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 attempt 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 equity returns 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. This can be regarded as a normal decisionmaking process of a hedge fund focusing on investments into emerging markets. In our analysis we compared and contrasted two approaches with which one can overcome the shortcomings of the variance as a risk measure. First of all, we solved in the presence of conflicting higher moment preferences a multi-objective portfolio optimisation problem for different sets of preferences. In addition, portfolio optimisation was performed in the mean-CVaR framework characterised by using CVaR as a measure of risk. As a part of the analysis, the pair-wise comparison of the different higher moment metrics of the meanvariance and the mean-CVaR efficient portfolios were also made. Throughout the work special attention was given to implied preferences to the different higher moments in optimising CVaR. We also examined the extent to which model risk, namely the risk of wrongly assuming normally-distributed returns can deteriorate our optimal portfolio choice.