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李冬树 · 2020年11月29日

问一道题：NO.PZ2016031001000079

  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-second-call is closest to:

选项：

A.

2.97%.

B.

5.72%.

C.

5.94%.

解释：

C is correct.

The yield-to-second-call is 5.94%. Given the second call date is exactly four years away, the formula for calculating this bond’s yield-to-second-call is:

PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)7+PMT+FV(1+r)8PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cdots+\frac{PMT}{{(1+r)}^7}+\frac{PMT+FV}{{(1+r)}^8}

where:

PV = present value, or the price of the bond

PMT = coupon payment per period

FV = call price paid at call date

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)7+3+101(1+r)8101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cdots+\frac3{{(1+r)}^7}+\frac{3+101}{{(1+r)}^8}

r = 0.0297

To arrive at the annualized yield-to-second-call, the semiannual rate of 2.97% must be multiplied by two. Therefore, the yield-to-second-call is equal to 2.97% × 2 = 5.94%.

老师可以解释一下Yield to second call,yield to call区别吗？

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1 个答案

吴昊_品职助教 · 2020年11月30日

同学你好：

yield-to-second-call的意思是，债券第二次call回，回到表格，第二次被赎回发生在第四年。债券在第四年call回，赎回价格为101，即FV=101。

yield-to-call就是发生赎回的ytm。但在本题中有一个call schedule，债券可以在不同的年份被赎回，也就是说有不同的ytc，yield-to-second-call专指债券第二次被回时的收益率。

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NO.PZ2016031001000079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-seconcall is closest to:A.2.97%.B.5.72%.C.5.94%. C is correct.The yielto-seconcall is 5.94%. Given the seconcall te is exactly four years away, the formula for calculating this bons yielto-seconcall is:PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)7+PMT+FV(1+r)8PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cts+\frac{PMT}{{(1+r)}^7}+\frac{PMT+FV}{{(1+r)}^8}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+⋯+(1+r)7PMT​+(1+r)8PMT+FV​where:PV = present value, or the priof the bonMT = coupon payment per perioV = call pripaicall ter = market scount rate, or requirerate of return per perio01=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)7+3+101(1+r)8101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cts+\frac3{{(1+r)}^7}+\frac{3+101}{{(1+r)}^8}101=(1+r)13​+(1+r)23​+(1+r)33​+⋯+(1+r)73​+(1+r)83+101​r = 0.0297To arrive the annualizeyielto-seconcall, the semiannurate of 2.97% must multiplietwo. Therefore, the yielto-seconcall is equto 2.97% × 2 = 5.94%. 考点YTC解析求的是yielto-seconcall，第二次赎回价格为101，因此FV=101，N=4×2=8，PMT=3，PV= -101，求得I/Y=2.97，再乘2得YTC为5.94%，故C正确。 没看懂为啥FV和PV都是101

2023-07-05 17:00 1 · 回答

NO.PZ2016031001000079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-seconcall is closest to:A.2.97%.B.5.72%.C.5.94%. C is correct.The yielto-seconcall is 5.94%. Given the seconcall te is exactly four years away, the formula for calculating this bons yielto-seconcall is:PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)7+PMT+FV(1+r)8PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cts+\frac{PMT}{{(1+r)}^7}+\frac{PMT+FV}{{(1+r)}^8}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+⋯+(1+r)7PMT​+(1+r)8PMT+FV​where:PV = present value, or the priof the bonMT = coupon payment per perioV = call pripaicall ter = market scount rate, or requirerate of return per perio01=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)7+3+101(1+r)8101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cts+\frac3{{(1+r)}^7}+\frac{3+101}{{(1+r)}^8}101=(1+r)13​+(1+r)23​+(1+r)33​+⋯+(1+r)73​+(1+r)83+101​r = 0.0297To arrive the annualizeyielto-seconcall, the semiannurate of 2.97% must multiplietwo. Therefore, the yielto-seconcall is equto 2.97% × 2 = 5.94%. 考点YTC解析求的是yielto-seconcall，第二次赎回价格为101，因此FV=101，N=4×2=8，PMT=3，PV= -101，求得I/Y=2.97，再乘2得YTC为5.94%，故C正确。 按计算器的时候，N=8，PMT=3，FV=101，PV是怎么算出来的呀

2023-03-13 07:55 1 · 回答

NO.PZ2016031001000079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-seconcall is closest to:A.2.97%.B.5.72%.C.5.94%. C is correct.The yielto-seconcall is 5.94%. Given the seconcall te is exactly four years away, the formula for calculating this bons yielto-seconcall is:PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)7+PMT+FV(1+r)8PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cts+\frac{PMT}{{(1+r)}^7}+\frac{PMT+FV}{{(1+r)}^8}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+⋯+(1+r)7PMT​+(1+r)8PMT+FV​where:PV = present value, or the priof the bonMT = coupon payment per perioV = call pripaicall ter = market scount rate, or requirerate of return per perio01=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)7+3+101(1+r)8101=\frac3{{(1+r)}^1}+\frac3{{(1+r)}^2}+\frac3{{(1+r)}^3}+\cts+\frac3{{(1+r)}^7}+\frac{3+101}{{(1+r)}^8}101=(1+r)13​+(1+r)23​+(1+r)33​+⋯+(1+r)73​+(1+r)83+101​r = 0.0297To arrive the annualizeyielto-seconcall, the semiannurate of 2.97% must multiplietwo. Therefore, the yielto-seconcall is equto 2.97% × 2 = 5.94%. 考点YTC解析求的是yielto-seconcall，第二次赎回价格为101，因此FV=101，N=4×2=8，PMT=3，PV= -101，求得I/Y=2.97，再乘2得YTC为5.94%，故C正确。 如题。……………..

2023-03-06 09:18 1 · 回答

n=8 pmt=3 pv=-101 fv=100 这么摁计算机为什么不对？ 算出来2.858 2.858*2=5.72

2020-08-31 23:14 1 · 回答