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Extreme Events – Charts sourced from Nematrian – Chapter 3

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Charts:

 

-          Figure 3.1: Standard bivariate normal probability density function with rho = 0

-          Figure 3.2: Standard bivariate normal probability density function with rho = -0.3

-          Figure 3.3: Standard bivariate normal probability density function with rho = +0.6

-          Figure 3.4: Cumulative distribution function for standard bivariate normal with rho = 0

-          Figure 3.5: Cumulative distribution function for standard bivariate normal with rho = -0.3

-          Figure 3.6: Gaussian copula with rho = 0, also known as the product or independence copula

-          Figure 3.7: Gaussian copula with rho = -0.3

-          Figure 3.8: Difference between Gaussian copula (rho = -0.3) and Product copula (expressed as difference between copula gradients/densities)

-          Figure 3.9: Scatter plot of weekly sector relative returns for MSCI ACWI Utilities vs Transport

-          Figure 3.10: Scatter plot of weekly sector relative returns for MSCI ACWI Utilities vs Transport (rank of relative returns)

-          Figure 3.11: Decile-decile plot between MSCI ACWI Utilities and Transport sectors

-          Figure 3.12: Fractile-fractile plot of sector relative return rankings showing number of observations in each fractile pairing, averaged across all sector pairings and all +/- combinations of such pairs

-          Figure 3.13: Excess kurtosis of each series sector relative return series. x-axis shows the number of the relevant data series

-          Figure 3.14: Fractile-fractile plot of principal component rankings of sector relative returns showing number of observations in each fractile pairing, averaged across all principal component pairings and all +/- combinations of such pairs

-          Figure 3.15: Magnitudes of the eigenvalues of each principal component derived from the relative return series used in Figure 3.13 (most important principal components to the left of the chart)

-          Figure 3.16: Excess kurtosis of each principal component derived from the relative return series used in Figure 3.13 (most important principal components to the left of the chart)

-          Figure 3.17: Skewness of each principal component derived from the relative return series used in Figure 3.13 (most important principal components to the left of the chart)

-          Figure 3.18: Impact of adjusting each relative return series by its own recent past volatility

-          Figure 3.19: Impact of adjusting every series simultaneously by recent past cross-sectional volatility

-          Figure 3.20: A one-dimensional ‘upwards’ QQ-plot

-          Figure 3.21: A two-dimensional ‘upwards’ QQ-plot characterising all (linear) combinations of two return series

-          Figure 3.22: Illustrative cluster analysis of the sector relative return series used in Figure 3.12. The distance along the x-axis corresponds to the average ‘distance’ between the individual elements of the cluster.

 


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