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小锦鲤要加油 · 2020年01月20日

问一道题：NO.PZ201602270200001902 第2小题 [ CFA II ]

  1. CFA II
  2. Fixed Income

* 问题详情，请 查看题干

问题如下：

2. Based on Exhibits 2 and 3 and using Method 1, the amount (in absolute terms) by which the Hutto-Barkley corporate bond is mispriced is closest to:

选项：

A.

0.3368 per 100 of par value.

B.

0.4682 per 100 of par value.

C.

0.5156 per 100 of par value.

解释：

C is correct.

The first step in the solution is to find the correct spot rate (zero-coupon rates) for each year’s cash flow. The benchmark bonds in Exhibit 2 are conveniently priced at par so the yields to maturity and the coupon rates on the bonds are the same. Because the one-year issue has only one cash flow remaining, the YTM equals the spot rate of 3% (or z1z_1= 3%). The spot rates for Year 2 ( z2z_2) and Year 3 (z3z_3 ) are calculated as follows:

beginarrayl100=41.0300+104(1+z2)2;z2=4.02%100=51.0300+5(1.0402)2+105(1+z3)3;z3=5.07%begin{array}{l}100 = \frac{4}{{1.0300}} + \frac{{104}}{{{{(1 + {z_2})}^2}}};{z_2} = 4.02\% \\100 = \frac{5}{{1.0300}} + \frac{5}{{{{(1.0402)}^2}}} + \frac{{105}}{{{{(1 + {z_3})}^3}}};{z_3} = 5.07\%

The correct arbitrage-free price for the Hutto-Barkley Inc. bond is:

P0=3(1.0300)+3(1.0402)2+103(1.0507)3=94.4828P_0=\frac3{(1.0300)}+\frac3{{(1.0402)}^2}+\frac{103}{{(1.0507)}^3}=94.4828

Therefore, the bond is mispriced by 94.4828 – 94.9984 = –0.5156 per 100 of par value.

A is incorrect because the correct spot rates are not calculated and instead the Hutto-Barkley Inc. bond is discounted using the respective YTM for each maturity. Therefore, this leads to an incorrect mispricing of 94.6616 – 94.9984 = –0.3368 per 100 of par value.

B is incorrect because the spot rates are derived using the coupon rate for Year 3 (maturity) instead of using each year’s respective coupon rate to employ the bootstrap methodology. This leads to an incorrect mispricing of 94.5302 – 94.9984 = –0.4682 per 100 of par value.

怎样通过表2能看出来债券ytm等于coupon？

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1 个答案

吴昊_品职助教 · 2020年01月20日

嗨，爱思考的PZer你好：


表格二的名称是par curve，说明表2中的利率都是par rate，par rate就是当债券价格等于面值的coupon rate。


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


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NO.PZ201602270200001902 问题如下 2. Baseon Exhibits 2 an3 anusing Metho1, the amount (in absolute terms) whithe Hutto-Barkley corporate bonis mispriceis closest to: A.0.3368 per 100 of pvalue. B.0.4682 per 100 of pvalue. C.0.5156 per 100 of pvalue. C is correct.The first step in the solution is to finthe correspot rate (zero-coupon rates) for eayear’s cash flow. The benchmark bon in Exhibit 2 are conveniently pricepso the yiel to maturity anthe coupon rates on the bon are the same. Because the one-yeissue honly one cash flow remaining, the YTM equals the spot rate of 3% (or z1z_1z1​= 3%). The spot rates for Ye2 ( z2z_2z2​) anYe3 (z3z_3z3​ ) are calculatefollows: beginarrayl100=41.0300+104(1+z2)2;z2=4.02%100=51.0300+5(1.0402)2+105(1+z3)3;z3=5.07%begin{array}{l}100 = \frac{4}{{1.0300}} + \frac{{104}}{{{{(1 + {z_2})}^2}}};{z_2} = 4.02\% \\100 = \frac{5}{{1.0300}} + \frac{5}{{{{(1.0402)}^2}}} + \frac{{105}}{{{{(1 + {z_3})}^3}}};{z_3} = 5.07\% beginarrayl100=1.03004​+(1+z2​)2104​;z2​=4.02%100=1.03005​+(1.0402)25​+(1+z3​)3105​;z3​=5.07%The correarbitrage-free prifor the Hutto-Barkley Inbonis:P0=3(1.0300)+3(1.0402)2+103(1.0507)3=94.4828P_0=\frac3{(1.0300)}+\frac3{{(1.0402)}^2}+\frac{103}{{(1.0507)}^3}=94.4828P0​=(1.0300)3​+(1.0402)23​+(1.0507)3103​=94.4828Therefore, the bonis misprice94.4828 – 94.9984 = –0.5156 per 100 of pvalue.A is incorrebecause the correspot rates are not calculateaninstethe Hutto-Barkley Inbonis scounteusing the respective YTM for eamaturity. Therefore, this lea to incorremispricing of 94.6616 – 94.9984 = –0.3368 per 100 of pvalue.B is incorrebecause the spot rates are riveusing the coupon rate for Ye3 (maturity) insteof using eayear’s respective coupon rate to employ the bootstrmethology. This lea to incorremispricing of 94.5302 – 94.9984 = –0.4682 per 100 of pvalue. 公式完全正确，但我每步计算都保留了小数点后四位，结果算出来的结果更接近B。后来我把中间步骤保留小数点后两位，再计算基本是C。所以到底怎么保留小数点?

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2022-08-14 20:03 2 · 回答

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2021-07-23 19:02 1 · 回答