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Quantitive Methods > Lecture Two > Flashcards

Lecture Two Flashcards

1
Q

What do financial and accounting studies have instead of price of assets

A

Returns

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2
Q

What are returns to average investors?

A

Return of an asset is a complete scale dree summary of an investment opportunity

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3
Q

Which are easier to handle Returns or price series?

A

Returns

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4
Q

Why are returns more attractive then price series

A

Because they have more statical properties

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5
Q

What is returns position

A

Stationary

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6
Q

What does returns stationary imply?

A

Statistical values (e.g. mean and variance) REMAIN CONSTANT OVER TIME

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7
Q

What does returns being stationary assist with

A

Making returns more suitable for analysis

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8
Q

What do returns allow for

A

Easier comparison between different assets regardless of price levels

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9
Q

Why are returns easy to compare?

A

Because they get rid of the scale. No matter how different and incomparable the numbers itself are they use percentage and therefore anything is comparable to 100%

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10
Q

What are returns bound to

A

The downside (cant lose more then 100%)

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11
Q

What are returns = to?

A

Percentage change

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12
Q

What does negative variation actually mean?
-give example

A

You are making a loss
-e.g. if u invest £100 today and by the end of the month that same value of investment fell to £70
-You loss £30 if u were to sell it at this value

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13
Q

What does positive variation actually mean?
-give example

A

This is a positive variation when u are actually making a more then inital
- e.g. invest £100 today, but at the end of the month the price for that same investment is £130= u made a return of £30

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14
Q

When does the stationary condition get violated

A

there is a lot of variations

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15
Q

Where are returns always moving around?

A

Returns are always moving around 0 (-1 to 1)

-if u compute variances and averages in different time periods they wont be far away from each other
= harder to violate the stationary condition

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16
Q

What is the equation of return (net)

A

new price - old price / old price

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17
Q

What is the gross return equation

A

New price / old price - 1

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18
Q

What is the relationship between the gross and net equation

A

they are equal to eachother

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19
Q

Why are the net/gross return equations equal to each other

A

The price you will get paid in the future is equal to the price u paid + the return

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20
Q

What can the return help you to do?

A

Work out the dispersion

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21
Q

What is dispersion

A

A measure of risk

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22
Q

What is the corrolation between dispersion and risk

A

The more dispersed something is is the more riskier it is

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23
Q

What side of the graph is the left side

A

Negative side - THE LOSSES

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24
Q

What does central tendency do?

A

gives us information about the location of the returns in a distributional sense.

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25
Q

What can the central tendency help us work out

A

-gives information about whether as an investor ur going to make a profit or a loss

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26
Q

What are the subsections of central tendency

A

Arithmetic mean, Median and the Mode

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27
Q

What are the subheadings of Variation

A

Range, Interquartile Range, Variance, Standard deviation, Coefficient of variation

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28
Q

What are the two measures in of distribution

A

Population and Sample

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29
Q

What is meant by population

A

the whole group of ppl
e.g every single individual in uk rn

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30
Q

Why isnt population a good measure

A

its time consuming to measure and difficult

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31
Q

What is meant by sample

A

smaller population = a % of that population THAT IS REPRESENTATIVE OF THAT POPULATION

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32
Q

What must u do when using sample as a measure of distribution

A

must be equal sample. Not only one group of people
e.g. selecting only adults from 50+ its not collecting from younger – not good.

Need to be random so there’s no bias in selection - need to be from all different ages/different characteristics

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33
Q

How to calculate the mean

A

all values added then divided by the number of values all together in dataset

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34
Q

what does the sign ∑ mean

A

which is used to represent the sum of a number of similar terms

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35
Q

What is the mean also known as?

A

Average

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36
Q

what is an outlier

A

something completely different relative to the group that I have

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37
Q

How does the outliars affect the mean

A

The mean becomes bias and not accurate

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38
Q

What must be used in place of the mean

A

Median

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39
Q

What does the median display

A

instead works out THE LOCATION that corresponds to the 50% distribution. Not the value

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40
Q

What must u do before working out the median

A

Put numbers into ascending order

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41
Q

How do u work out the median

A

Put in ascending order
2. Find the middle value (middle number position) if its odd

If its even then find the Two middle numbers then divide them both to find the average of them both

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42
Q

What must u do to find the median of even number of values

A

If its even then find the Two middle numbers then divide them both to find the average of them both

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43
Q

What does working out the median instead of the mean enable

A

There to be extreme values because the medians arent affected by outliars, what the value is doesnt count - only the position. can be alot more effective then mean

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44
Q

What is the mode

A

the value that occurs the most often

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45
Q

is the mode effected by extreme values?

