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rabbit · 2021年04月06日

再投资部分

  1. CFA I
  2. Fixed Income

NO.PZ2016031001000112

问题如下：

An investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. After the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. Assume that interest rates remain unchanged at 8% over the five-year holding period.

Assuming that all coupons are reinvested over the holding period, the investor’s five-year horizon yield is closest to:

选项：

A.

5.66%.

B.

6.62%.

C.

7.12%.

解释：

B is correct.

The investor’s five-year horizon yield is closest to 6.62%. After five years, the sale price of the bond is 96.69 and the future value of reinvested cash flows at 8% is 41.0662 per 100 of par value. The total return is 137.76 (= 41.07 + 96.69), resulting in a realized five-year horizon yield of 6.62%:

100=137.76(1+r)5100=\frac{137.76}{{(1+r)}^5}

r = 0.0662

41.0662=7 + 7*1.08 + 7*1.08^2 + 7*1.08^3 + 7*1.08^4

96.6879=7/1.08 + 7/1.08^2 + 7/1.08^3 + 107/1.08^4

老师，再投资部分用计算器怎么算。
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1 个答案

吴昊_品职助教 · 2021年04月07日

嗨，爱思考的PZer你好：


同学你好：

再投资部分：N=5，PMT=7，PV=0，I/Y=8，求得FV=41.0662

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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NO.PZ2016031001000112 问题如下 investor purchases a nine-year, 7% annucoupon payment bona priequto pvalue. After the bonis purchaseanbefore the first coupon is receive interest rates increase to 8%. The investor sells the bonafter five years. Assume thinterest rates remain unchange8% over the five-yeholng perio Assuming thall coupons are reinvesteover the holng perio the investor’s five-yehorizon yielis closest to: A.5.66%. B.6.62%. C.7.12%. B is correct.The investor’s five-yehorizon yielis closest to 6.62%. After five years, the sale priof the bonis 96.69 anthe future value of reinvestecash flows 8% is 41.0662 per 100 of pvalue. The totreturn is 137.76 (= 41.07 + 96.69), resulting in a realizefive-yehorizon yielof 6.62%:100=137.76(1+r)5100=\frac{137.76}{{(1+r)}^5}100=(1+r)5137.76​r = 0.066241.0662=7 + 7*1.08 + 7*1.08^2 + 7*1.08^3 + 7*1.08^496.6879=7/1.08 + 7/1.08^2 + 7/1.08^3 + 107/1.08^4考点Horizon Yiel析由题干可知，一个九年期的债券持有五年。现在要我们计算五年的Horizon Yiel首先求出5年后卖出债券时所有的Coupon + Coupon Reinvestment，将现金流复利到第五年末，得到41.07。然后求出5年后卖出时的债券价格，要算5年后卖出债券的价格，实际上是将债券剩余4年的现金流折现到第五年末。于是，N=4，PMT=7，I/Y=8，FV=100，得到 PV = -96.69，所以5年后债券的卖出价格是96.69。将以上两个部分相加总得到持有期总收益为137.76。计算年化收益率100*(1+r)^5=137.76，求出r = 6.62%，故B正确。 阔以一下为什么N=4而不是5呢？是跟第一次付息前，利率变化有关么，这个变化是怎么影响的N取值的呀？谢谢老师

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