Considering Tail Events in Hedge Fund Portfolio Optimization

Abstract: The Fourth Swedish National Pension Fund (AP4), as well as many other large investors, has noted deficiencies the Mean-Variance framework for portfolio management of asset with non-normal characteristics. The main problem apparent in the Mean-Variance framework, when investing in alternative assets such as hedge funds, is the lacking systematic control of the balance between the measurements of risk due normal variation and tail-risk. Hedge funds constitute an asset class distinguished by non-normal characteristics such as negative skewness and heavy excess kurtosis, which suggests normality should not be assumed when optimizing a portfolio of hedge funds. Certain hedge fund strategies aim to be uncorrelated to other hedge funds and the major asset markets and are thus expected to have the capacity to hedge against extreme market events. Hedge fund performance during historically volatile market periods, including heavy losses and liquidations, has however proved this untrue. Outcomes in the tail of hedge fund distributions rather appear to occur in conjunction with increased correlation toward external indicators such as the equity stock market. With the aim to consider tail events in a portfolio of hedge funds and index futures, an optimization model intending to capture the asymmetric covariance between hedge fund assets and the equity market is developed and evaluated. The theory of copulas is applied to estimate the multivariate distribution by separating assumptions regarding univariate characteristics and dependence between assets. The estimated multivariate distribution is thereafter utilized in a scenario-based optimization model applying the Conditional Value at Risk (CVaR) measure as a risk measure, to capture events in the left tail of the portfolio distribution. The proposed GARCH-C-Vine-Mean-CVaR model is presented and evaluated against two reference models, a GARCH-C-Vine-Mean-Variance model, and a model assuming a multivariate normal distribution, EWMA-Mean-Variance. The ability to capture realized outcomes is analyzed for all three models, where the proposed GARCH-C-Vine-Mean-CVaR as well as the GARCH-C-Vine-Mean-Variance model show to capture realized outcomes to a further extent than the model assuming a multivariate normal distribution. Further, applying the risk measure CVaR has in this study shown to capture the realized outcomes to the same extent as applying variance as the risk measure. In conclusion, the proposed model manages to capture tail-events in the data analyzed in this study, to a further extent than if assuming multivariate normality. The lack of regulations and bias that denote hedge fund reporting, does however prevent a conclusion on whether the proposed model captures actual realized tail-events of hedge fund returns.