Fat Tails and Extreme Events [19]

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Bullet points include: Suppose we have N instruments and estimate the factor structure from T observations per instrument where T much less than N (e.g. as would normally be the case for a whole market model). Then at most T-1 non-zero factors and random matrix theory (RMT) suggests most of the smaller ones often indistinguishable from ones that would arise randomly. Places fundamental limits on reliability of factor analysis (or any other risk modelling derived from historic return series). Means that fine structure of an optimised portfolio inherently depends on practitioner’s (or model creator’s) subjective views. Factor importance sorted by size.

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