LM 3: Statistical Measure of Asset Returns

Question 1

What is the measure of central tendency?

Answer 1

indicates where the data is centered

Question 2

Describe the 3 most common central tendency measures. MMM

Answer 2

1. mean (average)
2. mode (most)
3. median (organize low to high, then cross off 1 on each side until 1 left)

Question 3

What is the difference between unimodal, bimodal, and multimodal?

Answer 3

unimodal has 1 mode
bimodal has 2 modes
multimodal has 3 or more modes

Question 4

Whats the difference between trimmed mean and winsorized mean?

Answer 4

trimmed mean: removes the top and bottom x percentage of numbers

winsorized mean: gives all upper values a specific value and all lower values a specific value

Question 5

How is data divided for quartiles, quintiles, deciles, and percentiles?

Answer 5

quartiles: 4
quintiles: 5
deciles: 10
percentiles: 100

Question 6

What is the interquartile range?

Answer 6

IQR = Q3 - Q1

Question 7

What is the formula to determine what value a quartile should be plotted at?

Answer 7

Ly = (n+1) * y/100

y = position of percentile
n = #of observations

Question 8

On a box and whisker plot where are the arithmetic, median, Q3, Q1, and the interquartile range placed?

Answer 8

arithmetic mean = below median in the box (usually x)

median = above the arithmetic mean in the box (flat line = 50th percentile)

Q3 = highest value of the box

Q1 = lowest value of the box

Interquartile range: difference between Q3 and Q1

Question 9

What is the formula for determining where the percentile should be placed if between 2 observations?

Answer 9

interpolation formula = lower year spot rate yield + ((year you looking for spot rate - lower year) / (high year- lower year) * (higher year spot rate yield - lower year spot rate yield)

Eg. The current 5-year and 10-year Treasury spot yields are 2.10% and 2.85%, respectively.
Use linear interpolation to calculate the yield on a 7-year security.

2.10% + ((7-5)/(10-5)) * (2.85 -2.10)

Question 10

What is the difference between mean and dispersion?

Answer 10

mean focuses on reward

dispersion focuses on risk

Question 11

What are the 4 most common measures of absolute dispersion? RMVS

Answer 11

1. range
2. mean absolute deviation
3. variance
4. standard deviation

Question 12

What is the formula for range?

Answer 12

maximum value - minimum value

Question 13

What is the formula for mean absolute deviation?

Answer 13

MAD = ([observation1 - mean]+ [observation2 -mean]…)/ number of observations

Question 14

What is the formula for sample variance?

Answer 14

sample variance (s2) = (((observation1 - mean)^2) +
(observation2 -mean)^2)…)/ (number of observations -1)

Question 15

What is the formula for sample standard deviation?

Answer 15

sample standard deviation (s)= sqrt s2

s2 = sample variance

Question 16

What is the formula for target downside deviation and the one rule?

Answer 16

=sqrt
(((value of observation - target)^2) + ((value of observation - target)^2)…) / (n-1)

rule: if the value of observation is greater than the target then put 0.

Question 17

What is the coefficient of variation formula and the one rule?

Answer 17

CV = s/x

s = standard deviation (sqrt variance)
x = mean

rule: if x is negative statistic is meaningless

Question 18

What does a symmetric distribution mean and what are the 2 characteristics of a symmetric distribution?

Answer 18

means that the left side is a mirror image of the right side.

characteristics:
- mean and median are equal
- mean and variance describe the distribution

Question 19

What does a positively skewed distribution mean and in what order are mean, mode, and median from left to right? What does a positively skewed distribution look like?

Answer 19

mean it has frequent small losses and few extreme gains

mode>median>mean

big hump then flattens out

Question 20

What does a negatively skewed distribution mean and in what order are mean, mode, and median from left to right? What does a positively skewed distribution look like?

Answer 20

mean it has frequent small gains and few extreme losses

mean>median>mode

flat then a big hump

Question 21

What does a skewness of greater than 0, equal 0, and less than 0 mean?

Answer 21

greater than 0: positively skewed

equal to 0: symmetric

less than 0: negatively skewed

Question 22

What’s the formula for sample skewness?

Answer 22

skewness = (((value of1 - mean)^3)((value of2-mean)^3)…)/ ((N-1)*(standard deviation^3))

Question 23

Describe the 3 types of kurtosis.

Answer 23

1. mesokurtic (average)
2. leptokurtic (many outliers, fat tail (higher peak))
3. platykurtic (few outliers, thin tail(lower peak than mesokurtic))

Question 24

Whats the formula for kurtosis?

Answer 24

kurtosis = (((value of1 - mean)^4)((value of2-mean)^4)…)/ ((N-1)*(standard deviation^4))

Question 25

Whats the formula for excess kurtosis?

Answer 25

kurtosis = [(((value of1 - mean)^4)((value of2-mean)^4)…)/ ((N-1)*(standard deviation^4))] -3

Question 26

What is the relationship between kurtosis, excess kurtosis, distribution, and the tail?

Answer 26

kurtosis >3 = excess kurtosis >0 = fatter tailed than normal = leptokurtic

kurtosis = 3 = excess kurtosis =0 = similar tails to normal = mesokurtic

kurtosis <3 = excess kurtosis <0 = thinner tailed than normal = platykurtic

Question 27

What is the difference between covariance and correlation?

Answer 27

Covariance measures the direction of a relationship between two variables

Correlation measures the strength of that relationship

Question 28

What is the formula for sample covariance?

Answer 28

sxy = ((x- mean x) * (y- mean y)) / n-1

sxy = sample covariance between x and y

Question 29

What does the correlation coefficient tell us?

Answer 29

tells us how correlated they are

Question 30

What is the sample correlation coefficient formula?

Answer 30

rxy = sxy/ sx*sy

sxy = sample covariance
sx = sample standard deviation of x
sy = sample standard deviation of y

Question 31

What does a correlation coefficient of -1, 0, and 1 mean?

Answer 31

-1 = perfect inverse linear relationship

0 = no linear relationship

1 = perfect linear relationship