Evaluating Portfolio Risk Management: A New Evidence from DCC Models and Wavelet Approach

We analyzed the volatility dynamics of three developed markets (the UK, USA, and Japan), during the period 2003–2011, by comparing the performance of several multivariate volatility models, namely, Constant Conditional Correlation (CCC), Dynamic Conditional Correlation (DCC), and consistent DCC (cDCC) models. To evaluate the performance of models, we used four statistical loss functions on the daily Value-at-Risk (VaR) estimates of a diversified portfolio in three stock indices: FTSE 100, S&P 500, and Nikkei 225. We based on one-day ahead conditional variance forecasts. To assess the performance of the abovementioned models and to measure risks over different timescales, we proposed a wavelet-based approach, which decomposes a given time series on different time horizons. Wavelet multiresolution analysis and multivariate conditional volatility models are combined for volatility forecasting to measure the co-movement between stock market returns and to estimate daily VaR in the time-frequency space. Empirical results show that the asymmetric cDCC model of (Aielli, G. P. Consistent estimation of large scale dynamic conditional correlations, working paper n.47, University of Messina, Department of Economics, Statistics, Mathematics and Sociology, 2008) is the most preferable according to statistical loss functions under raw data. The results also suggest that wavelet-based models increase predictive performance of financial forecasting in low scales according to number of violations and failure probabilities for VaR models.