Exact estimation of CAPM betas is important in program trading. But the market model used traditionally has a little problems. One problem is that the CAPM betas are constant over time and another problem is that the data interval for estimation is predetermined by ad-hoc method.
To ease this problems I suggest models with time-varying parameters. In those models, the procedures of maximum likelihood estimation are introduced and finally a model with time-varying parameter and conditionally hetero-scedasticious disturbances is introduced.
As applications step, the procedures to construct an KOSPI200 tracking portfolio is settled down, and for each beta estimation model, optimal portfolios are made of 30~50 assets and their tracking abilities are compared in the view of statistical aspects.
