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Creating portfolio risk and return models [21]

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Bullet points include: Use a blended importance criterion, e.g. Maximise f(a) = sigma (1+cK), across possible a with |a|=1, where: K is the kurtosis of a, sigma2 = aTVa c is some constant that represents a trade-off between concentrating on maximising variance and concentrating on maximising kurtosis (if c = 0 then equivalent to PCA, if c is large then will approximate ICA) Can be re-expressed to be akin to the Cornish-Fisher 4th moment asymptotic expansion for estimating quantiles of a Non-Normal distribution (with zero skew) E.g. 99.5%ile, x = N -1(0.995) = - 2.576 and c = 0.39

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