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Catégorie :Category: nCreator TI-Nspire
Auteur Author: Nass23232
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.48 Ko KB
Mis en ligne Uploaded: 20/12/2019 - 05:30:15
Mis à jour Updated: 20/12/2019 - 05:43:37
Uploadeur Uploader: Nass23232 (Profil)
Téléchargements Downloads: 51
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a2528020
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.48 Ko KB
Mis en ligne Uploaded: 20/12/2019 - 05:30:15
Mis à jour Updated: 20/12/2019 - 05:43:37
Uploadeur Uploader: Nass23232 (Profil)
Téléchargements Downloads: 51
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a2528020
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
Nominal scales categorize data but do not rank them. - Examples: fund style, country of origin, manager gender " Ordinal scales sort data into categories that are ordered with respect to the characteristic along which the scale is measured. - Examples: star rankings, class rank, credit rating " Interval scales provide both the relative position (rank) and assurance that the differences between scale values are equal. - Example: temperature " Ratio scales have all the characteristics of interval scales and a zero point at the origin. Relative frequency is the absolute frequency divided by the total number of observations. " Cumulative (relative) frequency is the relative frequency of all observations occurring before a given interval. Arithmetic Mean - idea: describe a typical outcome of an investment - sum of the observations divided by the number of observations - population mean: ýý = somme ^n i=1 xi / N - samplemean: ýý=somme n i=1 xi / n - sample mean is often interpreted as fulcrum, or center of gravity, Geometric Mean à - Used to calcualte average percentage rates: growth rates, rates of return - Requires that all numbers are non-negative - Represents the growth rate or compounded return on an investment when X is 1+ R Harmonic Mean à - weighted mean in which each observation s weight is inversely proportional to its magnitude - example: Cost averaging The mode is the most frequently occurring value in a distribution. - Distributions are unimodal when there is a single most frequently occurring value and multimodal if there is more than one frequently occurring value. - Examples: Bimodal and trimodal (see bottom of this slide) - Problem: continuous distributions may not have a mode Example: return distribution on preceding slide Action: group the data into intervals Quantiles are values that identify the location of data at or below which specified proportions lie: - " " " " " Median: divides a distribution in half Quartiles: divide distribution into quarters Quintiles: divide distribution into fifths Deciles: divide distribution into tenths Percentiles: into hundredths - so, P y = 0.25 or 0.20 or 0.10 or 0.01 the yth percentile is the value at/below which y% of observations lie: Dispersion - measures variability around a measure of central tendency - if mean return represents reward, then dispersion represents risk (2) Range - The distance between the maximum value in the data and the minimum value in the data. - For the country return data in slide 30: [ 2.97% ( 44.05%)] = 41.08% - Advantage: easy to calculate - Disadvantage: uses only two pieces of information from the data set Mean absolute deviation - Uses all available data! - arithmetic average of the absolute value of deviations from the mean: Semivariance - idea: only look at downside of the possible outcomes in other words, the losses (remember: risk is a symmetric term incorporating both a chance and a danger - Semivariance is the average squared deviationbelowthemean: - Both measures of dispersion focus only on observations below the mean - Target semivariance, by analogy, is the average squared deviation below some specified target rate, B , and represents the downside risk of being below the target, B. (7) Sharpe ratio - ratio of the mean excess return rate) per unit of standard deviation: (mean return minus the mean risk-free sp= ýý ýý ýý ýý / ýý ýý - Comparison: Coefficient of Variation and the Sharpe Ratio Consider a portfolio with a mean return of 25.26% and a standard deviation of returns of 9.95%. " The coefficient of variation is " If the risk-free rate is 3%, then the Sharpe Ratio is - Interpretation: units of risky return (excess return) per unit of risk. - slope of a line in expected return/standard deviation space (see graph below) 1.8 Symmetry and Skewness in Return Distribution - We now combine centrality, dispersion and symmetry - If observations are equally dispersed around the mean, the distribution is said to be symmetrical. - For a symmetrical distribution, the mean, median, and mode (if it exists) will all be at the same location - The degree of symmetry in the dispersion of values around the mean is known as skewness a symmetrical distribution has no skew Sample Skewness " distribution with perfect symmetry: skewness = zero. " Because cubing preserves the sign of the original difference between X i and its mean, if deviations from the mean are equally distributed on each side of the mean, they will cancel each other out, leading to skewness of zero. - If there are some very large values, they become even larger when cubed, and the skewness measure will then reflect this. Large negative values à Negative sample skewness Large positive value à Positive sample skewnes 1.9 Kurtosis - Kurtosis measures the relative peakedness of a distribution: Peakedness: how many returns
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Compatible OS 3.0 et ultérieurs.
