The High-Frequency Trading Arms Race: Frequent Batch Auctions as a Market Design Response

Budish, Eric, Peter Cramton, and John Shim, “The High-Frequency Trading Arms Race:  Frequent Batch Auctions as a Market Design Response,” SSRN, December 23, 2013, <http://ssrn.com/abstract=2388265>.

Purpose:  To argue that the continuous limit order book design of current securities markets is socially wasteful, reduces trading depth (large trades are less available), and increases trading spreads; and to propose batch auctions as a better market design.

Motivation:  High-frequency trading firms (HFTs) spend hundreds of millions of dollars to increase their communication speeds with financial markets by just a few thousandths of a second.  Is this “arms race” a healthy competition, or does it reveal a flaw in the design of our financial markets?

Findings:

  • Very high correlations that are observed between securities traded on different exchanges break down over very short time intervals (a few milliseconds).
  • Arbitrage opportunities available to the fastest traders may amount to billions of dollars annually.
  • Time horizons for HFT have shrunk over time, but competition has not reduced the size of the opportunity
  • The continuous limit order book (first come, first served) market design increases bid-ask spreads and penalizes liquidity providers who would offer large trades, thus keeping markets thin
  • The arms race hurts social welfare by incentivizing investment in expensive high-speed technology
  • Frequent batch auctions (such as once per second) would eliminate these shortcomings
    • By greatly reducing the advantage of high speed
    • By forcing HFTs to compete on price instead of on speed alone
  • Batch auctions may also improve both market stability and regulators’ ability to oversee trading activity

Data/Methods:

  • Direct-feed data is from the NYSE and the CME for the period 1/1/2005 to 12/31/2011, including all activity on the exchanges’ limit order books with millisecond-level time stamps. This is the same data that HFTs use.
    • Compute correlation between % changes in the bid-ask midpoints of highly correlated securities.
    • Calculate arbitrage profits by assuming the ability to instantaneously trade and summing the profits from arbitrage opportunities over a period.
  • Model: investors, (quantity) N HFTs, and security x perfectly correlated (with latency) with a public signal y.
    • 1 HFT acts as the “liquidity provider” and N-1 act as “stale-quote snipers.”
    • When the public signal moves, the liquidity provider adjusts its prices, and the snipers simultaneously try to buy or sell at the old prices; snipers are successful with probability 1/N.
    • The liquidity provider builds the probability of getting sniped into its bid-ask spreads.

Conclusions:

  • In equilibrium, the cost of HFTs investments in speed, the total profits to be made by HFTs’ technical arbitrage, and the revenue extracted from investors by the liquidity provider’s bid-ask spreads are all equal.
  • In the model, a positive bid-ask spread exists even in the case of perfect information, so investors lose out.
  • Prisoners’ Dilemma: HFTs would be better off mutually agreeing not to invest in speed
  • Both empirically and theoretically, the size of the arms-race price does not depend on the speed of HFTs.
  • The HFT arms race hurts both investors and society, and could be corrected by moving to batch auctions.

 

The figure below plots the time series of the bid-ask midpoints of two highly correlated securities:  the E-mini S&P 500 future (ES, in blue) and SPDR S&P 500 ETF (SPY, in green).  The series are shown for an ordinary trading day (08/09/2011), using four different time horizons.  Note the very high correlation between the lines in (a) and the low correlation in (d).  At 10 milliseconds, there is virtually zero correlation.  For details, see original paper.

HFT correlation