day 1 quantitative methods for investment management by binam ghimire
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Day 1 Quantitative Methods for Investment Management by Binam Ghimire. Objective. Statistical Concepts and market returns and Probability Concepts Identify measures of central tendency and measures of Dispersion - PowerPoint PPT PresentationTRANSCRIPT
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Day 1Quantitative Methods for Investment
Managementby Binam Ghimire
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Statistical Concepts and market returns and Probability Concepts
Identify measures of central tendency and measures of Dispersion
Understand that measures of central tendency give an indication of the expected return of an investment and measures of dispersion measure riskiness of an investment
Use of Excel on the topic
Objective
Basic ConceptStatistics
Descriptive statisticsInferential statisticsPopulation
ParameterSample
Statistics
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Basic ConceptVariable Measurement Scale
Variable ScaleNominalOrdinalIntervalRatio
Guides what type of test we need to perform
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Less Informative
More Informative
Descriptive Statistics:Histogram and Frequency Polygons
Histogram: Grouped data. The area of each rectangle is proportion to the frequency
Frequency Polygon: a line graph drawn by joining all the midpoints of the top of the bars of a histogram
Activity: Excel – Histogram and Frequency Polygon
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Measures of location - Averages
Meaning & CalculationMean: Arithmetic, Weighted and GeometricModeMedian
Formula Activity: Football Game
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Weighted Mean as Portfolio Return
Weighted Mean is useful to find return of a portfolioReturn of Portfolio is basically (W1xR1) + (W2xR2) + (W3xR3) … (WnxRn)
where W is weight and R is return
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Weighted Mean as a Portfolio Return
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Example:Actual Portfolio
Return Weight Cash 5% × 0.10 =
0.5% Bonds 7% ×0.35 = 2.45%
Stocks 12% × 0.55 = 6.6% Σ =
9.55%Same method works for expected portfolio returns!
Geometric Mean
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Geometric mean is used to calculate compound growth rates
If the returns are constant over time, geometric mean equals arithmetic mean
The greater the variability of returns over time, the more the arithmetic mean will exceed the geometric mean
Actually, the compound rate of return is the geometric mean of the price relatives, minus 1
1)]R)...x(1R)x(1R[(1R 1/nn21Geom
Geometric Mean: Example
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An investment account had returns of 15.0%, –9.0%, and 13.0% over each of three years
Calculate the time-weighted annual rate of return
= 5.75 %1)]R)...x(1R)x(1R[(1R 1/n
n21Geom
Measures of location Meaning and Calculation
MaximumMinimumQuantile: Quantile is a method for dividing a
range of numeric values into categoriesQuartile, Percentiles, Deciles
75% of the data points are less than the 3rd quartile
60% of the data points are less than the 6th decile
50% of the data points are less than the 50th percentile
FormulaActivity: Football Game 11
Measures of Dispersion
Meaning and CalculationRangeInter-quartile rangeSemi-interquartile rangeMean Absolute Deviation VarianceStandard Deviation
Formula Activity: Football Game
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Measures of Association
MeaningCo-varianceFormula:
Calculation
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_ _
Covariance = sXY = S(X - X)(Y - Y)n
Measures of Association:Covariance
Co-variance has a sign
Covariance = 10
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X values
Y va
lues
X Y12 2014 2416 2818 32
Measures of Association:Covariance
Co-variance has a sign
Covariance = -10
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X Y12 3214 2816 2418 20
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X values
Y va
lues
Measures of Association:Covariance
Co-variance has a sign
Covariance = 6.94
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X values
Y va
lues
X Y12 2015 2518 2814 2216 2619 3015 23
Measures of Association:Covariance
Co-variance has a sign
Covariance = -7.49
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X Y12 3017 2218 1714 2616 2619 2115 23
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X values
Y va
lues
Measures of Association:Covariance in Investment Management
For example, if two stock prices tend to rise and fall at the same time, these stocks would not deliver the best diversified earnings.
