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Alicess · 2020年07月06日

问一道题:NO.PZ2017092702000049 [ CFA I ]

问题如下:

The following table shows the annual MSCI World Index total returns for 2004–2013.

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

选项:

A.

20.65%.

B.

26.03%.

C.

27.37%.

解释:

B is correct.

Quintiles divide a distribution into fifths, with the fourth quintile occurring at the point at which 80% 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%, -5.02%, 9.57%, 10.02%, 12.34%, 15.25%, 16.54%, 20.65%, 27.37%, and 30.79%), the 8.8th position would be between the 8th and 9th entries, 20.65% and 27.37%, 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%

老师能不能解释一下插值法,也就是8·8位置的数为什么是0·8乘以两数相减
1 个答案

星星_品职助教 · 2020年07月06日

同学你好,

可以简单理解为第“8.8”个数就是在第8个数和第9个数距离之间的“0.8”或80%的位置上。在本题中,就相当于第8.8个数在20.65% 和27.37%之间80%的位置上

第8个数和第9个数的距离为(27.37%-20.65%),所以用0.8×(27.37%-20.65%)就可以得到5.38%

所以第8.8个数相当于第8个数再加上这个0.8位置上的数,也就是20.65%+5.38%=26.03%

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