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James · 2023年12月22日

这道题一定要按数值重新排序吗？

  1. CFA I
  2. Quantitative

NO.PZ2023060502000002

问题如下：

Exhibit 1 shows the annual MSCI World Index total returns for a 10-year

period.


The fourth quintile return for the MSCI World Index is closest to:

选项：

A.

20.65 percent.

B.

26.03 percent.

C.

27.37 percent.

解释：

B is correct. Quintiles divide a distribution into fifths, with the fourth quintile

occurring at the point at which 80 percent of the observations lie below it. The

fourth quintile is equivalent to the 80th percentile. To find the yth percentile (Py),

we first must determine its location. The formula for the location (Ly) of a yth

percentile in an array with n entries sorted in ascending order is Ly = (n + 1) ×

(y/100). In this case, n = 10 and y = 80%, so

L80 = (10 + 1) × (80/100) = 11 × 0.8 = 8.8.

With the data arranged in ascending order (−40.33 percent, −5.02 percent,

9.57 percent, 10.02 percent, 12.34 percent, 15.25 percent, 16.54 percent, 20.65

percent, 27.37 percent, and 30.79 percent), the 8.8th position would be between

the eighth and ninth entries, 20.65 percent and 27.37 percent, respectively. Using

linear interpolation, P80 = X8 + (Ly − 8) × (X9 − X8),

P80 = 20.65 + (8.8 − 8) × (27.37 − 20.65)

= 20.65 + (0.8 × 6.72) = 20.65 + 5.38

= 26.03 percent.

我是按年份顺序来计算8.8分位数值的…

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1 个答案

品职助教_七七 · 2023年12月23日

嗨，努力学习的PZer你好：


分位点计算的第一步是从小到大开始排序。必须排序，不能省略。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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NO.PZ2023060502000002问题如下 Exhibit 1 shows the annuMSWorlInx totreturns for a 10-yearperioThe fourth quintile return for the MSWorlInx is closest to: A.20.65 percent.B.26.03 percent.C.27.37 percent. B is correct. Quintiles vi a stribution into fifths, with the fourth quintileoccurring the point whi80 percent of the observations lie below it. Thefourth quintile is equivalent to the 80th percentile. To finthe yth percentile (Py),we first must termine its location. The formula for the location (Ly) of a ythpercentile in arrwith n entries sortein ascenng orr is Ly = (n + 1) ×(y/100). In this case, n = 10 any = 80%, soL80 = (10 + 1) × (80/100) = 11 × 0.8 = 8.8.With the ta arrangein ascenng orr (−40.33 percent, −5.02 percent,9.57 percent, 10.02 percent, 12.34 percent, 15.25 percent, 16.54 percent, 20.65percent, 27.37 percent, an30.79 percent), the 8.8th position woulbetweenthe eighth anninth entries, 20.65 percent an27.37 percent, respectively. Usinglineinterpolation, P80 = X8 + (Ly − 8) × (X9 − X8),P80 = 20.65 + (8.8 − 8) × (27.37 − 20.65)= 20.65 + (0.8 × 6.72) = 20.65 + 5.38= 26.03 percent. 问题如下Exhibit 1 shows the annuMSWorlInx totreturns for a 10-yearperioThe fourth quintile return for the MSWorlInx is closest to:A.20.65 percent.B.26.03 percent.C.27.37 percent.B is correct. Quintiles vi a stribution into fifths, with the fourth quintileoccurring the point whi80 percent of the observations lie below it. Thefourth quintile is equivalent to the 80th percentile. To finthe yth percentile (Py),we first must termine its location. The formula for the location (Ly) of a ythpercentile in arrwith n entries sortein ascenng orr is Ly = (n + 1) ×(y/100). In this case, n = 10 any = 80%, soL80 = (10 + 1) × (80/100) = 11 × 0.8 = 8.8.With the ta arrangein ascenng orr (−40.33 percent, −5.02 percent,9.57 percent, 10.02 percent, 12.34 percent, 15.25 percent, 16.54 percent, 20.65percent, 27.37 percent, an30.79 percent), the 8.8th position woulbetweenthe eighth anninth entries, 20.65 percent an27.37 percent, respectively. Usinglineinterpolation, P80 = X8 + (Ly − 8) × (X9 − X8),P80 = 20.65 + (8.8 − 8) × (27.37 − 20.65)= 20.65 + (0.8 × 6.72) = 20.65 + 5.38= 26.03 percent.

2024-02-10 14:26 1 · 回答