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tetexe · 2020年02月24日

问一道题：NO.PZ2020010304000047

  1. FRM I
  2. Quantitative

问题如下：

Suppose you wish to test whether the default rate of bonds that are rated as investment grade by S&P is the same as the default rate on bonds rated as investment grade by Fitch. What are the null and alternative hypotheses? What data would you need to test the null hypothesis?

选项：

解释：

The null is that the IG (investment grade) default rate is the same for S&P rated firms as it is for Fitch-rated firms. If Si are default indicators for S&P rated firms, and Fi are default indicators for Fitch-rated firms, then the null is H0:μS=μFH_0: \mu_S = \mu_F

which states that the mean values are the same.

The null can be equivalently expressed as

H0:μS−μF=0H_0: \mu_S - \mu_F = 0

The alternative is

H1:μS≠μFH_1: \mu_S \neq \mu_F

or equivalently

H1:μS−μF≠0H_1: \mu_S - \mu_F \neq 0

The data required to test this hypothesis would be binary random variables where 1 indicates that an IG bond defaulted and 0 if it did not within a fixed time frame (e.g., a quarter).

请问，解答中的SI和Fi是什么意思？

另外，老师说要把真实想证实的内容放在Ha，这道题目中真实想证实的内容是他们两家评级公司评出的债券违约率是相等的。这样的话，Ha：Us=Uf呀。。。。为什么现在是相反的呢？

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1 个答案

orange品职答疑助手 · 2020年02月24日

同学你好。1、它就是想检验两个评级机构评出来的投资级债券的违约率是否相同，它所需要的数据，自然就是两个数据集，每个数据集里都是1，0，0，1，…… 分别代表着违约，不违约，不违约，违约。SI和FI分别代表着两个数据集里的1和0。这样就可以把标普评级的公司里违约的个数，转化成S数据集里1的个数，相当于数量化了。

2、在假设检验里，我们是把等号放在原假设里的。

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NO.PZ2020010304000047问题如下Suppose you wish to test whether the fault rate of bon thare rateinvestment gra S P is the same the fault rate on bon rateinvestment gra Fitch. Whare the null analternative hypotheses? Whta woulyou neeto test the null hypothesis? The null is ththe IG (investment gra) fault rate is the same for S P ratefirms it is for Fitch-ratefirms. If Si are fault incators for S P ratefirms, anFi are fault incators for Fitch-ratefirms, then the null is H0:μS=μFH_0: \mu_S = \mu_FH0​:μS​=μF​whistates ththe mevalues are the same.The null cequivalently expresseasH0:μS−μF=0H_0: \mu_S - \mu_F = 0H0​:μS​−μF​=0The alternative isH1:μS≠μFH_1: \mu_S \neq \mu_FH1​:μS​​=μF​or equivalentlyH1:μS−μF≠0H_1: \mu_S - \mu_F \neq 0H1​:μS​−μF​​=0The ta requireto test this hypothesis woulbinary ranm variables where 1 incates thIG bonfaultean0 if it not within a fixetime frame (e.g., a quarter).老师，为什么fault rate 和均值是一个意思呢

2024-05-13 16:20 1 · 回答

The ta requireto test this hypothesis woulbinary ranm variables where 1 incates thIG bonfaultean0 if it not within a fixetime frame (e.g., a quarter).--这句话如何理解？

2020-01-20 11:35 1 · 回答