In this paper we formulated mean-VaR portfolio optimization through CAPM Koyck
transformation. We assumed that lagged of risk premium which have highly influence on stock
returns is infinite, while model parameters decrease geometrically. We also assumed that rate of
return in risk premium market index is not constant, in other word has a non-constant volatility
rate, and also has a long memory effect. The later was analyzed using ARFIMA. Non constant
volatility rate was modeled via GARCH model. The portfolio optimization was constructed using
Langrangian multiplier and the Kuhn-Tucker theorem was employed to obtain the solution by
the least square method. Finally, we provide a numerical example of the optimization model
based on several stocks traded in Indonesian capital market.