Using GARCH Models in Estimating the Volatility isk of Portfolio with Taiwan Equity Market
Date Issued
2009
Date
2009
Author(s)
Lu, Hsi-Man
Abstract
Investors can make appropriate decisions if they can grasp and control volatility of the stock return rate in advance. The objective of this research is to find an appropriate VaR (Value at Risk) model that can estimate the time-varying volatility of a portfolio. When developing the VaR model, the portfolio return covariance matrix is a key factor. This matrix contains two parts. The first part consists of a univariate GARCH model and an asymmetric GARCH model called TGARCH. And the second part consists of a simplified multivariate GARCH model which, in turn, can be a Constant Correlation GARCH model or an Orthogonal GARCH model. The former is then incorporated into the latter part to generate four different time-varying covariance matrices. The other factor affecting a VaR model are weights of the stocks invested. Entropy weighting method is used to obtain weights of stocks in the portfolio. Finally, covariance matrices and weights are used to compute VaR under different confidence levels. It is found that, considering all principal components, a VaR model can provide more accurate estimation if the Orthogonal GARCH model is employed. On the other hand, the assumption that stock correlation matrix is constant under Constant Correlation GARCH model may underestimate VaRs. The above proposed VaR model is used to analyze a few selected common stocks from Taiwan equity market. The forecasting results of VaR models are compared with the actual return of portfolio to examine the appropriateness of the proposed model. It is found that the VaR model under Orthogonal GARCH model gives us more accurate result than that under Constant Correlation GARCH model.
Subjects
Volatility
GARCH Model
VaR
Portfolio
Orthogonal
Back testing
Type
thesis
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