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Ivana 🍭 · 2022年09月09日

请问A要怎么计算

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.

老师请问A要怎么计算

1 个答案

星星_品职助教 · 2022年09月10日

同学你好,

本题的bond和stock都服从正态分布。所以probability of a negative return相当于是return<0的概率。

由于普通正态分布无法查表和比较这个概率,所以要将bond和stock的return分别做标准化。

对于bond而言,P(X<0%)转化为z<(0%-2%)/5%=z<-0.4;

同理,stock收益率为负的概率标准化后为z<-0.67。

由于-0.67落在了-0.40的左侧,对应的面积小。所以可以得出:stock收益率为负的概率<bond收益率为负的概率。


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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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