| dcterms.abstract | The quantitative approach to analyzing equity market risk generally involves three steps: first, build an underlying statistical model for the asset return time series; then quantify risk value for the given asset/portfolio return distribution, using carefully defined risk measure; finally, apply risk-reward analysis to optimize assets allocations, manage the portfolio risk and improve its performance. The contribution of this thesis is therefore threefold, corresponding to these steps in risk management. First, we propose the time series model of ARMA(1,1)-GARCH(1,1) with subordinated Gaussian innovations, in order to capture the stylized facts observed in daily equity returns data. Two multivariate distributions from the normal mixture family are mainly discussed and compared using empirical in-sample and out-of-sample tests. Normal Tempered Stable (NTS) distribution is constructed using Classic Tempered Stable (CTS) as subordinator; while Generalized Hyperbolic (GH) distribution has Generalized Inverse Gaussian (GIG) as its mixture. Both proposed models can capture higher moments of the innovation distribution, namely the skewness and leptokurticity. Moreover, we can benefit from their Gaussian structure when building multivariate model and applying linear transformation. Second, a novel ordinal approach to deriving risk measures is introduced, together with the "cardinal" definitions of Aumann-Serrano (AS) and Foster-Hart (FH) risk measures. We review their operational interpretations and the set of desired mathematical properties. A whole methodology is developed to generalize AS and FH risk measures definitions to L^1 distributions, and applying both of them to real financial return data. We compared the ordinal approach derived risk measures with the traditional value-at-risk (VaR) and average value-at-risk (AVaR), which are downside risk measures required by the Basel Accords. We noticed that the newly defined conditional FH risk measure behaves more conservatively, and more sensitively to extreme events, based on our empirical study of DJIA stocks in recent ten years testing period. As a final contribution of this thesis, we have performed the mean-AS risk portfolio optimization on DJIA component stocks. The allocation of this fully-invested portfolio is rebalanced on daily basis, using the most recent data from a five-year moving window. The ten-year backtesting period from Dec 2004 to Sep 2015 is divided into three subperiods: pre-recession, Great Recession, and post-recession. A two-step optimization scheme is applied to solve the convex portfolio optimization problem. By comparing the realized cumulative returns and drawdowns of each portfolios, we find that mean-AS outperforms mean-AVaR optimal portfolio in all three subperiods. This is true especially for the Great Recession period from Dec 2007 to Jun 2009, when the benchmark equally-weighted portfolio is killed by a nearly 70% drawdown, and mean-AVaR hardly survived after suffering a 20\% loss, while mean-AS risk portfolio ends up with a convincing 10% profit even in such a market turmoil. | |
