开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

Olivia.W🌸 · 2024年07月15日

N为什么等于6，一共不是5年期债券吗？

  1. CFA I
  2. Fixed Income

NO.PZ2016031001000078

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-first-call is closest to:

选项：

A.

3.12%.

B.

6.11%.

C.

6.25%.

解释：

C is correct.

The yield-to-first-call is 6.25%. Given the first call date is exactly three years away, the formula for calculating this bond’s yield-to-first-call is:

PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)5+PMT+FV(1+r)6PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cdots+\frac{PMT}{{(1+r)}^5}+\frac{PMT+FV}{{(1+r)}^6}

101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)5+3+102(1+r)6101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cdots+\frac3{{(1+r)}^5}+\frac{3+102}{{(1+r)}^6}

r = 0.03123

To arrive at the annualized yield-to-first-call, the semiannual rate of 3.123% must be multiplied by two. Therefore, the yield-to-first-call is equal to 3.123% × 2 = 6.25% (rounded).

考点：YTC

解析：可利用计算器：N=3×2=6，PMT=3，PV= -101，FV=102，算出来I/Y=3.12，再乘2得：YTC=3.12×2=6.25%，故选项C正确。

N为什么等于6，一共不是5年期债券吗？

添加评论
1 个答案

吴昊_品职助教 · 2024年07月15日

嗨，爱思考的PZer你好：


N代表的是期数，而不是年数。

现在题目中有：interest paid semiannually，说明债券是半年付息一次的。求的是yield-to-first-call，第一次赎回是在第三年末执行的。一年有两期，所以N=2×3=6，所以N=6而不等于5。

----------------------------------------------
努力的时光都是限量版，加油！

  • 1

    回答

  • 0

    关注

  • 193

    浏览
相关问题

NO.PZ2016031001000078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-first-call is closest to:A.3.12%.B.6.11%.C.6.25%. C is correct.The yielto-first-call is 6.25%. Given the first call te is exactly three years away, the formula for calculating this bons yielto-first-call is:PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)5+PMT+FV(1+r)6PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cts+\frac{PMT}{{(1+r)}^5}+\frac{PMT+FV}{{(1+r)}^6}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+⋯+(1+r)5PMT​+(1+r)6PMT+FV​101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)5+3+102(1+r)6101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cts+\frac3{{(1+r)}^5}+\frac{3+102}{{(1+r)}^6}101=(1+r)13​+(1+r)23​+(1+r)33​+⋯+(1+r)53​+(1+r)63+102​r = 0.03123To arrive the annualizeyielto-first-call, the semiannurate of 3.123% must multiplietwo. Therefore, the yielto-first-call is equto 3.123% × 2 = 6.25% (roun. 考点YTC解析可利用计算器N=3×2=6，PMT=3，PV= -101，FV=102，算出来I/Y=3.12，再乘2得YTC=3.12×2=6.25%，故C正确。 为什么这里coupon是3而不是3%乘PV

2024-05-16 00:52 1 · 回答

NO.PZ2016031001000078 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-first-call is closest to: A.3.12%. B.6.11%. C.6.25%. C is correct.The yielto-first-call is 6.25%. Given the first call te is exactly three years away, the formula for calculating this bons yielto-first-call is:PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)5+PMT+FV(1+r)6PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cts+\frac{PMT}{{(1+r)}^5}+\frac{PMT+FV}{{(1+r)}^6}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+⋯+(1+r)5PMT​+(1+r)6PMT+FV​101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)5+3+102(1+r)6101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cts+\frac3{{(1+r)}^5}+\frac{3+102}{{(1+r)}^6}101=(1+r)13​+(1+r)23​+(1+r)33​+⋯+(1+r)53​+(1+r)63+102​r = 0.03123To arrive the annualizeyielto-first-call, the semiannurate of 3.123% must multiplietwo. Therefore, the yielto-first-call is equto 3.123% × 2 = 6.25% (roun. 考点YTC解析可利用计算器N=3×2=6，PMT=3，PV= -101，FV=102，算出来I/Y=3.12，再乘2得YTC=3.12×2=6.25%，故C正确。 为什么pv不是100？

2024-04-01 10:42 1 · 回答

我用 N=10， PMT=3， Pv=-101 fv=102 算出来 I/y= 3.056 那里出错了？

2019-10-02 21:57 1 · 回答

老师你好，这道题目fist to call 的时候pv不是102嚒，谢谢解答

2018-08-12 11:22 1 · 回答