statistics tools for riskdescriptive statistics are ... inferential statistics is the process of...
TRANSCRIPT
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Statistics tools for Risk
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Statistics...
A set of mathematical procedures for
describing, synthesizing, analyzing, and
interpreting quantitative data
…the selection of an appropriate
statistical technique is determined by
the research design, hypothesis, and
the data collected
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Descriptive statistics are
numerical estimates that organize
and sum up or present the data.
Inferential statistics is the process
of inferring from a sample to the
population.
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Preparing data for analysis...
Data must be accurately scored and
systematically organized to facilitate
data analysis:
tabulating: organizing the data in a
systematic manner
coding: assigning numerals (e.g., ID)
to data
scoring: assigning a total to each
participant’s instrument
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descriptive statistics...
…permit the researcher to describe many
pieces of data with a few indices
statistics...
…indices calculated by the researcher for a
sample drawn from a population
parameters...
…indices calculated by the researcher for an
entire population
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Types of descriptive statistics…
1. graphs
2. measures of central tendency
3. measures of variability
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graphs...
…representations of data enabling the
researcher to see what the distribution
of scores look like
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1. Graphs…
frequency polygon
pie chart
boxplot
stem-and-leaf chart
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measures of central tendency...
…indices enabling the researcher to
determine the typical or average score
of a group of scores
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2. Measures of central tendency…
mode
median
mean
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mode...
…the score attained by more participants than
any other score
median...
…the point in a distribution above and below
which are 50% of the scores
mean...
…the arithmetic average of the scores
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Mean (arithmetic mean)
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Example
2003 2004 2005 2006 2007 2008 2009 2010 2012
12 10 16 11 16 10 11 12 16
Data of Stock Return in Percentage
Find: Mode, Median, Mean, Geometric
Mean, Standard Deviation
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Geometric Mean
The average of a set of products,
the calculation of which is commonly
used to determine the performance
results of an investment or portfolio.
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XXX ngeomean n
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measures of variability...
…indices enabling the researcher to
indicate how spread out a group of
scores are
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3. Measures of variability…
range
quartile deviation
variance
standard deviation
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range...
…the difference between the highest and
lowest score in a distribution
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quartile deviation...
…one half of the difference between the
upper quartile (the 75%’ile) and the
lower quartile (the 25%’ile) in a
distribution
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variance...
…a summary statistic indicating the
degree of variability among participants
for a given variable
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standard deviation...
…the square root of variance providing an
index of variability in the distribution of
scores
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Statistics in Finance
Geometric mean
Expected Return
The average of a probability distribution of
possible returns
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Risk (standard deviation)
Coefficient of Variation (CV)
n
iiPRERi
1
2
))((
)(RECV
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Example
Suppose there are data about stock return on different investment conditions
Investment Condition Probability Return
Very bullish
Bullish
Average
Bearish
Very bearish
0.1
0.2
0.4
0.2
0.1
27%
18%
14%
8%
4%
Find: Expected Return, Risk, and CV