Portfolio Optimization : A DCC-GARCH forecast with implied volatility

Abstract: This thesis performs portfolio optimization using three allocation methods, Certainty Equivalence Tangency (CET), Global Minimum Variance (GMV) and Minimum Conditional Value-at-Risk (MinCVaR). We estimate expected returns and covariance matrices based on 7 stock market indices with a DCC-GARCH model including an ARMA (1.1) process and an external regressor of an implied volatility index (VIX). We then simulate returns using a rolling window of 500 daily observations and construct portfolios based on the allocation methods. The results suggest that the model can sufficiently estimate expected returns and covariance matrices and we can outperform benchmarks in form of equally weighted and historical portfolios in terms of higher returns and lower risk. Over the whole out-of-sample period the CET portfolio yields the highest mean returns and GMV and MinCVaR can significantly lower the variance. The inclusion of VIX has marginal effects on the forecasting accuracy and it seems to impair the estimation of risk.