This paper investigates dynamic correlations of stock-bond returns for different stock indices and bond maturities. Evidence in the US shows that stock-bond relations are time-varying and display a negative trend. The stock-bond correlations are negatively correlated with implied volatilities in stock and bond markets. Tests show that stock-bond relations are positively correlated with economic policy uncertainty, however, are negatively correlated with the monetary policy and fiscal policy uncertainties. Correlation coefficients between stock and bond returns are positively related to total policy uncertainty for returns of the Dow-Jones Industrial Average (DJIA) and the S&P 500 Value stock index (VALUE), but negatively correlated with returns of S&P500 (Total market), the NASDAQ Composite Index (NASDAQ), and the RUSSELL 2000 (RUSSELL).