A

no

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46
Q

What data is the mode usually used for

A

numerical or categorical

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47
Q

does there have to be a mode in each dataset?

A

no there can be non or loads

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48
Q

What happens to graph when more then 1 mode

A

more peaks in the data = not what we want for easy readable data = inconvenience

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49
Q

How to find average/mean using excel

A
  1. Type =AVERAGE(
  2. Select all the values u want to work out
  3. Close bracket & press enter
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50
Q

How to find median using excel

A

Median:
1. Type =MEDIAN(
2. Select all the values u want to work out
3. Close bracket & press enter

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51
Q

How to find mode using excel

A

Mode:
1. Type =MODE(
2. Select all the values u want to work out
3. Close bracket & press enter

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52
Q

What can be used to describe how data is distributed

A

the shape of the distribution ( the line)

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53
Q

What two things affect the way the distribution is presented?

A

The mean and median

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54
Q

What are the measures of the distribution shape

A

symmetrical or skewed.

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55
Q

When is the distribution left skewed

A

When the Median > Mean

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56
Q

When is the data distribution right skewed

A

Median < Mean

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57
Q

When is the data distribution symmetric ?

A

Mean = Median

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58
Q

What do Percentiles and Quartiles indicate

A

The position of a value relative to the entire set of data

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59
Q

When are Percentiles and Quartiles usually used

A

Used to describe LARGE datasets

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60
Q

What do quartiles do?

A

Split the data into 4 segments with an equal number of VALUES per segment -

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61
Q

What can be different when it comes to quartiles

A

The width may differ

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62
Q

What is usually the first Q1

A

25%

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63
Q

How to compute the quartile

A

P/100(n+1)

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64
Q

Explain what the quartile equation is

A
  1. order the data in ascending order
  2. Then compute percentage of specific group
    e.g want 25%25/100 = 0.25
    N = number of observations u have so:
    15 values = 15+1 = 16

16x0.25 = 4 (rounded)

= this gave u the LOCATION of ur data that is sorted in ascending order

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65
Q

What’s the order of quartile

A

Minimum < First Quartile < Median < Third Quartile < Maximum

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66
Q

What are the measures of variation

A

Range, Interquartile Range, Variance, Standard Deviation , Coefficient of Variation

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67
Q

What do measures of variation give

A

They give information on the spread or variability of data values

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68
Q

What happens if there’s more variation in terms of investment

A

This means its an RISKIER INVESTMENT -more chance investment will fall to the left

69
Q

What is the range?

A

Difference between the highest value and the lowest value

70
Q

What are the disadvantages for the range

A

U can have have HUGE outliners - meaning an outward bias will be there

71
Q

What is the interquartile range

A

its the difference between the third quartile range (75%) and the first quartile (25%)
Q3-Q1 =IQR

72
Q

What is better range or interquartile range?

A

This is better then the range because it gets rid of any bias of outliers, it makes a better proxy for distribution

73
Q

What graph uses quartile

A

Box Plot - the graph shows each min, q1, MEDIAN, q3, MAX

74
Q

How to find the min on excel

A

=MIN(select all values)

75
Q

How to find the max on excel

A

=MAX(select all values

76
Q

How to find the Quartiles on excel

A

=QUARTILE:EXC(select all values)

-it comes up with a pop up to select which one u want to pick (q1 or q3 etc)

77
Q

What is the variance

A

creates the measure of dispersions around the mean value

78
Q

Are variances sensitive to outliers?

A

Yes

79
Q

How to calculate the variance (in words)

A

It is calculated by taking the differences between each number in the data set - the mean,

squaring the differences to make them positive,

and then dividing the sum of the squares by the number of values in the data set.

80
Q

Population variance symbol

A

σ^2

81
Q

Sample variance symbol

A

s^2

82
Q

Variance equation

A

(xi - ¯x)^2 / N or n

83
Q

∑ mean?

A

Sum of

83
Q

What can be taken away from the standard deviation answer

A

A low standard deviation means the values are close to the mean,
while a high standard deviation means the values are spread out

83
Q

What does standard deviation do?

A

Tell us how spread out the data is from the mean

83
Q

What is the most used measure of variation

A

standard deviation

84
Q

What is standard deviation used for?

A

identify outliers and determine if a value is statistically significant.

It’s also used in business to manage risk by quantifying the uncertainty of different outcomes.

