  We show how to reduce the problem of computing VaR and CVaR with Student T
return distributions to evaluation of analytical functions of the moments. This
allows an analysis of the risk properties of systems to be carefully attributed
between choices of risk function (e.g. VaR vs CVaR); choice of return
distribution (power law tail vs Gaussian) and choice of event frequency, for
risk assessment. We exploit this to provide a simple method for portfolio
optimization when the asset returns follow a standard multivariate T
distribution. This may be used as a semi-analytical verification tool for more
general optimizers, and for practical assessment of the impact of fat tails on
asset allocation for shorter time horizons.
