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 掌握計(jì)算和比較：
◆ 理解：variance 比MAD 要好，因?yàn)関ariance 是連續(xù)的，處處可導(dǎo)。MAD 計(jì)算的
是值，相對(duì)比較繁瑣。但是variance 和MAD 都是表示風(fēng)險(xiǎn)的。考到MAD 的 計(jì)算，這是好幾年沒有預(yù)估到的考點(diǎn)，一定要注意到MAD＜=σ
知識(shí)點(diǎn)對(duì)應(yīng)的試題如下：
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%
