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hwqjulia001 · 2023年07月11日

折现问题（spot rate VS forward rate）

  1. CFA II
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ201701230200000203

问题如下：

3. In presenting Investment 2, Smith should show an annual return closest to:

选项：

A.

4.31%.

B.

5.42%.

C.

6.53%.

解释：

C is correct.

The swap spread is a common way to indicate credit spreads in a market. The four-year swap rate (fixed leg of an interest rate swap) can be used as an indication of the four-year corporate yield. Riding the yield curve by purchasing a four-year zero-coupon bond with a yield of 4.75% {i.e., 4.05% + 0.70%, [P4 = 100/(1 + 0.0475)4 = 83.058]} and then selling it when it becomes a two-year zero-coupon bond with a yield of 3.00% {i.e., 2.70% +0.30%, [P2 = 100/(1 + 0.0300)2 = 94.260]} produces an annual return of 6.53%: (94.260/83.058)0.5 - 1.0 = 0.0653.

两年期折现的时候为什么不用 S2与S4推导出来的 f(2,2) 来折 而是用 spot rate

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1 个答案

pzqa31 · 2023年07月11日

嗨，爱思考的PZer你好：


因为题目中说了，收益率曲线稳定不变，interest rate remains stable，也就是2年期的国债spot rate一直都是2.7%。现在是要看在2年期这个时间点的债券估值，当然要用站在t=2时刻两年期的spot rate来折现。


我们再来回忆一下forward rate的含义，forward rate是隐含在当前即期利率中的利率，也就是当前市场上可以观察到的利率，所以你用S2和S4推导出来的，是站在0时刻看到的f(2,2),不能用于t=2时刻的折现。

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NO.PZ201701230200000203问题如下3. In presenting Investment 2, Smith shoulshow annureturn closest to:A.4.31%.B.5.42%.C.6.53%.C is correct. The swspreis a common wto incate cret sprea in a market. The four-yeswrate (fixeleg of interest rate swap) cuseincation of the four-yecorporate yiel Ring the yielcurve purchasing a four-yezero-coupon bonwith a yielof 4.75% {i.e., 4.05% + 0.70%, [P4 = 100/(1 + 0.0475)4 = 83.058]} anthen selling it when it becomes a two-yezero-coupon bonwith a yielof 3.00% {i.e., 2.70% +0.30%, [P2 = 100/(1 + 0.0300)2 = 94.260]} proces annureturn of 6.53%: (94.260/83.058)0.5 - 1.0 = 0.0653.所以ring the yiel赚的是extra coupon reinvestment return 吧？

2024-07-07 12:45 1 · 回答

NO.PZ201701230200000203问题如下 3. In presenting Investment 2, Smith shoulshow annureturn closest to:A.4.31%.B.5.42%.C.6.53%.C is correct. The swspreis a common wto incate cret sprea in a market. The four-yeswrate (fixeleg of interest rate swap) cuseincation of the four-yecorporate yiel Ring the yielcurve purchasing a four-yezero-coupon bonwith a yielof 4.75% {i.e., 4.05% + 0.70%, [P4 = 100/(1 + 0.0475)4 = 83.058]} anthen selling it when it becomes a two-yezero-coupon bonwith a yielof 3.00% {i.e., 2.70% +0.30%, [P2 = 100/(1 + 0.0300)2 = 94.260]} proces annureturn of 6.53%: (94.260/83.058)0.5 - 1.0 = 0.0653.请问这里的P2 P4为什么不能用spot rate 一期期往前折 而是直接用了S2 S4

2024-04-17 21:00 1 · 回答

NO.PZ201701230200000203 请问答案说的P4和P2分别是什么？如果是用骑乘策略，不应该是站在第2年末分别算出4年和2年零息债券的价格吗？

2022-01-27 14:45 1 · 回答

NO.PZ201701230200000203 (94.260/83.058)0.5 - 1.0 = 0.0653 不明白使用什么复利公式计算的，麻烦老师一下。

2021-09-10 00:26 1 · 回答