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jacqie · 2022年04月03日

为什么carry roll down还要加上coupon利息的部分？

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000208

问题如下：

The term structure is initially flat at 5%, and an investor buys a five-year bond with a face value of USD 100 and a coupon of 4% at a spread of ten basis points. At the end of six months the term structure is flat at 6% and the spread is zero. Carry out a P&L decomposition.

选项：

解释：

First we calculate the carry roll-down. The cash-carry is 2%. In this case, the assumption underlying the carry roll-down is that the term structure remains flat at 5%. (This is true for all three definitions of carry roll-down.) The initial price paid for the bond is

The price of the bond, if six months passes without rates changing or the spread changing, is

The carryroll-down is therefore: 2+95.626-95.199=2.427

This can also be calculated as 0.0255 × 95.199.

The value of the bond at the end of six months, assuming no spread change, is

After the spread change is considered, the value of the bond is

This leads to the following table

The bond price in six months is 92.214 and the investor receives a coupon of 2.000 just before the end of the six months. The initial bond price is 95.199. The gain is therefore:
92.214 + 2.000－95.199 = ﹣0.985
The P&L decomposition splits this into:
(a) A carry roll-down of 2.427,
(b) The impact of a term structure change of -3.782, and
(c) A spread change of 0.370.
﹣0.985 = 2.427－3.782 + 0.370

例题中是不是说coupon在半年度没有支付的意思？

如果例题中coupon在半年度支付了，还需要加么？

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1 个答案

DD仔_品职助教 · 2022年04月04日

嗨，努力学习的PZer你好：


同学你好，

coupon是支付了的，我们一般默认，在期初买了债券，在期间卖出的时候都会先收到coupon，然后再卖出债券。

除非特殊说明sell the bond immediately before coupon，代表还没收到coupon就卖了，收益就不包含coupon。

所以对于这个投资者他是以95.199的价格买入债券，6个月后，利率没变化的话，就以95.626的价格卖出债券，同时还收到了6个月月底支付的coupon2块钱。

所以这个操作的获利就是2+95.626-95.199=2.427。

利率变化了的情况同理，只是卖价不一样了，但都是会收到coupon。

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