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leozhenlin · 2020年09月28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.

老师我想问一下X~N(....)括号中,“0”代表的是什么意思,一般来说我们说满足正态分布,括号里都需要写什么

1 个答案

星星_品职助教 · 2020年09月28日

同学你好,

正态分布是由两个参数决定的,均值和方差,所以一般的写法都是X~N(μ,σ^2)。

以这道题的stock为例,X服从的就是均值为0.1,标准差为0.15的正态分布。这两个参数都可以在题干中的表格里找到。此后进一步做标准化,代入标准化的公式就可以解题了。

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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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2022-07-06 14:07 2 · 回答

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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