AliciaLi · 2021年08月09日

confidence level没给啊

NO.PZ2020010304000051

问题如下：

You collect 50 years of annual data on equity and bond returns. The estimated mean equity return is 7.3% per year, and the sample mean bond return is 2.7% per year. The sample standard deviations are 18.4% and 5.3%, respectively. The correlation between the two-return series is -60%. Are the expected returns on these two assets the same? Does your answer change if the correlation is 0?

选项：

解释：

The null hypothesis is $H_0: \mu_E = \mu_B$ .

The alternative is $H_1: \mu_E ≠ \mu_B$ .

The test statistic is based on the difference of the average returns, $\delta$ = 7.3% - 2.7% = 4.6%.

The estimator of the variance of the difference is $\sigma_E^2+\sigma_B^2-2\sigma_{BE}$ , which is $0.184^2+0.053^2-2*(-0.6)*0.184 * 0.053 = 0.0483.$

The test statistic is $\frac\delta{\sqrt{\displaystyle\frac{0.0483}{50}}}=1.47$

The critical value for a two-sides test is $\pm1.96$ using a size of 5%. The null is not rejected.

If the correlation was 0, then the variance estimate would be 0.0366, and the test statistic is 1.69. The null would still not be rejected if the size was 5%, although if the test size was 10%, then the critical value would be $\pm1.645$ and the correlation would matter.

这个题目里没说confidence level 5%啊，这个是从哪里来的？

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2 个答案

品职答疑小助手雍 · 2021年08月09日

嗨，爱思考的PZer你好：

Testing The Equality of Two Means课里讲过这部分内容。

检验两个均值是否相等用t检验，本题算出来t检验值两种情况分别是1.47和1.69，常规的检验分位点都是用的95%的，也就是1.96，所以两次都没有拒绝原假设：H0: μE=μB

题目也解析了如果把检验confidence level调整到90%，会拒绝原假设。

这题的解析是个分析的过程，不是单纯的判断是否。

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努力的时光都是限量版，加油！

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