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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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NO.PZ2017092702000100问题如下 analyst velops the following capitmarket projections.Assuming the returns of the asset classes are scribenormstributions, whiof the following statements is correct?A.Bon have a higher probability of a negative return thstocks.B.On average, 99% of storeturns will fall within two stanrviations of the mean.C.The probability of a bonreturn less thor equto 3% is termineusing a Z-score of 0.25.A is correct.The chanof a negative return falls in the area to the left of 0% unr a stanrnormcurve. stanrzing the returns anstanrviations of the two assets, the likelihooof either asset experiencing a negative return mtermine Z-score (stanrzevalue) = (X – μ)/σ Z-score for a bonreturn of 0% = (0 – 2)/5 = –0.40. Z-score for a storeturn of 0% = (0 – 10)/15 = –0.67. For bon, a 0% return falls 0.40 stanrviations below the mereturn of 2%. In contrast, for stocks, a 0% return falls 0.67 stanrviations below the mereturn of 10%. A stanrviation of 0.40 is less tha stanrviation of 0.67. Negative returns thus occupy more of the left tail of the bonstribution ththe stostribution. Thus, bon are more likely thstocks to experiena negative return.A可以用 标准差/平均 来比较吗C要怎么算呢

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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