EFF/KRF: We know of no evidence on how high frequency trading has affected volatility. High frequency trading could affect valuations by changing transaction costs. The interesting question is whether high frequency traders push transaction costs up or down. Assume that, as a group, high frequency traders are profitable. Then the key is whether their gains come at the expense of investors or other liquidity providers. For example, if they are just anticipating what investors are about to do and stepping in front of them, high frequency traders' profits add to investors' trading costs and valuations should fall. If high frequency traders are better liquidity providers, they reduce transaction costs and valuations should rise.
By the way, we have yet to see evidence demonstrating that high frequency trading caused the Flash Crash. Apparently, many high frequency traders stopped trading when prices became erratic. To the extent that these traders are important liquidity providers, their withdrawal would have amplified the effect of unbalanced buy and sell orders. To go further and say they "caused" the Flash Crash, one would have to argue that other liquidity providers were no longer around to offset unusual price pressure because they had been displaced by high frequency traders.
Eugene Fama and Ken French are members of the Board of Directors for and provide consulting services to Dimensional Fund Advisors LP.