Dynamic Spectral Conditional Correlations

Abstract We present a new approach for modelling dynamic conditional correlations. It spans the whole space of allowable correlation matrices, and yet it is computable efficiently. We compare the new model, which we call dynamic spectral conditional correlations (DSCC), to the popular dynamic conditional correlations (DCC) in three ways. First, we demonstrate analytically the difference in span (or coverage) of the space of positive-definite correlation matrices. Second, we introduce a general numerical criterion, based on volumes of elliptopes, to benchmark how close any volatility model gets to filling the allowable space of positive-definite correlation matrices. We use it to illustrate how substantial this gap can be here: DSCC achieves the full potential which can be up to double the coverage of DCC for three-dimensional matrices. Third, we present the methodology for DSCC’s forecasting then apply it. We construct dynamically minimum-variance portfolios of up to 1,000 stocks, showing that we attain systematically higher returns than the best of DCC-based methods, for a comparable risk, and with more stable portfolio allocations. The gains are substantial, almost double DCC’s portfolio value over the sample period.