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aileen20180623 · 2024年02月25日

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  1. CFA II
  2. Fixed Income

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NO.PZ201602270200001902

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.

老师这题我用的题目要求的hb公司处以benchmark'的yield，2年算出的spot rate和3年的spot rate，但是我看到答案写的是用2.3年的yield 作为2年，3年的cupon然后分别求出的spot rate，嗯我有些分不清什么时候用benchmark的coupon什么时候用给的公司的coupon

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1 个答案

品职答疑小助手雍 · 2024年02月26日

同学你好，首先要分清的其实是YTM和spot rate的区别。 YTM的意思是每年用同一个折现算价格（表二给的条件），而spot rate相当于每期用不同的折现率算价格（method1要求的计算方式）。

所以本题要先把YTM转换出每期的spot rate。（用的是YTM等于coupon rate时，债券价格等于面值的原理计算）

然后把HB公司的每期的现金流分别用对应期限的spot rate折现。（用HB公司的coupon）


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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?

2024-04-12 05:45 1 · 回答

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. 老师，1、首先说了coupon rate，然而在下面计算的时候，二年期的CF用的4，三年期用的5，这数字都是怎么来的？2、没明白题目暗示怎么体现出来的？按照表格指向，指的是YTM的表格，难道不是用3%、4%、5%分别折算3,3,103三年现金流吗？请帮忙翻译并且查看下，谢谢

2022-08-29 08:59 1 · 回答

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. 1、他不是说了COUPON是3%吗？2、YTM和这个COUPON RATE为什么又等同了？为什么可以认为第二年、第三年的COUPON RATE是YTM？3、benchmark pcurve，为什么表格里面又说是YTM,？YTM和这个COUPON RATE为什么又等同了？4、为什么不能用YTM直接算，之前的答案并没有很清晰回答，感觉像是诡辩？他不是说了COUPON是3%吗？，那不是三年的话，3年的COUPO都是3%？，对应的YTM就是5%？

2022-08-14 20:03 2 · 回答

NO.PZ201602270200001902 0.4682 per 100 of pvalue. 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​=94.4828 Therefore, 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.何老师上课不是说YTM是sport rate的打包价么，为什么不可以直接用第三年的YTM 5%来进行折现呢？

2021-07-23 19:02 1 · 回答