问题如下图:
选项:
A.
B.
C.
D.
解释:
这道题为什么不可以从bond price的角度来求呢?99=104*(1-PD)+104*PD*0.5/【1+(0.055/2)】,100=109*(1-PD)+109*PD*0.5/1.06.这样算下来是C,请问哪里不对,谢谢
orange品职答疑助手 · 2018年05月14日
同学你好,这道题在经典题中也有出现,它是想考察YTM-Rf≈PD*(1-RR)这个知识点,但题目出的是有问题的,正如你所说的这样。同学你的做法大致是没有问题的,唯一的小问题是第二个bond它在0.5年时还要发一次coupon,这个也得考虑,但题目没有给多余条件。总而言之,是题目问题。
本题解析给的是错的,详细原因如下:
1、用100/1+ytm=[pd*RR+100*(1-PD)]/(1+Rf)来计算,是和YTM-Rf≈PD*(1-RR)等价的,因为YTM-Rf≈PD*(1-RR)就是从前式化简、变形而来。
2、但是,这个模型的前提假设是zero-coupon bond,我们 是在这个假设下,才推出了之后的这个结论。但本题中,是coupon bond,尤其是第二个债券,它在t=0.5和t=1时,都会付一次息,所以严格而言它有两次default的可能。所以,本题出的其实有问题。
3、忽略前提假设是zero coupon bond,假设本题可以用这个模型来算。第一个债券算出来的,其实是半年的PD,你用100/1+ytm=[pd*RR+100*(1-PD)]/(1+Rf)算,那么ytm和rf都要除以2,因为是半年;你用YTM-Rf≈PD*(1-RR)算,ytm与rf也得用ytm/2和rf/2来代。两种方法算出来的PD都是4.4%左右。 而第二个债券,如果不管它的coupon,当它是零息债券来算的话,算出来的将是一年的PD。因为时期不一样,那PD自然也不一样。
4、对于第一个bond,本题的解析,是直接用YTM-Rf≈PD*(1-RR)来算,其中ytm和rf都代的是一年的。这样求出来的PD,可以看作是半年的PD,再乘以2,也就是说把半年的PD“年化”了。但这个不是通法。我们也怀疑出题者有没有想这么多。
5、总而言之,本题是一道老题了,题目本身有不严谨的地方。但它想考察的知识点,绝对还是YTM-Rf≈PD*(1-RR)。所以掌握好这个知识点就好,本题不用过于纠结了。
Roseline · 2020年06月30日
老师好,这道题我感觉不用考虑那么复杂,感觉都没有考YTM-Rf≈PD*(1-RR)这个知识点。题目问题问的是XYZ这家公司的违约概率是在上半年高还是下半年高。XYZ公司一共包含了两个债券,第一个A债券只有半年,在第6个月付一次息,第二个B债券是一年,分别在第6个月和1年末付息;而题目还提到了在付息的时候可能会发生违约,那么其实在第6个月的时候,XYZ这家公司违约的概率就是A违约B不违约+B违约A不违约+AB都违约,而在1年末的违约概率是B违约,这样一比较,肯定是在第6个月的时候要更高吧?不知道我这么想对不对。
NO.PZ2016082406000034 Equbetween the two coupon perio Greater in the seconsix-month periothin the first Cannot terminefrom the information provi ANSWER: A First, we compute the current yielon the six-month bon whiis selling a scount. We solve for y* suth99=1041+y∗20099\text{=}\frac{104}{1+\frac{y\ast}{200}}99=1+200y∗104 anfiny∗=10.10%y\ast\text{=}10.10\%y∗=10.10%. Thus the yielsprefor the first bonis 10.1-5.5=4.6%10.1\text{-}5.5\text{=}4.6\%10.1-5.5=4.6%. The seconbonis par, so the yielis y∗=9%y\ast\text{=}9\%y∗=9%. The sprefor the seconbonis 9-6=3%\;9\text{-}6\text{=}3\%9-6=3%. The fault rate for the first periomust greater. The recovery rate is the same for the two perio, so it es not matter for this problem.我们求出来的是secon or remaining 6-month,这个和first 6-month有什么关系啊?
