Extreme events: blending PCA and ICA [38]

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Bullet points include: Calculate through time observed return divided by estimated tracking error. Each month, estimate out-of-sample covariance matrix and hence tracking error using prior monthly relative returns. Start 36 months into dataset. Apply to 100 x 23 random portfolios (100 with 1 sector position, 100 with 2 sector positions etc.). Calculate percentiles and moments for observed spread of this statistic. Cross-sectional adjustment not quite as effective as we might have hoped. Refine with “contemporaneous” estimates of volatility and average correlation? Kurtosis 90%ile 99%ile 99.9%ile. Unadjusted data. Longitudinal adjustment. Cross-sectional adjustment. c.f. expected if Gaussian

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