Lecture Two Flashcards
What do financial and accounting studies have instead of price of assets
Returns
What are returns to average investors?
Return of an asset is a complete scale dree summary of an investment opportunity
Which are easier to handle Returns or price series?
Returns
Why are returns more attractive then price series
Because they have more statical properties
What is returns position
Stationary
What does returns stationary imply?
Statistical values (e.g. mean and variance) REMAIN CONSTANT OVER TIME
What does returns being stationary assist with
Making returns more suitable for analysis
What do returns allow for
Easier comparison between different assets regardless of price levels
Why are returns easy to compare?
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%
What are returns bound to
The downside (cant lose more then 100%)
What are returns = to?
Percentage change
What does negative variation actually mean?
-give example
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
What does positive variation actually mean?
-give example
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
When does the stationary condition get violated
there is a lot of variations
Where are returns always moving around?
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
What is the equation of return (net)
new price - old price / old price
What is the gross return equation
New price / old price - 1
What is the relationship between the gross and net equation
they are equal to eachother
Why are the net/gross return equations equal to each other
The price you will get paid in the future is equal to the price u paid + the return
What can the return help you to do?
Work out the dispersion
What is dispersion
A measure of risk
What is the corrolation between dispersion and risk
The more dispersed something is is the more riskier it is
What side of the graph is the left side
Negative side - THE LOSSES
What does central tendency do?
gives us information about the location of the returns in a distributional sense.
What can the central tendency help us work out
-gives information about whether as an investor ur going to make a profit or a loss
What are the subsections of central tendency
Arithmetic mean, Median and the Mode
What are the subheadings of Variation
Range, Interquartile Range, Variance, Standard deviation, Coefficient of variation
What are the two measures in of distribution
Population and Sample
What is meant by population
the whole group of ppl
e.g every single individual in uk rn
Why isnt population a good measure
its time consuming to measure and difficult
What is meant by sample
smaller population = a % of that population THAT IS REPRESENTATIVE OF THAT POPULATION
What must u do when using sample as a measure of distribution
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
How to calculate the mean
all values added then divided by the number of values all together in dataset
what does the sign ∑ mean
which is used to represent the sum of a number of similar terms
What is the mean also known as?
Average
what is an outlier
something completely different relative to the group that I have
How does the outliars affect the mean
The mean becomes bias and not accurate
What must be used in place of the mean
Median
What does the median display
instead works out THE LOCATION that corresponds to the 50% distribution. Not the value
What must u do before working out the median
Put numbers into ascending order
How do u work out the median
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
What must u do to find the median of even number of values
If its even then find the Two middle numbers then divide them both to find the average of them both
What does working out the median instead of the mean enable
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
What is the mode
the value that occurs the most often
is the mode effected by extreme values?
no
What data is the mode usually used for
numerical or categorical
does there have to be a mode in each dataset?
no there can be non or loads
What happens to graph when more then 1 mode
more peaks in the data = not what we want for easy readable data = inconvenience
How to find average/mean using excel
- Type =AVERAGE(
- Select all the values u want to work out
- Close bracket & press enter
How to find median using excel
Median:
1. Type =MEDIAN(
2. Select all the values u want to work out
3. Close bracket & press enter
How to find mode using excel
Mode:
1. Type =MODE(
2. Select all the values u want to work out
3. Close bracket & press enter
What can be used to describe how data is distributed
the shape of the distribution ( the line)
What two things affect the way the distribution is presented?
The mean and median
What are the measures of the distribution shape
symmetrical or skewed.
When is the distribution left skewed
When the Median > Mean
When is the data distribution right skewed
Median < Mean
When is the data distribution symmetric ?
Mean = Median
What do Percentiles and Quartiles indicate
The position of a value relative to the entire set of data
When are Percentiles and Quartiles usually used
Used to describe LARGE datasets
What do quartiles do?