NO.PZ2016082406000034 Equbetween the two coupon perio Greater in the seconsix-month periothin the first Cannot terminefrom the information provi ANSWER: A First, we compute the current yielon the six-month bon whiis selling a scount. We solve for y* suth99=1041+y∗20099\text{=}\frac{104}{1+\frac{y\ast}{200}}99=1+200y∗104 anfiny∗=10.10%y\ast\text{=}10.10\%y∗=10.10%. Thus the yielsprefor the first bonis 10.1-5.5=4.6%10.1\text{-}5.5\text{=}4.6\%10.1-5.5=4.6%. The seconbonis par, so the yielis y∗=9%y\ast\text{=}9\%y∗=9%. The sprefor the seconbonis 9-6=3%\;9\text{-}6\text{=}3\%9-6=3%. The fault rate for the first periomust greater. The recovery rate is the same for the two perio, so it es not matter for this problem.请问这里为什么是y*/200?为什么是200呢
NO.PZ2016082406000034 Suppose XYZ Corp. htwo bon paying semiannually accorng to the following table: The recovery rate for eain the event of fault is 50%. For simplicity, assume theabonwill fault only the enof a coupon perio The market-implierisk-neutrprobability of fault for XYZ Corp. is Greater in the first six-month periothin the seconEqubetween the two coupon perio Greater in the seconsix-month periothin the first Cannot terminefrom the information provi ANSWER: A First, we compute the current yielon the six-month bon whiis selling a scount. We solve for y* suth99=1041+y∗20099\text{=}\frac{104}{1+\frac{y\ast}{200}}99=1+200y∗104 anfiny∗=10.10%y\ast\text{=}10.10\%y∗=10.10%. Thus the yielsprefor the first bonis 10.1-5.5=4.6%10.1\text{-}5.5\text{=}4.6\%10.1-5.5=4.6%. The seconbonis par, so the yielis y∗=9%y\ast\text{=}9\%y∗=9%. The sprefor the seconbonis 9-6=3%\;9\text{-}6\text{=}3\%9-6=3%. The fault rate for the first periomust greater. The recovery rate is the same for the two perio, so it es not matter for this problem. 我还以为是假设1个月付息一次,一年假设360天,然后计算量巨大
Suppose XYZ Corp. htwo bon paying semiannually accorng to the following table: The recovery rate for eain the event of fault is 50%. For simplicity, assume theabonwill fault only the enof a coupon perio The market-implierisk-neutrprobability of fault for XYZ Corp. is Greater in the first six-month periothin the seconEqubetween the two coupon perio Greater in the seconsix-month periothin the first Cannot terminefrom the information provi ANSWER: A First, we compute the current yielon the six-month bon whiis selling a scount. We solve for y* suth99=1041+y∗20099\text{=}\frac{104}{1+\frac{y\ast}{200}}99=1+200y∗104 anfiny∗=10.10%y\ast\text{=}10.10\%y∗=10.10%. Thus the yielsprefor the first bonis 10.1-5.5=4.6%10.1\text{-}5.5\text{=}4.6\%10.1-5.5=4.6%. The seconbonis par, so the yielis y∗=9%y\ast\text{=}9\%y∗=9%. The sprefor the seconbonis 9-6=3%\;9\text{-}6\text{=}3\%9-6=3%. The fault rate for the first periomust greater. The recovery rate is the same for the two perio, so it es not matter for this problem. 老师好,这道题我感觉不用考虑那么复杂,感觉都没有考YTM-Rf≈P(1-RR)这个知识点。题目问题问的是XYZ这家公司的违约概率是在上半年高还是下半年高。XYZ公司一共包含了两个债券,第一个A债券只有半年,在第6个月付一次息,第二个B债券是一年,分别在第6个月和1年末付息;而题目还提到了在付息的时候可能会发生违约,那么其实在第6个月的时候,XYZ这家公司违约的概率就是A违约B不违约+B违约A不违约+AB都违约,而在1年末的违约概率是B违约,这样一比较,肯定是在第6个月的时候要更高吧?之前有个同学这么理解的,我觉得很在理,想问问老师这么理解是不是正确的
Suppose XYZ Corp. htwo bon paying semiannually accorng to the following table: The recovery rate for eain the event of fault is 50%. For simplicity, assume theabonwill fault only the enof a coupon perio The market-implierisk-neutrprobability of fault for XYZ Corp. is Greater in the first six-month periothin the seconEqubetween the two coupon perio Greater in the seconsix-month periothin the first Cannot terminefrom the information provi ANSWER: A First, we compute the current yielon the six-month bon whiis selling a scount. We solve for y* suth99=1041+y∗20099\text{=}\frac{104}{1+\frac{y\ast}{200}}99=1+200y∗104 anfiny∗=10.10%y\ast\text{=}10.10\%y∗=10.10%. Thus the yielsprefor the first bonis 10.1-5.5=4.6%10.1\text{-}5.5\text{=}4.6\%10.1-5.5=4.6%. The seconbonis par, so the yielis y∗=9%y\ast\text{=}9\%y∗=9%. The sprefor the seconbonis 9-6=3%\;9\text{-}6\text{=}3\%9-6=3%. The fault rate for the first periomust greater. The recovery rate is the same for the two perio, so it es not matter for this problem. 请问公式中,y*/200是什么意思呢