why are returns used in financial studies
1 - reuturns of assets are complete and scale-free
2- return series are easier because they are stationary, easier to compare and naturally bounded (cant loose more than 100%)
describe the ruturns formula
current price minus price at previous time divided by previous price (change in price divided by pervious/ original
price)
what is central tendecy
what
finidng the “center of the data”
what do you use to find central tendency
arithmatic mean, mode and median
how do calcultae the arithmatic mean
when is the mean not useful in a data set
add up numbers and divide by how many numbers (values) there are
where there are outliers
how do you calculate the median
what is it useful for?
its the middle value when data is arranged in order. if number are even it the middle value of the central two.
useful when outliers are present as its more robust
how do you calcuate the mode
what is it useful for
The most frequently occurring value in the dataset.
useful for catagorical data to identify mosy frequent value
what is variation (dispersal)?
it tells us how spead out the data is
what do you use to find variation?
range, interquartile range, varience, standard deviation and coeffieicent variation
how do you calculate range
max value minus min value
how do you calculate interquartile range
third quartile value minus first quartile value (Q1 - Q3)
how do you calculate population and sample varience
big formula with the weird E in it
- find the mean of the data set,
- take each value and minus the mean from each value,
- square each individual value,
- find the mean of those numbers to find population variation.
- for sample you need to minus one from the bottom number in the second mean calculation
how do you calculate standard deviation
take the square root of the varience equation result
how do you calculate coefficient variation (population + sample)
divide the standard deviation by the mean x 100
same goes for sample
why is coeffiecient vairation used
its a relative measure of variability. Can compare to other data sets reguradless of their size
what are percentiles and quartiles
percentiles and quartiles indiciate the position of a value relative to the whole data set
e.g - being in the 90th percentile of IQ
what are quartiles
quartiles split percentiled data into four equal segments of data, however the width of the quartiles may vary
whats the fomula for finding quartiles
where n is number of values
for quartile 1 (Q1) its
- 0.25 x n+1 also shown as 0.25(n+1)
for Q2+3 its 0.5 and 0.75
why is interquartile range used?
what does it represent?
its eliminates outliers by ignoring the high and low values. represents the middle 50% of data
what is the five number summary
minimun, first quartile, median, third quartile, maximum
what is a box and whisker plot
- describes/ visualises distribution/ quaetiles
what do the different parts of a box and whiskser plot mean
- inner box shows range of Q1 to Q3
- two whiskers show the distance from the minimum to Q1 and the maximum from Q3
- median is the lin in the middle
what is mean absolute deviation
same calculation as varience except you dont square the deveiations you take the absolute value and dont allow for negative values
why does mean absolute deviation (MAD) only use positive numbers?
MAD finds the deviation(distance of the values frrom the mean) and treats this as a distance which cant be negative
