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

James · 2025年04月14日

请老师看下我的思路哪里出错了

* 问题详情,请 查看题干

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.

题干说根据表2和表3来计算债券错误定价了多少。

本题中债券是3年期,按照表3给定3年期的YTM为5%,意味着该债券的内在价值应该以YTM=5%折现得出,3/1+5%,3/(1+5%)^2,103/(1+5%)^3,得到94.5535,意味着按照题干给定的条件合理定价应该是94.5535,差价就是0.444896。



1 个答案

吴昊_品职助教 · 2025年04月14日

嗨,努力学习的PZer你好:


1、求的是错误定价了多少,换句话说要我们求的是债券的无套利价格。从而看一下市场定价和无套利价格之间相差了多少,这个差值就是misprice。

2、债券的无套利价格,必须用spot rate折现得到,而不能用YTM折现。你的问题就在这里。

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

  • 1

    回答
  • 0

    关注
  • 5

    浏览
相关问题

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. 老师这题我用的题目要求的hb公司处以benchmark'的yiel2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yiel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

2024-02-25 17:44 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