The focus of this article is using dynamic correlation models for the calculation of minimum variance hedge ratios between pairs of assets. Finding an optimal hedge requires not only knowledge of the variability of both assets, but also of the co-movement between the two assets. For this purpose, use is made of industry standard methods, like the naive hedging or the CAPM approach, more advanced GARCH techniques including estimating BEKK or DCC models and alternatively through the use of unobserved components models. This last set comprises models with stochastically varying variances and/or correlations, denoted by the TVR, SCSV and DCSV models, and an approximation to these with a single-source-of-error setup. Modelling the correlation explicitly is shown to produce the best hedges when applied to the simulated data. For financial time series on the daily S&P 500 cash versus futures returns, and also on weekly S&P 500 versus FTSE 100 returns, the correlations are compared to a realised correlation measure, extracted from high frequency data. Apart from the comparison of correlations, the reduction in portfolio variance produced by different hedging strategies is examined. The data suggests that the most important factor in reducing portfolio variance is the use of a flexible model for time varying volatility, rather than capturing time variation in correlations. GARCH-based models with time varying correlation are found to perform not as good on the present set of measures as the stochastic volatility models, with or without dynamic correlation.