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CFA一级知识点之多位数的解析

发表时间:2014-11-24 02:14 编辑: 告诉小伙伴:
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理解:variance 比MAD 要好,因为variance 是连续的,处处可导。MAD 计算的是绝对值,相对比较繁琐。但是variance 和MAD 都是表示风险的。

R2-9-1 Measure of dispersion:
?Range=highest value‐lowest value

◆ Coefficient of variation: measures the amount of dispersion in a distribution relative
to the distribution's mean. It can be used to measure the risk per unit of return.
R2-9-2 MAD 和 Variance 掌握计算和比较:

◆ 理解:variance 比MAD 要好,因为variance 是连续的,处处可导。MAD 计算的
是绝对值,相对比较繁琐。但是variance 和MAD 都是表示风险的。考到MAD 的 计算,这是好几年没有预估到的考点,一定要注意到MAD<=σ
知识点对应的试题如下:
R2-7 Describe, calculate, and interpret quartiles, quintiles, deciles, and percentiles

Q2-19Which of the following statements is most accurate?
A. The first quintile generally exceeds the median.
B. The first quintile generally exceeds the first decile.
C. The first quintile generally exceeds the first quartile.

Solution: B
The first quintile is the 20th percentile. The first decile is the 10th percentile, the first quartile is
the 25th percentile, and the median is the 50th percentile. While it is possible that these various
percentiles or some subsets of them be equal (for example the 10th percentile possibly could be
equal to the 20th percentile), in general the order from smallest to largest would be: first decile,
first quintile, first quartile, median.

Q2-20 The following table shows the volatility of a series of funds that belong to the same peer group,ranked in ascending order:

 

Volatility (%)

   

Volatility(%)

Fund 1

9.81

Fund 8

13.99

Fund 2

10.12

Fund 9

14.47

Fund 3

10.84

Fund 10

14.85

Fund 4

11.33

Fund 11

15.00

Fund 5

12.25

Fund 12

17.36

Fund 6

13.39

Fund 13

17.98

Fund 7

13.42

   

 

The value of the first quintile is closest to
A. 10.70%
B. 10.84%
C. 11.09%

Solution: A
The position of the first quintile is:
L = (n + 1) ×(y/ 100),
where
y is the percentage point at which we are dividing the distribution. In our case we have y = 20,
which corresponds to the 20 percentile (first quintile);
n is the number of observations (funds) in the peer group. In our case we have n = 13;
L corresponds to the location of the 20 percentile (first quintile)
L = (13 + 1) ×( 20/100} = 2.80.
Therefore, the location of the first quintile is between the volatility of Fund 2 and Fund 3(because they are ranked in ascending order).
Then, use linear interpolation to find the approximate value of the first quintile:
P ≈ X + (2.80 - 2) × (X - X ),
where
X is the volatility of Fund 2
X is the volatility of Fund 3
P is the approximate value of the first quintile
P ≈10.12% + (2.80 - 2} × (10.84% -10,12%) = 10.70%

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