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Zyy411 · 2019年12月13日

问一道题:NO.PZ2017092702000100

问题如下:

An analyst develops the following capital market projections.

Assuming the returns of the asset classes are described by normal distributions, which of the following statements is correct?

选项:

A.

Bonds have a higher probability of a negative return than stocks.

B.

On average, 99% of stock returns will fall within two standard deviations of the mean.

C.

The probability of a bond return less than or equal to 3% is determined using a Z-score of 0.25.

解释:

A is correct.

The chance of a negative return falls in the area to the left of 0% under a standard normal curve. By standardizing the returns and standard deviations of the two assets, the likelihood of either asset experiencing a negative return may be determined: Z-score (standardized value) = (X – μ)/σ Z-score for a bond return of 0% = (0 – 2)/5 = –0.40. Z-score for a stock return of 0% = (0 – 10)/15 = –0.67. For bonds, a 0% return falls 0.40 standard deviations below the mean return of 2%. In contrast, for stocks, a 0% return falls 0.67 standard deviations below the mean return of 10%. A standard deviation of 0.40 is less than a standard deviation of 0.67. Negative returns thus occupy more of the left tail of the bond distribution than the stock distribution. Thus, bonds are more likely than stocks to experience a negative return.

老师这道题目不是很理解,是否提干和三道答案都可以解释下?感谢

1 个答案

星星_品职助教 · 2019年12月16日

同学你好,

这道题目给了股票和债券各自的收益率和标准差,而且说明两种资产都是服从正态分布的。但两个服从不同正态分布的资产是没法直接进行比较的,只能将两个资产都转化为一个统一的标准或口径下才能进行比较。所以这道题本质考察的是正态分布的标准化。

选项A是比较bond和stock这两种资产中,哪个收益率为负的概率比较大。收益率为负的概率即收益率<0的概率。按照上课讲的公式进行标准化后,就转化为了股票收益率(Z-score)小于-0.67的概率,和债券收益率小于-0.4的概率这两个概率之间的比较。

由图可知,红色部分的面积代表Stock产生负回报的概率,绿色面积代表Bond产生负回报的概率,绿色面积大于红色面积,所以Bond相对于Stock来说产生负回报的概率更高,A选项的描述是正确的。

对于B选项,距离均值2倍标准差的概率应该是大约为95%,而不是99%的概率(因为根据上课背过的那组值,95%的概率对应的是1.96倍标准差,近似于2倍)。

对于C选项,相当于求Bond的return小于等于3%的概率,即P(X≤3%),求出来后对应的Z-score应该为0.2,而不是0.25




Jine · 2019年12月31日

星星的回答,品职NO.1,没有之一!

星星_品职助教 · 2019年12月31日

呀,谢谢!加油哦明年二级继续答疑~

为了求职冲呀 · 2020年03月09日

星星老师真的回答问题超级棒,很详细,很容易懂。

星星_品职助教 · 2020年03月10日

谢谢^-^

sarahjia · 2020年03月16日

真的我觉得星星老师讲的最清楚呜呜呜呜

星星_品职助教 · 2020年03月16日

谢谢谢谢~~

sarahjia · 2020年03月16日

星星老师你只负责回答quantitative的部分吗还是也有负责回答其他部分呢~

星星_品职助教 · 2020年03月16日

目前一级只负责数量,所以一定要通过呀,明年二级数量继续答疑~

AustinNZ · 2020年03月27日

星星老师你讲解的太清楚了,完全搞懂了~

星星_品职助教 · 2020年03月27日

加油^_^~

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2022-09-21 07:28 1 · 回答

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2022-09-09 22:07 1 · 回答

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2022-07-10 21:43 1 · 回答

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NO.PZ2017092702000100 老师这题是不是因为已知了正态分布,所以不用标准化,得出来的概率就可以直接比较大小?

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