Split the data into 4 segments with an equal number of VALUES per segment -
What can be different when it comes to quartiles
The width may differ
What is usually the first Q1
25%
How to compute the quartile
P/100(n+1)
Explain what the quartile equation is
- order the data in ascending order
- 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
What’s the order of quartile
Minimum < First Quartile < Median < Third Quartile < Maximum
What are the measures of variation
Range, Interquartile Range, Variance, Standard Deviation , Coefficient of Variation
What do measures of variation give
They give information on the spread or variability of data values
What happens if there’s more variation in terms of investment
This means its an RISKIER INVESTMENT -more chance investment will fall to the left
What is the range?
Difference between the highest value and the lowest value
What are the disadvantages for the range
U can have have HUGE outliners - meaning an outward bias will be there
What is the interquartile range
its the difference between the third quartile range (75%) and the first quartile (25%)
Q3-Q1 =IQR
What is better range or interquartile range?
This is better then the range because it gets rid of any bias of outliers, it makes a better proxy for distribution
What graph uses quartile
Box Plot - the graph shows each min, q1, MEDIAN, q3, MAX
How to find the min on excel
=MIN(select all values)
How to find the max on excel
=MAX(select all values
How to find the Quartiles on excel
=QUARTILE:EXC(select all values)
-it comes up with a pop up to select which one u want to pick (q1 or q3 etc)
What is the variance
creates the measure of dispersions around the mean value
Are variances sensitive to outliers?
Yes
How to calculate the variance (in words)
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.
Population variance symbol
σ^2
Sample variance symbol
s^2
Variance equation
(xi - ¯x)^2 / N or n
∑ mean?
Sum of
What can be taken away from the standard deviation answer
A low standard deviation means the values are close to the mean,
while a high standard deviation means the values are spread out
What does standard deviation do?
Tell us how spread out the data is from the mean
What is the most used measure of variation
standard deviation
What is standard deviation used for?
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.
What is the formula of standard deviation
Square root of the variance
What do u use to work out the variance
U use the return to work out the variance
Why dont we like the variance
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
Why is variance always positive?
Because u square the equation. U get rid of any minus
e.g. -1^2 = 1
1^2 = 1
What do u want to have when it comes to the value of the variance
A small variance - bc we dont know if we are making massive return or a massive loss
Do u have the same units with the variance?
No u have different units bc it cant be expressed as a percentage without it being a crazy number
What does standard variation do that variance cant
Represent the value in percentage
What does MAD stand for
Mean absolute deviation
What is the MAD
uses absolute values to eliminate the negative signs
What does standard deviation do in terms of number
Returns the number into a smaller presentable value
What is the mean absolute deviation and alternative to?
Alternative to the standard deviation
What does the MAD DO
Instead of squaring the variance like the SD does
- it does it without having to square
Work out the MAD
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.
What is the absolute value
the non-negative value of x without regard to its sign
e.g. -5 is 5
-10 is 10
Is the mean absolute deviation exposed to outliers
No
How to calculate the sample variance on excel
=Var.s(click on all values)
How to calculate the population variance on excel
=Var.p(click on all values)
How to calculate the sample standard deviation on excel
=STDEV.S(click on all values)
OR: =sqrt(select s variance)
How to calculate the popiulation standard deviation on excel
=STDEV.P(click on all values)
OR: =sqrt(select p variance)
What does CV stand for?
Coefficient of variance
What is the coefficient of variance ?
is a measure of the dispersion of data points around the mean in a series.
How to work out the Coefficient of Variation
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
What is the purpose of the CV
To compare the degree of variation from one data series to another. Even if means are very different
What does a lower CV indicate
The data points are closer to the mean = less variability
What does a higher variation indicate?
