The Limits to Minimum-Variance Hedging

Models of the time-varying conditional minimum-variance hedge ratio (MVHR) typically do not provide a significant improvement in terms of hedging performance over the unconditional MVHR model. In view of the widely documented success of conditional volatility models (on which models of the conditional MVHR are usually based), this is somewhat surprising. In this paper, using the recently developed realized beta framework of Andersen, Bollerslev, Diebold and Wu (2005), we explore the reasons for this finding. We firstly show that the reduction in hedged portfolio variance that conditional MVHR models offer falls far short of the ex post maximal reduction in variance obtained using an estimate of the unobserved ‘integrated’ MVHR. We investigate the statistical properties of the forecasts of conditional MVHR models and show that while they do contain significant information about the integrated MVHR, they are systematically biased and inefficient. However, correcting for this bias and inefficiency does little to improve their hedging performance, suggesting that their poor performance is more likely to be attributable to the unpredictability of the integrated MVHR.