High Frequency Trading with Speed Hierarchies

Traders differ in speed and their speed differences matter. I model strategic interactions induced when high frequency traders (HFTs) have different speeds in an extended Kyle (1985) framework. HFTs are assumed to anticipate incoming orders and trade rapidly to exploit normal-speed traders' latencies. Upon observing a common noisy signal about the incoming order flow, faster HFTs react more quickly than slower HFTs. I find that these front-running HFTs effectively levy a speed tax on normal-speed traders, making markets less liquid and prices ultimately less informative. Even when infinitely many HFTs compete, in general their negative effects on market quality persist and such effects are more severe when HFTs have more heterogeneous speeds. I analyze policy proposals concerning HFTs and find that (1) lowering the frequency of periodic uniform price auctions reduces the negative impact of HFTs on market quality and (2) randomizing the sequence of order execution can degrade market quality when the randomizing interval is short. Consistent with empirical findings, a small number of HFTs can generate a large fraction of the trading volume and HFTs' profits depend on their speeds relative to other HFTs