Asset Pricing, Volatility Modeling And Risk Measuring With The Introduction Of Higher Moments

The characteristics of asymmetry, peakedness, and heavy tails in the distribution of asset returns and the preference of investors to these higher moments are commonly existed in the returns of Chinese and foreign stock markets. However, due to the wide application of‘mean-variance’analysis, the preferable features of normal distribution, the existence of the Central Limit Theorem, they are usually ignored when some authors of the literature discussing such issues as asset pricing, volatility modeling, and risk measuring, which are the most important three topics in finance. Along with the development of the related theoretical and empirical studies, more and more researchers have realized the importance of higher moments in asset pricing, volatility modeling and risk measuring.After reviewing the relevant literature, this dissertation investigates the existence of the characteristics of asymmetry, peakedness and thick tails in Chinese stock market by non-parametric method. Then, the generating mechanisms of the higher moments are analyzed by employing Autoregressive Conditional Density model.The main work of this dissertation is included in the following four parts.Firstly, this dissertation makes a reinvestigation on the two outstanding anomalies, the momentum effect and contrarian effect, of the stock returns based on capital asset pricing model with the consideration of higher moments. The results show that the returns from all of the loser and zero portfolios, and part of the winner portfolios can be better explained when the risk factors of higher order moments are added into the classic models, such as the "mean-variance" capital asset pricing model (CAPM) and the three-factor-model (TFM). The risk factors of higher moments can well explain the significant abnormal returns produced by the losers in momentum effect. As for the existence of the two effects, the results indicate that the contrarian effect is significant but the momentum is not. This dissertation makes further comparison of the risk load of the losers and winners. The results show that the former exhibits higher risk of factors and higher-order moments.The second and third parts investigate the performances of volatility prediction of the GARCH-family models with the introduction of higher moments of returns by parametric and non-parametric approach respectively. By the first approach, the dissertation simulates and investigates the asymptotic features of the Maximum Likelihood procedure (MLE) estimators conditional on the symmetric but heavy tailed distribution when the conditional distribution of the returns are asymmetric and heavy tailed. The simulated results are consistent with the predictions from the relevant theoretic literature. That is, with the assumption of a symmetric and heavy tailed distribution, the MLE is asymptotically biased, while the asymptotic consistency can be assured to some extent conditional on normal distribution. This implies that the performance of volatility prediction conditional on normal distribution may be better than that conditional on other symmetric and heavy tailed distributions when the data is both asymmetric and heavy tailed. Based on the daily returns of Shanghai and Shenzhen stock market index, the dissertation further empirically compared the performance of volatility prediction made by ten GARCH-family models conditional on six types of distributions. To produce statistical results and deal with the‘data snooping’problem, the dissertation employs the method of Ordinary Least Squares (OLS) and Superior Prediction Ability (SPA) test. Based on four loss functions, the results show that the GARCH-family models may produce better performance of volatility prediction conditional on normal distribution than that conditional on other symmetric but heavy tailed distributions. The results from OLS test consistently show that the performance of model prediction conditional on skewed and heavy tailed distributions is better than that conditional on symmetric and heavy tailed distributions. The results from SPA test document that the GARCH-family models conditional on skewed and heavy tailed distributions, especially the distribution of generalized skewed t (Skewed-GT), can produce superior prediction ability in most situations in spite of the fact that some GARCH-family models have better prediction ability conditional on normal distribution.The third part adopts an efficient non-parametric approach, Estimating Function (EF) method to introduce higher moments into GARCH-family models. With the daily returns of the Shanghai stock market index, this part compares the performance of volatility prediction of ten types of GARCH-family models based on the estimating method of EF and QMLE (Quasi-Maximum Likelihood Estimation). OLS and SPA test are also employed in this part to give statistical results and deal with the‘data snooping’problem. The results from the OLS test shows that some GARCH-family models can significantly produce better performance when EF method than QMLE is employed to make estimation. The SPA test shows further that among all of the predicted series from the ten models and two estimating method, the EGARCH models and APARCH models estimated by EF method exhibit superior prediction ability.The final part is on measuring risk with the consideration of higher moments. The part compares the performance of VaR (Value at Risk) prediction from several asymmetric and heavy tailed distributions with deffering higher moments (FZHM). The FZHM reflects the adaptation ability of a specified distribution to various features of higher moments exhibited in a variety of samples. Therefore, the FZHM is an important factor influencing the performance of VaR prediction. By sampling daily returns from four main market indices in the world, the part empirically compares the VaR predictions conditional on three asymmetric and heavy tailed distributions, i.e., Skewed-T, Skewed-GT and SUN distribution, the FZHMs of which are wider and wider. For comparasion with the existing literature, three of symmetric distributions, such as Normal distribution, Student-T, and Generalized Error Distribution are also involved. The results show that the samples’higher moments, and thus VaRs are likely to be over-estimated conditional on the SUN distribution, the one with the widest FZHM among the asymmetric and heavy tailed distributions, while the symmetric and heavy tailed distributions are likely to under-estimate VaR. In addition, VaR predictions conditional on Skewed-GT and Skewed-T distribution have similarly good performances though the FZHM of the former is larger. Therefore, wider FZHM of a distribution does not imply better performance of VaR prediction. If the FZHM of a distribution is too large, the higher moments of sample data, and thus VaR are likely to be over-estimated. Thus, the empirical evidences in this dissertation provide helpful insights on the future improvement of VaR prediction performance.