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梦梦 · 2024年08月28日

关于利率分解的经典题

NO.PZ2023091701000023

问题如下:

A fixed-income analyst is decomposing the profit and loss (P&L) of a bond over the past 6 months. The bond has a 2% coupon rate, paid semi-annually, and had exactly 2 years remaining until maturity at the start of the 6-month period. Relevant information about the bond and market rates (semi-annually compounded) is shown below:

The analyst has calculated the bond’s carry roll-down, and under the forward rate assumption made for the purpose of that calculation, the ending value of the bond is SGD 100.55. Given this information, what is the component of the bond’s P&L attributable to the change in rates over the 6-month period?

选项:

A.SGD 0.54

B.SGD 0.69

C.SGD 0.74

D.SGD 0.99

解释:

A is correct. Calculating the impact of the change in rates is the second step in decomposing the P&L of a bond, after calculating the carry roll-down. The impact of a rate change is calculated as the value of the bond at the end of the period using the ending forward rate curve (and the bond’s beginning-of-period spread), minus the end-of-period value of the bond calculated using the forward rates assumed for the purpose of determining carry roll-down (which represent some sense of “no change” in the interest rate environment). The value of the bond under the ending forward rate curve is:

Therefore, the impact of the rate change is:

SGD 101.09 - SGD 100.55 = SGD = 0.54

老师,

1、在真题中,forward rate 也会给的这么不清楚吗?这里的forward rate 到底是在0时刻,0.5至1的利率,还是0.5时刻?forward rate 不应该是站在现在时刻,未来某一时间开始到更未来的利率吗?但听了讲解,感觉是站在0.5时刻。

而且既然是forward rate,还有啥真实的利率的概念?就是ending ?真实的就是当前市场的吧,还能是forward rate吗?这里不是特别明白。

2、计算carry roll down明明是个债券价值差的概念

the ending value of the bond是BVt(R’ St-1)的通用表述吗?这题的英文和表格,整体都感觉不清不楚,真题也这样吗?

3 个答案
已采纳答案

李坏_品职助教 · 2024年09月16日

嗨,从没放弃的小努力你好:


The bond has a 2% coupon rate, paid semi-annually, and had exactly 2 years remaining until maturity at the start of the 6-month period.


这句话的意思是,现在是t=0.5的时刻,如果从这半年的起始点(也就是从t=0开始算),这个债券完整的年限是2年。

说明债券的生命期是t=0一直到t=2,但是现在是t=0.5的时刻。


你说的对,forward rate可以指未来任何一个时间点到另一个时间点之间的利率。

这种表格的写法,左边描述的是时间段,0-0.5意思就是从0开始一直到0.5,而0是Beginning, 0.5对应的是Ending。


表格中的利率,我们只能用Ending rate( value of the bond at the end of the period)。

0-0.5的Ending rate实际上就是站在0.5时刻往前看半年,看到的forward rate,所以对应的时间周期应该是t=0.5到t=1。

而0.5-1.0的Ending rate是站在t=1的时刻,往前看半年,对应的是t=1到t=1.5。

而1.0-1.5的Ending rate对应的是t=1.5到t=2。

把未来的三笔现金流分别用Ending rate折现即可。


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虽然现在很辛苦,但努力过的感觉真的很好,加油!

梦梦 · 2024年09月16日

“0-0.5的Ending rate实际上就是站在0.5时刻往前看半年,看到的forward rate,所以对应的时间周期应该是t=0.5到t=1。”我理解“0-0.5”的beginning rate是预测的0-0.5的利率,0-0.5的endding rate是0.5时刻的真实利率;而您说的t=0.5到t=1的利率,预测利率是1.4%,1时刻的真实利率是1%吧?

李坏_品职助教 · 2024年11月11日

嗨,从没放弃的小努力你好:


是的,t=0.5到t=1的利率,预测利率是1.4%,1时刻的真实利率是1%.

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加油吧,让我们一起遇见更好的自己!

李坏_品职助教 · 2024年09月16日

嗨,爱思考的PZer你好:


没错,你可以这么理解。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

梦梦 · 2024年11月11日

老师这道题是经典题哪段的视频?我再听一下

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