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Drink H · 2020年01月20日

问一道题:NO.PZ2020010304000047

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:μSμF=0H_0: \mu_S - \mu_F = 0

The alternative is

H1:μSμFH_1: \mu_S \neq \mu_F

or equivalently

H1:μSμF0H_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).

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).--这句话如何理解?

1 个答案
已采纳答案

orange品职答疑助手 · 2020年01月20日

同学你好,这题有点无聊……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。说白了它就是在考该用什么分布来刻画一个债券是否违约:应该用binary distribution。