<<
Nominal scales categorize data but do not rank them. - Examples: fund style, country of origin, manager gender " Ordinal scales sort data into categories that are ordered with respect to the characteristic along which the scale is measured. - Examples: star rankings, class rank, credit rating " Interval scales provide both the relative position (rank) and assurance that the differences between scale values are equal. - Example: temperature " Ratio scales have all the characteristics of interval scales and a zero point at the origin. Relative frequency is the absolute frequency divided by the total number of observations. " Cumulative (relative) frequency is the relative frequency of all observations occurring before a given interval. Arithmetic Mean - idea: describe a typical outcome of an investment - sum of the observations divided by the number of observations - population mean: ýý = somme ^n i=1 xi / N - samplemean: ýý=somme n i=1 xi / n - sample mean is often interpreted as fulcrum, or center of gravity, Geometric Mean à - Used to calcualte average percentage rates: growth rates, rates of return - Requires that all numbers are non-negative - Represents the growth rate or compounded return on an investment when X is 1+ R Harmonic Mean à - weighted mean in which each observation s weight is inversely proportional to its magnitude - example: Cost averaging The mode is the most frequently occurring value in a distribution. - Distributions are unimodal when there is a single most frequently occurring value and multimodal if there is more than one frequently occurring value. - Examples: Bimodal and trimodal (see bottom of this slide) - Problem: continuous distributions may not have a mode Example: return distribution on preceding slide Action: group the data into intervals Quantiles are values that identify the location of data at or below which specified proportions lie: - " " " " " Median: divides a distribution in half Quartiles: divide distribution into quarters Quintiles: divide distribution into fifths Deciles: divide distribution into tenths Percentiles: into hundredths - so, P y = 0.25 or 0.20 or 0.10 or 0.01 the yth percentile is the value at/below which y% of observations lie: Dispersion - measures variability around a measure of central tendency - if mean return represents reward, then dispersion represents risk (2) Range - The distance between the maximum value in the data and the minimum value in the data. - For the country return data in slide 30: [ 2.97% ( 44.05%)] = 41.08% - Advantage: easy to calculate - Disadvantage: uses only two pieces of information from the data set Mean absolute deviation - Uses all available data! - arithmetic average of the absolute value of deviations from the mean: Semivariance - idea: only look at downside of the possible outcomes in other words, the losses (remember: risk is a symmetric term incorporating both a chance and a danger - Semivariance is the average squared deviationbelowthemean: - Both measures of dispersion focus only on observations below the mean - Target semivariance, by analogy, is the average squared deviation below some specified target rate, B , and represents the downside risk of being below the target, B. (7) Sharpe ratio - ratio of the mean excess return rate) per unit of standard deviation: (mean return minus the mean risk-free sp= ýý ýý ýý ýý / ýý ýý - Comparison: Coefficient of Variation and the Sharpe Ratio Consider a portfolio with a mean return of 25.26% and a standard deviation of returns of 9.95%. " The coefficient of variation is " If the risk-free rate is 3%, then the Sharpe Ratio is - Interpretation: units of risky return (excess return) per unit of risk. - slope of a line in expected return/standard deviation space (see graph below) 1.8 Symmetry and Skewness in Return Distribution - We now combine centrality, dispersion and symmetry - If observations are equally dispersed around the mean, the distribution is said to be symmetrical. - For a symmetrical distribution, the mean, median, and mode (if it exists) will all be at the same location - The degree of symmetry in the dispersion of values around the mean is known as skewness a symmetrical distribution has no skew Sample Skewness " distribution with perfect symmetry: skewness = zero. " Because cubing preserves the sign of the original difference between X i and its mean, if deviations from the mean are equally distributed on each side of the mean, they will cancel each other out, leading to skewness of zero. - If there are some very large values, they become even larger when cubed, and the skewness measure will then reflect this. Large negative values à Negative sample skewness Large positive value à Positive sample skewnes 1.9 Kurtosis - Kurtosis measures the relative peakedness of a distribution: Peakedness: how many returns
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