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kevinzhu · 2020年02月26日

问一道题：NO.PZ2016031001000077

  1. CFA I
  2. Fixed Income

问题如下：

A bond with 5 years remaining until maturity is currently trading for 101 per 100 of par value. The bond offers a 6% coupon rate with interest paid semiannually. The bond is first callable in 3 years, and is callable after that date on coupon dates according to the following schedule:

The bond’s annual yield-to-maturity is closest to:

选项：

A.

2.88%.

B.

5.77%.

C.

5.94%.

解释：

B is correct.

The yield-to-maturity is 5.77%. The formula for calculating this bond’s yield-to-maturity is:

PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)9+PMT+FV(1+r)10PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cdots+\frac{PMT}{{(1+r)}^9}+\frac{PMT+FV}{{(1+r)}^{10}}

where:

PV = present value, or the price of the bond

PMT = coupon payment per period

FV = future value paid at maturity, or the par value of the bond

r = market discount rate, or required rate of return per period

101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)9+3+100(1+r)10101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cdots+\frac3{{(1+r)}^9}+\frac{3+100}{{(1+r)}^{10}}

r = 0.02883

To arrive at the annualized yield-to-maturity, the semiannual rate of 2.883% must be multiplied by two. Therefore, the yield-to-maturity is equal to 2.883% × 2 = 5.77% (rounded).

n=5*2=10 pv=-101 fv=100 pmt=100*0.06/2=3,求出i/y=2.883 2.883*2=5.77

那么表格里面的end of the year和call price对于这道题目有意义吗? 仅仅只是干扰项？

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1 个答案

吴昊_品职助教 · 2020年02月27日

这道题相当于是一道大题，对于这道小题表格里的数据均用不上。

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NO.PZ2016031001000077问题如下 A bonwith 5 years remaining until maturity is currently trang for 101 per 100 of pvalue. The bonoffers a 6% coupon rate with interest paisemiannually. The bonis first callable in 3 years, anis callable after thte on coupon tes accorng to the following schele: The bons annuyielto-maturity is closest to:A.2.88%.B.5.77%.C.5.94%. B is correct.The yielto-maturity is 5.77%. The formula for calculating this bons yielto-maturity is: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)9+PMT+FV(1+r)10PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cts+\frac{PMT}{{(1+r)}^9}+\frac{PMT+FV}{{(1+r)}^{10}}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+⋯+(1+r)9PMT​+(1+r)10PMT+FV​101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)9+3+100(1+r)10101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cts+\frac3{{(1+r)}^9}+\frac{3+100}{{(1+r)}^{10}}101=(1+r)13​+(1+r)23​+(1+r)33​+⋯+(1+r)93​+(1+r)103+100​r = 0.02883To arrive the annualizeyielto-maturity, the semiannurate of 2.883% must multiplietwo. Therefore, the yielto-maturity is equto 2.883% × 2 = 5.77% (roun.考点YTM解析债券每年付息两次，可利用计算器N=5×2=10，PMT=100×6%/2=3，PV= -101，FV=100，求得I/Y=2.88，再乘2得5.77%，故B正确。 在101行权是第四年，n为什么不等于8而是10呢

2023-11-05 00:45 1 · 回答

请问如何从题干中得知一直持有至到期？

2020-09-29 10:18 1 · 回答

如果Ytc的话，需要怎么计算呢？

2019-05-02 23:55 1 · 回答

    所以fv是选择用-101，还是callable price102呢？以及原因是什么

2019-03-28 23:21 1 · 回答