Realized Hedge Ratio: Predictability and Hedging Performance
by Dr. Chryssa Markopoulou, Research Fellow
The increased availability of high-frequency data has stimulated the interest of practitioners and academics, giving rise to a new area of research in financial modeling where multi-dimensional high-frequency data are utilized to estimate, model and forecast the second moments of asset returns. Based on the theory of quadratic variation, Andersen, Bollerslev, Diebold, & Labys (2001) and Andersen, Bollerslev, Diebold, & Ebens (2001), showed that, as the sampling frequency tends to infinity, the realized measures are consistent estimators of the true latent processes. Realized measures are essentially "model-free" thus exhibiting notably advantageous properties and information content over previously reported estimators that rely on parametric models that induce econometric or mathematical misspecification.
Andersen et al. (2006) extended their previous work on realized volatility and correlation, and defined realized beta as the ratio of realized covariance between asset and market returns to market variance, as computed from intraday return data. Their study proves that any common persistence trait of the covariance and variance processes is neutralized when forming the beta ratio. In a similar context, the Realized Minimum Variance Hedge Ratio (RMVHR, hereafter) is defined as the ratio of the realized covariance of futures and spot returns divided by the futures realized variance.
Motivated by previous findings within the beta framework, this study addresses the question whether direct modeling and forecasting the dynamics of the RMVHR per se results in substantial benefit to the hedger in terms of risk reduction and economic value. Obtained results are compared with conventional models that model the variance-covariance matrix, construct out-of-sample forecasts and ultimately, calculate the hedge ratio.
The study makes three contributions to the ongoing discussion about the value of employing high-frequency data to the estimation of the hedge ratio. First, a thorough evaluation of the time-series characteristics of the realized volatility, realized covariance and RMVHR is performed and the differential properties of the distributions are assessed. Second, a horse race among alternative model specifications is performed and the statistical significance of the predictability of the RMVHR series per se is evaluated. Third, the improvement in hedging performance against conventional modeling and forecasting techniques is examined. Finally, an extensive dataset of equity indices and foreign exchange rates is used and differentiated patterns across asset classes are examined.
Overall, empirical results from alternative time-series specifications support the existence of predictable patterns in the dynamic evolution of the RMVHR series per se. Under alternative econometric specifications, our methodology predicts successfully the directional change of the series approximately 70% of the times throughout the out-of-sample period, while results do not vary significantly across models. Importantly, the direct forecast of the RMVHR series, based on intraday data, improves hedging portfolio performance in terms of risk reduction, Sharpe ratio and mostly in terms of economic gains. Notably, the hedger's benefit is substantial when taking into account both the average return and the variance of the hedge portfolio. The results hold across the different asset classes, although the benefits are lower in the case of exchange rates.
Andersen, T. G., Bollerslev, T., Diebold, F. X., & Ebens, H. (2001). The distribution of realized stock return volatility. Journal of Financial Economics, 61, 43-76.
Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2001). The distribution of realized exchange rate volatility. Journal of the American statistical association, 96, 42-55.
Andersen, T. G., Bollerslev, T., Diebold, F. X., & Wu, G. (2006). Realized beta: Persistence and predictability. Advances in econometrics, 20, 1-39.