The data points are further away from the mean = more variability
What is the skewness
a measure of asymmetry of probability distribution, can be positive/ zero or negative
What does skewness indicate
-it indicates if the data is concentrated on one side
What does the skewness depend on
depends on what side the TAIL is leading to
What is the highest peak in the diagram
-the mode is the highest point in the diagram
What does positive skewness indicate
asymmetry with more (or more extreme) outliers to the right tail
What does the positive skewness mean
mean > median > mode
What does negative skewness indicate
indicates asymmetry with more (or more extreme) outliers in the right tail
What does the positive skewness mean
mean < median < mode
What does 0 skewness indicate
the distribution is symmetric - or normal
what does zero skewness mean
mean = median = mode
Why is skewness important
Tells us where the data is situated
How to work out skewness
Skew = 3 * (Mean – Median) / Standard Deviation
What does the power of three do for the skewness
power of 3 allows u to magnetify the value – and the negative value – overall most of values inside of the distribution –
What type of data uses the general rule of thumb for the skewness
Categorical data
Why is it true for categorical data
Because it usually only has one mode
For what data type may there be violations for the skewness rule of thumb
dISCRETE
What are the two violations for the rule of thumb for the skewness
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).
What is the kurtosis
a measure of the combined weight of tails of distribution relative to the rest of the distribution
What does kurtosis define
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.
What does the kurtosis compare to
normal distribution (3)
What happens when kurtosis is big
When a distribution has fatter tails than the normal distribution is fat-tailed (bigger then 3)
kurtosis is ontop of normal on graph
What is fat tailed also known as?
leptokurtic
What happens when kurtosis is small
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
What can be kurtosis be used to measure
probability of risk (more negative = more fatter tails)
Another word for thin tails
platikurtic
What happens when kurtosis is similar to normal
When a distribution that is similar to the normal distribution as
concerns relative weight in the tail
another word for kurtosis closer to normal
mesokurtic
How to calculate the kurtosis
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
What is excess kurtosis
characterises kurtosis relative to normal distribution
How to work out excess kurtosis
Excess kurtosis = kurtosis - 3
What does excel compute
ONLY EXCESS kurtosis
What is normal in terms of excess kurtosis
3-3 = 0. therefore kurtosis is 0.
What does the numbers mean in terms of excess kurtosis
<0 = thinner tails (smaller tails) (negative is platikuratic)
0 = normal kurtosis
+0 = bigger -fatter tails (positive is leptokurtic)
What are the two measures of relationships between variables
Covariance
What is covariance
a measure of the direction of a linear relationship between two variables
(raw estimate of joint estimates of two variables)
What does the covariance give us
Gives us a value if the two assets move in the same direction or if they move in different directions
What does negative covariance do
two variables move different /opposite directions
what does positive covariance do?
two variables move in the same direction
What does a 0 covariance do
then we have no information
What isnt good about covariance
doesn’t give u the strength of how they move:
We don’t know if one increases so does the other straight away.
What do we use instead of covariance
Correlation
What is the correlation
A measure of both direction and the strength of a linear relationship between two variables
-standardised form of the covariance
sample correlation coefficent equation
r = S x,y / SxSy
Do correlations have units?
No they are unit free
How to work out the correlation
Take covariance and divide the standard deviation of asset x and asset y
What does the correlation range from
-1 to 1
What happens when correlation is closer to 1
they move exactly in the same way
What happens when correlation is closer to -1
when one increases the other one decreases - exactly opposite
What happens when correlation is closer to 0
we have no information
What type of table is used to present the correlation or covariance
a matrix / cross table
What does “correlation does not imply causation” refer to
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
How to computer sample covariance on excel
COVARIANCE.S(array1,array2) function computes the
sample covariance of two variables.
How to computer correlation on excel
CORREL(array1,array2)
function computes correlation
coefficient between two datasets.
How to computer population covariance on excel
COVARIANCE.P(array1,array2) f
function computes the
population covariance of two variables
How to computer kurtosis on excel
KURT(number1,number2,…)
function computes the excess
kurtosis of a distribution
How to computer skew on excel
SKEW(number1,number2,…)
function computes the
skewness of a distribution
How to computer geometric mean on excel
GEOMEAN(number1,number2,…)
function returns the
geometric mean of an array or range of positive data
