Optimisasi Portofolio Mean-VaR di bawah CAPM Transformasi Koyck dengan Volatilitas Tak Konstan dan Efek Long Memory

Authors

  • Sukono Sukono Fakultas Matematika dan Ilmu Pengetahuan Alam, Juruan Matematika, Universitas Padjajaran
  • Subanar Subanar Fakultas Matematika dan Ilmu Pengetahuan Alam, Juruan Matematika, Universitas Gajah Mada
  • Dedy Rosadi Fakultas Matematika dan Ilmu Pengetahuan Alam, Juruan Matematika, Universitas Gajah Mada

DOI:

https://doi.org/10.9744/jti.12.2.pp.%2089-94

Keywords:

ARFIMA, GARCH, CAPM, Koyck, VaR, Kuhn-Tucker.

Abstract

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.

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Published

2010-12-06