In this paper, I study the correlation between stock and bond returns. We can define flight-to-quality from stocks to bonds as the decrease in the correlation between the two assets in falling stock markets periods (bear state), since the two assets returns move in the opposite direction. On the contrary, a movement in the same direction between the two asset classes as the economy is at a bear state, can be classified as contagion. Firstly, I show that a two-state model, with regimes characterised as bear and bull states, is required in order to capture and explain the dynamics of equity returns at the bivariate level. Secondly, the analysis I have conducted shows statistically significant evidence of flight-to-quality phenomena from stock to bond returns, in the US and UK for the period 1986-2010. Finally, I have found evidence of time-variation in the structure of the predictability patterns linking financial markets and monetary policy, as the latter is expressed through short-term interest rates. These results have not only important implications for portfolio diversification and asset allocation, but they are also adding to the ongoing debate on how the time variation in the stock-bond correlation is driven by changing macroeconomic conditions.