We investigate the dynamic return-volatility relation between stock indices returns (S&P 500, Nasdaq 100, Dax 30 and Dow Jones Euro Stoxx 50) and changes in the newly constructed model-free implied volatility indices (VIX, VXN, VDAX, and VSTOXX) at the daily level. We find pronounced contemporaneous negative and asymmetric return-volatility relations between each stock market index and its corresponding volatility index. The VIX presents the highest asymmetric return-volatility relation followed by the VSTOXX, VDAX and VXN volatility indices, respectively. Our findings do not support either leverage or volatility feedback hypotheses. Instead our results could be explained by investors' heterogeneity, i.e., that there are clusters of pessimist investors (who overestimate volatility underestimate returns) and cluster of optimist investors (who underestimate volatility and overestimate returns) that leads to the strong observed short-term negative and asymmetric return-volatility relation. Our results have implications for trading, hedging, and risk management practices.