Investment Portfolio Selection Using Multivariate Exponential Weighted Moving Average (EWMA) Model and Dynamic Conditional Correlation (DCC) Model

The Mexican stock exchange (BMV) has experienced significant volatility in recent years, making portfolio optimization a challenging task for investors. Traditional methods, such as Mean-Variance (MV) models, often fail to account for the dynamic nature of asset correlations and volatility. This study proposes a conditional covariance matrix approach to address these limitations and provide more effective portfolio optimization strategies for BMV investors. This study employs EWMA, DCC, and MV models due to their established track record in capturing conditional covariance. EWMA's exponential weighting scheme allows for adaptability to changing market conditions, while DCC accounts for dynamic correlations between assets. MV provides a baseline for comparison.

DCC uses the univariate GARCH model for each series of returns. These models were selected based on their ability to address the specific challenges of the BMV, such as volatility and correlation. All three models were applied to the main 15 assets of the Mexican Stock Exchange (BMV). To get the optimal portfolio, the method known as quadratic programming was used, which allows, unlike the method of Lagrange multipliers, to obtain positive weights.

The findings suggest that investors can reduce portfolio risk by up to 47.78% using the EWMA model. and 25.45%, in the case of the Dynamic Conditional Correlation model, both compared with the unconditional covariance matrix model. Likewise, the evaluation of portfolios shows an increase in performance in the long term, for both cases constructed by using a conditional covariance matrix.