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十种笠 · 2022年08月14日

benchmark par curve,为什么用来做算SPOT RATE的对应COUPON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.

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 par curve,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%?


2 个答案

pzqa015 · 2022年08月17日

嗨,爱思考的PZer你好:


1、他不是说了COUPON是3%吗?

---

那是Hutto-Barkley corporate bond这只公司债的coupon,我们要计算的是benchmark的spot rate,这样得出来的才是无套利价格。

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?

---------

哪个ytm和哪个coupon rate等同了?第二年和第三年的coupon rate是spot rate,不是ytm。

3、benchmark par curve,为什么表格里面又说是YTM,?YTM和这个COUPON RATE为什么又等同了?

-----------

建议你翻译一下讲义,看看par rate的定义。

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%?

-------

这个知识点你回去重新听下吧。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

十种笠 · 2022年08月17日

你这相当于让我自己回去看书,我要是看懂了,我来这问干嘛?就是没搞懂才要解释

十种笠 · 2022年08月17日

说了很多次让你解释了,你还是这样敷衍,如果是这样子,还需要你们的课程服务干嘛呢?随便找个课程听不就得了?我要是全听懂了,还需要来问吗

pzqa015 · 2022年08月15日

嗨,爱思考的PZer你好:


关于par rate以及用par rate通过bootstraping来得到spot rate的讲义见下图

题目让计算mispriced,首先要根据par rate来反推出spot rate,用spot rate计算的是无套利价格,它与ytm计算的价格之差,就是mispriced。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

十种笠 · 2022年08月15日

我又不是没有这些PPT,我就是没看懂才问你,你能否直接用中文回答下我的问题

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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 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