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nothing107 · 2020年03月12日

问一道题:NO.PZ201812310200000105

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问题如下:

Bond B3 will have a modified duration of 2.75 at the end of the year. Based on the representative one-year corporate transition matrix in Exhibit 7 of the reading and assuming no default, how should the analyst adjust the bond’s yield to maturity (YTM) to assess the expected return on the bond over the next year?

选项:

A.

Add 7.7 bps to YTM.

B.

Subtract 7.7 bps from YTM.

C.

Subtract 9.0 bps from YTM.

解释:

B is correct. For each possible transition, the expected percentage price change, computed as the product of the modified duration and the change in the spread as per Exhibit 7 of the reading, is calculated as follows:

From AA to AAA: –2.75 × (0.60% – 0.90%) = +0.83%

From AA to A: –2.75 × (1.10% – 0.90%) = –0.55%

From AA to BBB: –2.75 × (1.50% – 0.90%) = –1.65%

From AA to BB: –2.75 × (3.40% – 0.90%) = –6.88%

From AA to B: –2.75 × (6.50% – 0.90%) = –15.40%

From AA to C: –2.75 × (9.50% – 0.90%) = –23.65%

The expected percentage change in the value of the AA rated bond is computed by multiplying each expected percentage price change for a possible credit transition by its respective transition probability given in Exhibit 7 of the reading, and summing the products:

(0.0150 × 0.83%) + (0.8800 × 0%) + (0.0950 × –0.55%) + (0.0075 × –1.65%) + (0.0015 × –6.88%) + (0.0005 × –15.40%) + (0.0003 × –23.65%)= –0.0774%.

Therefore, the expected return on the bond over the next year is its YTM minus 0.0774%, assuming no default.

“我们不是在期初购买好债券会有一个YTM,这个YTM是预期我们持有债券至到期每年的收益。持有下一年,假设没有任何变化的情况下,下一年的预期收益率也是YTM。……考虑到债券评级变化之后的影响,债券的价格会下降0.0774%,YTM - 0.0774%算的是持有下一年的预期收益。


若债券下跌0.0774%后,会有一个新的债券价格,会有一个新的YTM。此后,假设市场条件没有发生变化,债券并持有至到期,每年预期能的收益就是这个新的YTM。

这个新的YTM是债券价格变动之后的YTM,与上面算的经历价格变动实现的收益不同。”

老师,您好,我看了上述你们对其他同学提问的解答,有点似懂非懂。您能具体解释一下这新的YTM与评级变化带来的YTM-0.0774%之间的区别吗?也就是本题说的下一年的预期收益率到底是什么,怎么界定的?

评级改变前,YTM是下一年的预期收益率。评级变化后,YTM-0.0774%是预期收益率。价格下跌了0.0774%,会有一个新的YTM。既然评级变化前,YTM是下一年的预期收益率,那么评级变化后,新的YTM应该是预期收益率。

同为预期收益率,YTM-0.0774%与新的YTM应该相等,或者至少变化方向相同吧。为什么债券价格下跌,按YTM-0.0774%来判断,预期收益率变小,而按新的YTM来判断,预期收益率会变大?


1 个答案

吴昊_品职助教 · 2020年03月13日

How should the analyst adjust the bond's yield to YTM to assess the expcted return on the bond over the next year?

我们为了计算下一年的expected return,我们需要把原先的YTM调整多少。

expected return=YTM+△P/P

正常投资一年,我们获得就是YTM的收益率。现在信用质量发生改变,债券价格会发生改变。所以expected return要在YTM的基础上调整一个价格的变动率。这道题问的是要计算expected return,我们需要把YTM调整多少?其实我们调整的部分就是价格的变动率。现在我们考虑到了转移矩阵,考虑债券评级变化之后的影响,债券的价格会下降0.0774%,以这个预期收益率YTM为基准的情况下,要扣减掉0.0774%的债券价格下降预期。

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