85
Q

What is the formula of standard deviation

A

Square root of the variance

86
Q

What do u use to work out the variance

A

U use the return to work out the variance

87
Q

Why dont we like the variance

A

Because we dont know if a large variance which means larger return -
BECAUSE VARIANCE IS ALWAYS POSITIVE BC WE SQUARE THE VALUE = MAKING IT ALWAYS POSITIVE

could be negative or positive because we dont have the units we dont know if its super positive or super positive

88
Q

Why is variance always positive?

A

Because u square the equation. U get rid of any minus

e.g. -1^2 = 1
1^2 = 1

89
Q

What do u want to have when it comes to the value of the variance

A

A small variance - bc we dont know if we are making massive return or a massive loss

90
Q

Do u have the same units with the variance?

A

No u have different units bc it cant be expressed as a percentage without it being a crazy number

91
Q

What does standard variation do that variance cant

A

Represent the value in percentage

92
Q

What does MAD stand for

A

Mean absolute deviation

93
Q

What is the MAD

A

uses absolute values to eliminate the negative signs

94
Q

What does standard deviation do in terms of number

A

Returns the number into a smaller presentable value

95
Q

What is the mean absolute deviation and alternative to?

A

Alternative to the standard deviation

96
Q

What does the MAD DO

A

Instead of squaring the variance like the SD does
- it does it without having to square

97
Q

Work out the MAD

A

Take each number in the data set, subtract the mean, and take the absolute value.

Then take the sum of the absolute values.

dividing the sum above by the total number of values in the data set.

Finally, round to the nearest tenth.

98
Q

What is the absolute value

A

the non-negative value of x without regard to its sign

e.g. -5 is 5
-10 is 10

99
Q

Is the mean absolute deviation exposed to outliers

A

No

100
Q

How to calculate the sample variance on excel

A

=Var.s(click on all values)

101
Q

How to calculate the population variance on excel

A

=Var.p(click on all values)

102
Q

How to calculate the sample standard deviation on excel

A

=STDEV.S(click on all values)
OR: =sqrt(select s variance)

103
Q

How to calculate the popiulation standard deviation on excel

A

=STDEV.P(click on all values)
OR: =sqrt(select p variance)

104
Q

What does CV stand for?

A

Coefficient of variance

105
Q

What is the coefficient of variance ?

A

is a measure of the dispersion of data points around the mean in a series.

106
Q

How to work out the Coefficient of Variation

A

Find the mean of the data

Find the standard deviation of the data

Divide the standard deviation by the mean

Multiply the result by 100

107
Q

What is the purpose of the CV

A

To compare the degree of variation from one data series to another. Even if means are very different

108
Q

What does a lower CV indicate

A

The data points are closer to the mean = less variability

109
Q

What does a higher variation indicate?

A

The data points are further away from the mean = more variability

110
Q

What is the skewness

A

a measure of asymmetry of probability distribution, can be positive/ zero or negative

111
Q

What does skewness indicate

A

-it indicates if the data is concentrated on one side

112
Q

What does the skewness depend on

A

depends on what side the TAIL is leading to

113
Q

What is the highest peak in the diagram

A

-the mode is the highest point in the diagram

114
Q

What does positive skewness indicate

A

asymmetry with more (or more extreme) outliers to the right tail

115
Q

What does the positive skewness mean

A

mean > median > mode

116
Q

What does negative skewness indicate

A

indicates asymmetry with more (or more extreme) outliers in the right tail

117
Q

What does the positive skewness mean

A

mean < median < mode

118
Q

What does 0 skewness indicate

A

the distribution is symmetric - or normal

119
Q

what does zero skewness mean

A

mean = median = mode

120
Q

Why is skewness important

A

Tells us where the data is situated

121
Q

How to work out skewness

A

Skew = 3 * (Mean – Median) / Standard Deviation

122
Q

What does the power of three do for the skewness

A

power of 3 allows u to magnetify the value – and the negative value – overall most of values inside of the distribution –

123
Q

What type of data uses the general rule of thumb for the skewness

A

Categorical data

124
Q

Why is it true for categorical data

A

Because it usually only has one mode

125
Q

For what data type may there be violations for the skewness rule of thumb

A

dISCRETE

126
Q

What are the two violations for the rule of thumb for the skewness

A

1- For discrete data this may occur when the areas to the left
and right of the median are not equal.

2 For continuous data may occur if the data has more than one
mode, and when one tail is longer but the other is heavy (or
fat).