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Measures of Distributions
Distribution ShapeSkewnessKurtosis
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Measures of Distributions:Skewness
Concept: Skewness characterizes the degree of
asymmetry of a distribution around its meanPositive skewness indicates a distribution with
an asymmetric tail extending toward more positive values
Negative skewness indicates a distribution with an asymmetric tail extending toward more negative values
No Skewness: symmetrical
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Measures of DistributionPositive Skewness
Skewness = 0.45
Tail to the higher values. Mean > Median > Mode Exercise in Excel
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Frequency Distribution
X values
Freq
uenc
ies
Measures of Distribution :Negative Skewness
Skewness = - 0.45
Tail to the lower. Mean < Median < Mode Exercise in Excel
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0123
4567
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Frequency Distribution
X values
Freq
uenc
ies
Measures of Distribution :No Skewness
Skewness = 0
Tail to the lower. Mean = Median = Mode (Symmetrical/ Normal)
Exercise in Excel 23
0123456789
Frequency Distribution
X values
Freq
uenc
ies
Measures of DistributionKurtosis
ConceptKurtosis characterizes the relative peakedness
or flatness of a distribution compared with the normal distribution
Positive kurtosis indicates a relatively peaked distribution
Negative kurtosis indicates a relatively flat distribution
No or zero Kurtosis = normal distribution
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Measures of Distribution Positive Kurtosis
Kurtosis = 1.68
Positive Kurtosis: Peaked relative to the Normal Exercise in Excel
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02468
1012141618
Frequency Distribution
X values
Freq
uenc
ies
Measures of Distribution Negative Kurtosis
Kurtosis = - 0.34
Negative Kurtosis: Flat relative to the Normal Zero Kurtosis: Peak similar to Normal Distribution Exercise in Excel 26
0123456789
Frequency Distribution
X values
Freq
uenc
ies
Kurtosis:Other names
A distribution with a high peak is called leptokurtic (Kurtosis > 0), a flat-topped curve is called platykurtic (Kurtosis < 0), and the normal distribution is called mesokurtic (Kurtosis = 0)
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Semivariance
Semivariance is calculated by only including those observations that fall below the mean on the calculation.
Sometimes described as “downside risk” with respect to investments.
Useful for skewed distributions, as it provides additional information that the variance does not.
Target semivariance is similar but based on observations below a certain value, e.g values below a return of 5%.
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Coefficient of Variance (CV)
Coefficient of Variance (CV)
= standard deviation mean
In investments for example; CV measures the risk (variability) per unit of expected return (mean).
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CV
Example: Suppose you wish to calculate the CV for two investments, the monthly return on British T-Bills and the monthly return for the S&P 500, where: mean monthly return on T-Bills is 0.25% with SD of 0.36%, and the mean monthly return for the S&P 500 is 1.09%, with a SD of 7.30%.
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CV
CV (T-Bills) = 0.36/0.25 = 1.44 CV (S&P 500) = 7.30/1.09 = 6.70
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CV
Interpretation: CV is the variation per unit of return, indicating that these results indicate that there is less dispersion (risk) per unit of monthly returns for T-Bills than there is for the S&P 500, i.e. 1.44 vs 6.70.
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We now should know the followings Concept, Formula and Calculation
Mean Median Quartiles Percentile Range Interquartile and semi-interquartile Range Mean Deviation Variance, Semi Variance Standard Deviation Covariance, Coefficient of Variance
Use of Excel for the above and Skewness and Kurtosis
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Can we solve the following?
An investor holds a portfolio consisting of one share of each of the following stocks:
For the 1-year holding period, the portfolio return is closest to: a) 6.88% b) 9.13% c) 13.13% and, d) 19.38%
Now practice Examples Day 1 (Some questions require knowledge from other chapters)
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Stock Price at the beginning of the
year
Price at the end of the year
Cash dividend during the year
X £20 £10 £0 Y £40 £50 £2 Z £100 £105 £4