(2)statistical Estimation for Capm with Long Memory Dependence

In the estimation of portfolios, it is natural to assume that the utility function depends on exogenous variable.From this point of view, in this paper, we develop the estimation under the utility function depending on exogenous variable. To estimate the optimal portfolio, we introduce a function consists of mean and variance of the return process, the covariance of the return processes and the exogenous variable, the 3-rd cumulant of the return process and the exogenous variable. Assuming that exogenous variable is a random process, we derive the asymptotic distribution of sample portfolio.Then, the influence of exogenous variable on the return process is illuminated when exogenous variable has a shot noise in the frequency domain. Assuming that exogenous variable is a sequence non-stochastic, we derive the asymptotic distribution of sample portfolio. Then, the influence of exogenous variable on the return process is illuminated when exogenous variable has a harmonic trend. We evaluate the influences of exogenous variable on return process numerically. (2)Statistical estimation for CAPM with long memory dependence Kato, K., Amano, T. and Taniguchi, M. (Waseda University) ABSTRACT In this paper we investigate Capital Asser Pricing Model (CAPM) with time dimension. By using time series analysis, we discuss the estimation of CAPM in the case when market portfolio and the error process are long memory process and correlated each other. We give sufficient condition that the return of assets in the CAPM is short-memory. In this setting, we propose a two-stage least squares estimator for the regression coefficient, and derive the asymptotic distribution. Some numerical studies will de given. They show an interesting feature of this model.In this paper we investigate Capital Asser Pricing Model (CAPM) with time dimension. By using time series analysis, we discuss the estimation of CAPM in the case when market portfolio and the error process are long memory process and correlated each other. We give sufficient condition that the return of assets in the CAPM is short-memory. In this setting, we propose a two-stage least squares estimator for the regression coefficient, and derive the asymptotic distribution. Some numerical studies will de given. They show an interesting feature of this model. (3) Bayesian Forecasting for Financial Risk Management, Pre and Post the Global Financial Crisis Chen, C. W. S.(1), Gerlach, R. H.(2), Lin, EMH(1), Lee, W.(1) ((1)Feng Chia University, Taiwan.Email: [email protected]) ((2)University of Sydney, Australia) ABSTRACT Value-at-Risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models are compared, including standard, threshold nonlinear and Markov switching GARCH specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student-t, skewed-t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia-Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models out-performed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre-crisis; while at the 1% level during and post-crisis, for a 1 day horizon, models with skewed-t errors ranked best, while IGARCH models were favoured at the 5% level; (iii) all models forecasted VaR less accurately and anti-conservatively post-crisis.Value-at-Risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models are compared, including standard, threshold nonlinear and Markov switching GARCH specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student-t, skewed-t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia-Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models out-performed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre-crisis; while at the 1% level during and post-crisis, for a 1 day horizon, models with skewed-t errors ranked best, while IGARCH models were favoured at the 5% level; (iii) all models forecasted VaR less accurately and anti-conservatively post-crisis.