Conditional Covariance Estimation Using CCC-GARCH for Markowitz Portfolio Optimization

Abstract

The time-varying volatility and heteroskedasticity of stock returns require appropriate volatility modeling for portfolio construction. This study aims to model stock return volatility using the Constant Conditional Correlation Generalized Autoregressive Conditional Heteroskedasticity (CCC-GARCH) and apply the estimated conditional covariance matrix to optimal portfolio construction based on the Markowitz model. The study employs daily returns of seven sector-representative stocks listed in the LQ45 Index from February 2020 to August 2025. The analysis consists of ARMA-GARCH modeling to estimate the conditional volatility of individual stock returns, CCC-GARCH estimation to obtain the conditional covariance matrix, and portfolio optimization using the Markowitz model. Portfolio performance was evaluated using the Sharpe Ratio. The results indicate that all stock returns exhibit heteroskedasticity, with the ARMA-GARCH(1,1) model providing the best volatility specification for each stock. The CCC-GARCH-based conditional covariance matrix produced an optimal portfolio with an expected return of 0.00041210, a portfolio variance of 0.00011439, and a Sharpe Ratio of 0.02103415. These findings show that the CCC-GARCH model provides a more representative estimate of portfolio risk and supports optimal portfolio construction under dynamic market conditions.