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, <>.

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?


  • 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


  • 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.


  • 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


The Cross-Section of Expected Stock Returns

Fama, Eugene F. and Kenneth R. French, 1992, “The Cross-Section of Expected Stock Returns,” The Journal of Finance 47 (2), 427-465.

Purpose:  This paper evaluates the joint effect of market beta, firm size, E/P ratio, leverage, and book-to-market equity in explaining the cross-section of average stock returns on NYSE, AMEX, and NASDAQ.

Findings:  Beta does not explain the cross-section of average returns.  Size and book-to-market equity each have explanative power both when used alone and in the presence of other variables.

Motivation:  The Sharpe, Lintner, and Black asset pricing model (beta) has been very influential, but there are notable exceptions to its premises.  Banz (1981) finds a significant size effect.  Bhandari (1988) finds a leverage effect.  Others have argued for effects of the book-to-market equity ratio and the earnings-to-price ratio.  Furthermore, Reinganum (1981) and Lakonishok and Shapiro (1986) find that the beta-return relationship disappears after 1963.


  • Data:  Nonfinancial NYSE, AMEX, and NASDAQ firms from 1962-1989
    • Monthly return data from CRSP
    • Annual accounting data from COMPUSTAT
  • Create portfolios based on size and pre-ranked beta (using trailing data)
  • Calculate the beta for each portfolio-year and assign it to each stock in that portfolio-year
  • Fama-MacBeth Regressions
    • Beta-size portfolios
      • For each month, for the entire cross-section, regress average return on beta, ln(ME), ln(BE/ME), ln(A/ME), ln(A/BE), and E/P
      • Sort stocks into 10 size deciles and then into 100 sub-deciles on “pre-ranking” beta
        • pre-ranking beta is each security’s beta for the 60 months prior to portfolio creation (requiring at least 24 months of data for inclusion in any portfolio)
        • Pre-ranking beta cutoffs are established using only NYSE stocks
    • Book-to-market portfolios and E/P portfolios
      • formed in a similar manner, with stocks sorted on either BE/ME or E/P
    • Size & book-to-market portfolios
      • Match accounting data for fiscal year-ends in calendar year t-1 to returns for the period starting in July of year t and ending in June of year t+1.
      • Use market equity in December of year t-1 to calculate leverage, book-to-market, and E/P ratios.
      • Use market equity in June of year t to measure size.
      • sort stocks into 10 market equity deciles, then into 100 book-to-market sub-deciles.


  • Controlling for size, there is no relationship between beta and average return
  • Size is significant in predicting average returns
  • Book-to-market equity is also significant in predicting average returns, and has an even bigger effect than size
  • The effects of leverage and E/P are captured by size and book-to-market equity