127
Q

What is the kurtosis

A

a measure of the combined weight of tails of distribution relative to the rest of the distribution

128
Q

What does kurtosis define

A

how heavily the tails of distribution differ from tails of normal distribution

. In other words, kurtosis identifies whether the tails of a given distribution contain extreme values.

129
Q

What does the kurtosis compare to

A

normal distribution (3)

130
Q

What happens when kurtosis is big

A

When a distribution has fatter tails than the normal distribution is fat-tailed (bigger then 3)
kurtosis is ontop of normal on graph

131
Q

What is fat tailed also known as?

A

leptokurtic

132
Q

What happens when kurtosis is small

A

When a distribution has thinner tails than the normal distribution is
referred to as being thin-tailed (below 3)

kurtosis is under of normal on graph

133
Q

What can be kurtosis be used to measure

A

probability of risk (more negative = more fatter tails)

134
Q

Another word for thin tails

A

platikurtic

135
Q

What happens when kurtosis is similar to normal

A

When a distribution that is similar to the normal distribution as
concerns relative weight in the tail

136
Q

another word for kurtosis closer to normal

A

mesokurtic

137
Q

How to calculate the kurtosis

A

Calculate the mean and standard deviation of the dataset

Standardize each data point by subtracting the mean and dividing by the standard deviation

Raise each standardized value to the power of 4

Sum all the standardized values raised to the power of 4

Multiply the result by (n(n+1)/(n-1)(n-2)(n-3)) and subtract (3(n-1)^{3}/(n-2)(n-3)) to obtain the sample kurtosis

138
Q

What is excess kurtosis

A

characterises kurtosis relative to normal distribution

139
Q

How to work out excess kurtosis

A

Excess kurtosis = kurtosis - 3

140
Q

What does excel compute

A

ONLY EXCESS kurtosis

141
Q

What is normal in terms of excess kurtosis

A

3-3 = 0. therefore kurtosis is 0.

142
Q

What does the numbers mean in terms of excess kurtosis

A

<0 = thinner tails (smaller tails) (negative is platikuratic)

0 = normal kurtosis

+0 = bigger -fatter tails (positive is leptokurtic)

143
Q

What are the two measures of relationships between variables

A

Covariance

144
Q

What is covariance

A

a measure of the direction of a linear relationship between two variables

(raw estimate of joint estimates of two variables)

145
Q

What does the covariance give us

A

Gives us a value if the two assets move in the same direction or if they move in different directions

146
Q

What does negative covariance do

A

two variables move different /opposite directions

147
Q

what does positive covariance do?

A

two variables move in the same direction

148
Q

What does a 0 covariance do

A

then we have no information

149
Q

What isnt good about covariance

A

doesn’t give u the strength of how they move:
We don’t know if one increases so does the other straight away.

150
Q

What do we use instead of covariance

A

Correlation

151
Q

What is the correlation

A

A measure of both direction and the strength of a linear relationship between two variables

-standardised form of the covariance

152
Q

sample correlation coefficent equation

A

r = S x,y / SxSy

153
Q

Do correlations have units?

A

No they are unit free

154
Q

How to work out the correlation

A

Take covariance and divide the standard deviation of asset x and asset y

155
Q

What does the correlation range from

A

-1 to 1

156
Q

What happens when correlation is closer to 1

A

they move exactly in the same way

157
Q

What happens when correlation is closer to -1

A

when one increases the other one decreases - exactly opposite

158
Q

What happens when correlation is closer to 0

A

we have no information

159
Q

What type of table is used to present the correlation or covariance

A

a matrix / cross table

160
Q

What does “correlation does not imply causation” refer to

A

refers to the
inability to legitimately deduce a cause-and-effect relationship
between two events or variables solely on the basis of an observed
association or correlation between them

161
Q

How to computer sample covariance on excel

A

COVARIANCE.S(array1,array2) function computes the
sample covariance of two variables.

162
Q

How to computer correlation on excel

A

CORREL(array1,array2)
function computes correlation
coefficient between two datasets.

163
Q

How to computer population covariance on excel

A

COVARIANCE.P(array1,array2) f

function computes the
population covariance of two variables

164
Q

How to computer kurtosis on excel

A

KURT(number1,number2,…)

function computes the excess
kurtosis of a distribution

165
Q

How to computer skew on excel

A

SKEW(number1,number2,…)

function computes the
skewness of a distribution

166
Q

How to computer geometric mean on excel

A

GEOMEAN(number1,number2,…)

function returns the
geometric mean of an array or range of positive data

Quantitive Methods (6 decks)

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