MEAN-VaR. PORTOFOLIO OPTIMIZATION UNDER CAPM WITH LAGGED, NON CONSTANT VOLATILTY AND THE LONG MEMORY EFFECT - Sukono, Sukono (JOURNAL OF QUANTITATIVE METHODS, 2009)
In this paper, we discus the method of portfolio optimiz.ation based on the mean and the Value-at-Risk (VaR) under the Capital Asset Pricing Model (CAPM) framework with lagged, non-constant volatility and the long memory effect. In CAPM, the returns of individual stocks (or portfolios) are assumed influenced by the market returns and risk-free return. II ere, we estimate the stock return betas by extending the CAPM model with lagged market factors, where the market returns are assumed has non-constant volatility, which will be estimated using GARCH models. The l(mg memory ctTcct will be modeled using ARFIMA model. The risk is measured by VaR that is calculated using normal distribution with a confidence level c.Mean and VaR will be used for the formulation of portfolio optimi7.alion problems. The portfolio optimization is performed using the Lagrangean Multiplier nnd the solution is obtained by the Kuhn-Tucker theorems. We illustrate these methods using some stocks from the Indonesian capital market