The relationship between a market index and its constituent stocks is complicated. While an index is a weighted average of its constituent stocks, when the investigated time scale is one day or longer the index has been found to have a stronger effect on the stocks than vice versa. We explore how this interaction changes in short time scales using high frequency data. Using a correlation-based analysis approach, we find that in short time scales stocks have a stronger influence on the index. These findings have implications for high frequency trading and suggest that the price of an index should be published on shorter time scales, as close as possible to those of the actual transaction time scale.We would like to thank Yoash Shapira, Idan Michaeli and Dustin Plotnick for all of their help. DYK and EBJ acknowledge support in part by the Tauber Family Foundation and the Maguy-Glass Chair in Physics of Complex Systems at Tel Aviv University. HES and DYK thank the support of the Office of Naval Research (ONR, Grant N00014-09-1-0380, Grant N00014-12-1-0548), Keck Foundation and the NSF (Grant CMMI 1125290) for support. This work was also supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center (DoI/NBC) contract number D12PC00285. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DoI/NBC, or the U.S. Government. (Tauber Family Foundation; Maguy-Glass Chair in Physics of Complex Systems at Tel Aviv University; N00014-09-1-0380 - Office of Naval Research (ONR); N00014-12-1-0548 - Office of Naval Research (ONR); Keck Foundation; CMMI 1125290 - NSF; D12PC00285 - Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior National Business Center (DoI/NBC))Published versio
