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CIMA > Stats > Flashcards

Stats Flashcards

1
Q

Variance

A

Measures how far a set of numbers are spread out

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2
Q

Variance defined

A

average squared differences between the mean and each item in the population or in the sample

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3
Q

High variance means

A

data points are very spread out

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4
Q

Standard deviation defined

A

measure of dispersion expressed as the square root of the variance

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5
Q

Standard deviation measures

A

the amount of variability around the average or mean

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6
Q

Advantage of standard deviation

A

expresses dispersion in the same units as the original values in the sample or population

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7
Q

A low standard deviation indicates

A

data points gather close to the means

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8
Q

Semi variance measures

A

data that is below the mean or target value of a data set

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9
Q

Semi variance defined

A

average of the squared deviations of all values less than the average or mean

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10
Q

Coefficient of variation defined

A

ration of the standard deviation to the mean

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11
Q

CV formula

A

standard deviation/mean

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12
Q

CV result

A

shows the extent of variability of relation to mean of the population

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13
Q

CV application

A

for comparison of data sets with different units or widely different means, one should use the CV instead of SDEV

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14
Q

Skewness defined

A

describes asymmetry of data points from a normal distribution

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15
Q

Negative skew

A

skews to the left

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16
Q

Positive skew

A

Skews to the right

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17
Q

Non-normal distributions (Skewness applied)

A

standard mean-variance analysis is limited which means SDEV is less meaningful

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18
Q

For a negative skew - SDEV applications

A

underestimating the risk

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19
Q

For a positive skew - SDEV applications

A

overestimating the risk

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20
Q

Kurtosis measures

A

How fat the tails are on a distribution relative to a normal distribution curve

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21
Q

Positive Kurtosis (Leptokurtic)

A

will show more extreme outcomes, creating a tendency for the observations around the mean to seem great and appearing to have a higher peak

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22
Q

Low Kurtosis (Platykurtic)

A

will show thinner tails (fewer extreme outliers), flatter top, less peakedness

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23
Q

Higher kurtosis suggest greater

A

Risk than reflected in the normal distribution relied upon in the traditional mean-variance framework

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24
Q

Standard deviation is a good measure of risk when returns are

A

symmetric

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25
Q

What if excess returns are not normally distributed

A

Standard deviation is no longer a complete measure of risk; Sharpe ratio is not a complete measure of performance; need to consider skew and kurtosis

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26
Q

N vs. N-1

A

Use N when you are using all of the data available (I.e. Population) then use N-1 when only using a sample (I.e. calculating standard deviation)

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27
Q

z = -1

A

one SDEV covering about 16% of the mean representing 68% of the outcomes

28
Q

z = -2

A

covers two SDEV covering about 95% of the outcomes

29
Q

z = -3

A

covers three SDEV covering about 99% of the outcomes

30
Q

z = -1.65

A

covers 5% (useful for VaR)

31
Q

z = -2.33

A

covers 1 % (useful for VaR)

32
Q

Monte Carlo Simulation

A

stat modeling used to approximate the probability of future outcomes through multiple trials using random variables

33
Q

Investment Consultants Fallacy

A

shows graphically how portfolio risk decreases over time due to clustering of returns around a long term average

34
Q

Consultants Graph

A

the appearance that risk goes over time due to diversification

35
Q

Samuelson and Merton Graph

A

the expected terminal (ending) range of values of an investment is much wider with more potential outcomes due to uncertainty over time

36
Q

Covariance Defined

A

indicates how two variables are related

37
Q

Covariance measures

A

the degree to which the returns of two assets move together

38
Q

Assets possessing a high covariance with each other

A

does not offer much diversification

39
Q

Covariance calculation

A

Correlation coefficient times standard deviations of both assets

40
Q

Correlation coefficients defined

A

indicates the degree of relationship between two variables

41
Q

Correlation coefficients calculation

A

covariance divided by sdev * sdev

42
Q

Multiple regression R squared also known as

A

coefficient of determination

43
Q

R squared (coefficient of determination) gives us

A

the proportion of variation in one variable than can be explained by another variable

44
Q

R squared (coefficient of determination) metric indicates

A

the closeness or accuracy of the fit

45
Q

R squared applications

A

The higher the number, the more meaningful the relationship; it gives us an indication of the level of diversification; gauges the reliability of alpha as an indicator of the managers return and beta as an indicator of risk

46
Q

R squared below .6

A

benchmark is not as helpful as a comparative tool

47
Q

R squared calculation

A

Beta Squared times SDEV of market squared divided by SDEV of the portfolio squared

48
Q

Random Walk defined

A

event in which a set of events or samples follows a pattern of random unpredictable steps

49
Q

Random Walk Application

A

stock prices cannot be accurately predicted

50
Q

Benefits of multi-period forecasting

A

improved accuracy, consistency and smoothing of volatility

51
Q

Variance defined

A

as the expected value of the difference between the variable and its mean squared

52
Q

Variance used in

A

Monte Carlo analysis and portfolio optimization process

53
Q

Coefficient of variation formula

A

standard deviation divided by expected return

54
Q

A normal distribution has a kurtosis of

A

3

55
Q

Anything greater than kurtosis of 3 is considered

A

Fat tailed

56
Q

One tailed value for 95% percent of the curve tell us

A

95% of the values are less than 1.64 SDEV above the mean

57
Q

As the normal distribuiton is symetrical, that 5% of the value are great than

A

1.6 standard deviations below the mean

58
Q

The two tailed value tells us that 95% of the mass is

A

within + or - 1.96 standard deviations from the mean

59
Q

The two tailed value tell us that 2.5% of the outcomes are

A

Less than -1.96 standard deviations from the mean, 2.5% are greater than +1.96 Standard deviations from the mean

60
Q

Null hypothesis

A

default position that there is no relationship between the variables

61
Q

Alternative hypothesis

A

the opposite of the null hypothesis that is being tested for relevance

62
Q

Regression-based techniques use attribution based on

A

CAPM and estimating alpha of the manager

63
Q

A key advantage to Monte Carolo analysis is

A

being able to factor in a number of data points into one model

64
Q

An investor reviewing a sample population data set would want to observe

A

small standard errors

65
Q
A

CIMA (22 decks)

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