YTM can be obtained by solving the following equation for IRR:

$1101.24 = \frac{60}{1 + I R R} + \frac{60}{{(1 + I R R)}^{2}} + \frac{60}{{(1 + I R R)}^{3}} + \frac{1060}{{(1 + I R R)}^{4}}$

The solution to this equation is 3.26%.

Valuation of a four-year, 6% coupon bond under no default (VND) is computed in the solution to Question 8 as 1,144.63. So, the YTM of a theoretical comparable-maturity government bond with the same coupon rate as the corporate bond B2 can be obtained by solving the following equation for IRR:

$1144.63 = \frac{60}{1 + I R R} + \frac{60}{{(1 + I R R)}^{2}} + \frac{60}{{(1 + I R R)}^{3}} + \frac{1060}{{(1 + I R R)}^{4}}$

The solution to this equation is 2.18%. So, the credit spread that the analyst wants to compute is 3.26% – 2.18% = 1.08%, or 108 bps.

B is incorrect, because that is the spread over the four-year government par bond that has a YTM of 2.25% in Exhibit 2: 3.26% – 2.25% = 1.01%, or 101 bps. Although this spread is commonly used in practice, the analyst is interested in finding the spread over a theoretical 6% coupon government bond.

C is incorrect, because that is the YTM of the coupon four-year government bond in Exhibit 2.

这题为什么不能用B2的YTM直接减去Rf，也就是减去3%？

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已采纳答案

吴昊_品职助教 · 2020年03月17日

我们在spread中需要得到的government bond的YTM，并不是无风险收益率。

题目中明确说明我们是以相同期限，相同coupon rate的国债作为benchmark的。如果题目中没有说明需要相同coupon rate，那么我们可以直接用表格2中四年期的国债YTM作为benchmark。这个四年期国债，价格等于面值，所以它的YTM就是coupon rate=2.25%。但是现在题目中说benchmark不仅需要相同期限，还需要相同的coupon rate（6%）。所以我们只能用先前算出来的VND(1144.63)作为value反求出YTMg，从而再算出spread。

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oasislimp · 2022年02月01日

老师，请问为什么可以直接用表格2中四年期的国债YTM作为benchmark。这个四年期国债，价格等于面值，所以它的YTM就是coupon rate=2.25%。一定要选价格等于面值的吗？

pzqa015 · 2022年02月02日

嗨，努力学习的PZer你好：

本题不能直接用表2四年期国债ytm作为benchmark，因为题目说了要以comparable，same coupon rate bond的ytm作为benchmark，所以只能根据VND反求出的ytm作为benchmark。

我们选择benchmark跟价格是否等于面值无关，是找到ytm。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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问一道题：NO.PZ201812310200000109

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