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Kokonoi Hajime · 2023年10月14日

YTM和z2的区别？

  1. CFA I
  2. Derivative

NO.PZ2021061002000047

问题如下：

A portfolio manager observes the price and YTM of one-year (r1) and two-year ( r2) annual coupon government benchmark bonds currently available in the market. How the manager can determine a breakeven reinvestment rate in one year’s time to help decide whether to invest now for one or two years?

选项：

A.

Divide the square root of (1 + r2 ) by (1 + r1 ) and subtract 1 to arrive at a breakeven reinvestment rate for one year in one year’s time.

B.

Set (1 +r1) multiplied by 1 plus the breakeven reinvestment rate equal to (1 + r2) 2 and solve for the breakeven reinvestment rate.

C.

First substitute the one-year rate (r1) into the two-year bond price equation to solve for the two-year spot or zero rate (z2 ), then set (1 + r1 ) × (1 + breakeven reinvestment rate) = (1 + z2 ) 2 and solve for the breakeven reinvestment rate.

解释：

中文解析：

本题考察的是计算Implied forward rates(IFR)。

即题干说的：观察到市场上现有的一年期(r1)和两年(r2)年期国债的收益率，想确定一年内的盈亏平衡再投资率。

考察的公式为：


基于此公式，只有C选项描述正确。

如题，还有老师能不能讲一下我们是怎么用r1求z2的过程啊

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1 个答案

李坏_品职助教 · 2023年10月14日

嗨，爱思考的PZer你好：


r1和r2分别是1年期和2年期的附息国债的YTM，而Z2是spot rate。


2年期国债的定价公式如下：

price=利息/(1+r1) + (利息+本金)/(1+z2)^2，这里1年后收取的利息用1年期利率折现，2年后收取的现金流用2年期的spot rate折现。这里只有z2是未知数，可以求出Z2. 题目的意思是要把1年期利率r1代入2年期国债的定价公式里。


注意2年期国债也可以写成：price = 利息/（1+r2） + (利息+本金)/(1+r2)^2。（这里1年后和2年后都用r2折现，这就是YTM）



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