LM 3: Statistical Measure of Asset Returns Flashcards
What is the measure of central tendency?
indicates where the data is centered
Describe the 3 most common central tendency measures. MMM
- mean (average)
- mode (most)
- median (organize low to high, then cross off 1 on each side until 1 left)
What is the difference between unimodal, bimodal, and multimodal?
unimodal has 1 mode
bimodal has 2 modes
multimodal has 3 or more modes
Whats the difference between trimmed mean and winsorized mean?
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
How is data divided for quartiles, quintiles, deciles, and percentiles?
quartiles: 4
quintiles: 5
deciles: 10
percentiles: 100
What is the interquartile range?
IQR = Q3 - Q1
What is the formula to determine what value a quartile should be plotted at?
Ly = (n+1) * y/100
y = position of percentile
n = #of observations
On a box and whisker plot where are the arithmetic, median, Q3, Q1, and the interquartile range placed?
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
What is the formula for determining where the percentile should be placed if between 2 observations?
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)
What is the difference between mean and dispersion?
mean focuses on reward
dispersion focuses on risk
What are the 4 most common measures of absolute dispersion? RMVS
- range
- mean absolute deviation
- variance
- standard deviation
What is the formula for range?
maximum value - minimum value
What is the formula for mean absolute deviation?
MAD = ([observation1 - mean]+ [observation2 -mean]…)/ number of observations
What is the formula for sample variance?
sample variance (s2) = (((observation1 - mean)^2) +
(observation2 -mean)^2)…)/ (number of observations -1)
What is the formula for sample standard deviation?
sample standard deviation (s)= sqrt s2
s2 = sample variance
What is the formula for target downside deviation and the one rule?
=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.
What is the coefficient of variation formula and the one rule?
CV = s/x
s = standard deviation (sqrt variance)
x = mean
rule: if x is negative statistic is meaningless
What does a symmetric distribution mean and what are the 2 characteristics of a symmetric distribution?
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
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?
mean it has frequent small losses and few extreme gains
mode>median>mean
big hump then flattens out
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?
mean it has frequent small gains and few extreme losses
mean>median>mode
flat then a big hump
What does a skewness of greater than 0, equal 0, and less than 0 mean?
greater than 0: positively skewed
equal to 0: symmetric
less than 0: negatively skewed
What’s the formula for sample skewness?
skewness = (((value of1 - mean)^3)((value of2-mean)^3)…)/ ((N-1)*(standard deviation^3))
Describe the 3 types of kurtosis.
- mesokurtic (average)
- leptokurtic (many outliers, fat tail (higher peak))
- platykurtic (few outliers, thin tail(lower peak than mesokurtic))
Whats the formula for kurtosis?
kurtosis = (((value of1 - mean)^4)((value of2-mean)^4)…)/ ((N-1)*(standard deviation^4))
Whats the formula for excess kurtosis?
kurtosis = [(((value of1 - mean)^4)((value of2-mean)^4)…)/ ((N-1)*(standard deviation^4))] -3
What is the relationship between kurtosis, excess kurtosis, distribution, and the tail?
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
What is the difference between covariance and correlation?
Covariance measures the direction of a relationship between two variables
Correlation measures the strength of that relationship
What is the formula for sample covariance?
sxy = ((x- mean x) * (y- mean y)) / n-1
sxy = sample covariance between x and y
What does the correlation coefficient tell us?
tells us how correlated they are
What is the sample correlation coefficient formula?
rxy = sxy/ sx*sy
sxy = sample covariance
sx = sample standard deviation of x
sy = sample standard deviation of y
What does a correlation coefficient of -1, 0, and 1 mean?
-1 = perfect inverse linear relationship
0 = no linear relationship
1 = perfect linear relationship
