# Stats.pdf - STATISTICAL CONCEPTS MARKET RETURNS...

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STATISTICAL CONCEPTS & MARKET RETURNS
Footnote2Statistical tools can help in analyzing financial data“A company’s average EPS for the last 20 quarters”“A company’s average return for the past 10 years”In investments, measures of central tendencyare used to assess an investment’s return while measures of dispersion are used to assess the risk of investment.Two types of statistical methods Descriptive stats Inferential statsIntroduction
Footnote3Four propertiesWhere is the data centered? (central tendency)How far is the data dispersed? (dispersion)Whether the distribution of returns is symmetrically shaped or lopsided (skewness)Whether extreme outcomes are likely (kurtosis)
Footnote4Population:All members of a group A descriptive measure of a population is a Parameter All share JSE indexSampleA portion of the group A descriptive measure of a population is a Sample statisticTop 40 Fundamental concepts
Footnote5Holding period return We will apply descriptive statistics to investment returns. When analyzing rates of return, our starting point is the total return, or holding period return (HPR)HPR measures the total return for holding an investment over a certain period of time, and can be calculated using the following formula:
Footnote6Example - HPR𝐻𝑃𝑅 =𝐸𝑛?𝑖𝑛𝑔 ??𝑙?? −??𝑔𝑖𝑛𝑛𝑖𝑛𝑔 ??𝑙??+?𝑖?𝑖??𝑛?𝑠??𝑔𝑖𝑛𝑛𝑖𝑛𝑔 ??𝑙??A stock is currently worth R60. If you purchased the stock exactly one year ago for R50 and received R2 dividend over the course of the year, what is your holding period return?
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Footnote8Summarising dataFrequency DistributionsGraphic Presentation
Footnote9Frequency DistributionsA frequency distribution is a tabular display of data summarized into a relatively small number of groups or intervals. Frequency distributions help in the analysis of large amounts of statistical data, and they work with all types of measurement scales.Each interval has a lower limit and an upper limit. Intervals must be all-inclusive and non-overlapping. They must also be mutually exclusive so that each observation can only be placed in one interval
Footnote10Creating a Frequency table -Example using rates of returnUse holding period return (HPR)Follow the steps to construct a frequency distribution:Sort the data in ascending orderCalculate the range ( highest number -lowest number )Decide on the number of intervals (k)Determine the interval width (Range/ k)Determine the intervalsCount the number of observations in each intervalConstruct a table
Footnote11Example- Frequency tableLets say we calculate the HPR per month for 12 stocks and get the following:-4.57, -4.04, -1.64, 0.28, 1.34, 2.35, 2.38, 4.28, 4.42, 4.68, 7.16, 11.43Calculate the range ( highest number -lowest number )Range: 11.43 (-4.57) = 16Decide on the number of intervals (k)We choose 4 intervalsDetermine the interval width (Range/ k)Therefore 16/4 = 4 (this is the width of each interval
Footnote12Determine the intervalsCount the number of observations in each intervalConstruct a table
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