Value at risk analysis and downside risk measures: An empirical study of Taiwan stock market

This Dissertation concerns with the stock market VaR measures. Traditional risk measures have focused on the sensitivity of risk factor such as duration, convexity, and market beta or option price Greeks. As of 1994, when the financial dissert started, banking group has searched an easy risk disclose tool to express the system risk. Under this circumstance, value at risk (VaR) emerged and is becoming industry standard. Many banking and investment groupssuch as Banker Trust and RiskMetrics have promoted VaR measure and intend to make it the end-user measure tool. In this research, I focus on the VaR analysis such as VaR decomposing and VaR sensitivity associated with the downside risk measures. VaR decomposing for equity market can be the market volatility and investor preference. To estimate one day ahead market volatility, the EWMA and GARCH type conditional models such as the IGARCH, EGARCH, and LGARCH are applied in this research. To capture the leptokurtosis phenomena exhibiting commonly in the financial asset return distribution, t distribution, generalized error distribution (GED) and mixture normal distribution can be used. The EWMA (Minimizing by RMSE) and GARCH type models (Maximizing by MLE) could estimate decay factor, conditional volatility, and the parameters of distribution that together provide input factors for VaR computation. For unconditional volatility modeling, the mixture normal model and Markov switch models are used to demonstrate the volatility spread, persistent and clumped among return series. The mixture model also could be used to measure the unconditional VaR after the parameters have been searched. Concerning VaR sensitivity, Financial Engineering Associates (FEA) provides VaRdelat and VaRbeta and RiskMetrics offers incremental VaR and marginal VaR.; However, VaR could not estimate the full downside swing from the viewpoints of the moment measures. Therefore, we complement VaR estimate using the lower partial moment measure (LPM). LPM can be a better risk substitution for generally used variance since the risk should come from the downside swing but not the upside swing. In the downside market, the mean LPM also has been proved providing the better position selection than mean variance optimization. Finally, the simulation fulfills alternative VaR computation with GARCH type models and mixture models, and the volatility stressing and correlation stressing would find the VaR movement in different scenarios.