Gauging Risk with Higher Moments: Handrails in Measuring and Optimising Conditional Value at Risk

The aim of the paper is to study empirically the influence of higher moments of the return distribution on conditional value at risk (CVaR). To be more exact, we try to reveal the extent to which the risk given by CVaR can be estimated when relying on the mean, standard deviation, skewness and kurtosis. Furthermore, it is intended to study how this relationship can be utilised in portfolio optimisation. First, based on a database of 600 individual equities from 22 emerging world markets, factor models incorporating the first four moments of the return distribution have been constructed at different confidence levels for CVaR, and the contribution of the identified factors in explaining CVaR was determined. Following this the influence of higher moments was examined in portfolio context, i.e. asset allocation decisions were simulated by creating emerging market portfolios from the viewpoint of US investors. In our analysis we compare different approaches which take higher moments into account with the standard mean-variance framework. Throughout the work special attention is given to implied preferences to the different higher moments in optimising CVaR.