Using a model that separates the permanent and transitory components of stock prices, the authors analyze the role of high-frequency traders (HFTs) in price discovery and find that HFTs increase price efficiency in two ways. First, by trading in the direction of permanent price changes, HFTs incorporate information in stock prices. Second, by trading in the opposite direction of transitory pricing errors, HFTs reduce long-term investors’ trading costs. In addition, the authors find that HFTs supply liquidity during volatile days.

The results of this research are useful to practitioners in at least two ways. First, the authors demonstrate that HFTs enhance price efficiency. Therefore, the presence of HFTs benefits some investors. For example, by helping reduce transitory pricing errors, HFTs help long-term investors reduce their trading costs. But for short-term investors, the benefits are less clear. More research is needed to determine the effect, if any, of intraday reductions in pricing errors on the facilitation of better financing decisions and resource allocations by firms and investors.

Second, the authors find that HFTs supply liquidity in stressful times, such as during the most volatile days and around macroeconomic news announcements. This evidence is inconsistent with HFTs’ contributing directly to the instability of prices. In fact, the authors find that HFTs traded in the direction of reducing transitory pricing errors both on average days and on the most volatile days during 2008–2009, which helped reduce pricing errors even during the volatile periods.

The authors primarily use a dataset that the NASDAQ makes available to academics for identifying a subset of HFTs (namely, proprietary trading firms). The dataset covers trading data in 2008 and 2009 for 120 randomly selected stocks listed on the NASDAQ and NYSE. The NASDAQ classifies the firms in the data as HFTs or not. The NASDAQ bases this classification on its knowledge of the firm and through an analysis of the firm’s trading, such as the order duration and order-to-trade ratios. But the NASDAQ cannot identify all HFT firms using this methodology, such as those that are part of large integrated firms, such as Goldman Sachs and Morgan Stanley. The authors then supplement the NASDAQ HFT dataset with two other datasets. First, they use data from the National Best Bid and Offer from the NYSE Trade and Quote database, which measures the best prices prevailing across all markets. Second, they use the NASDAQ Best Bid and Offer, which measures the best available price on the NASDAQ. Lastly, the authors focus on continuous trading during normal hours, which means that the analysis excludes pre-market and post-market trading as well as the opening and closing crosses.

Next, the authors use a state space model, which decomposes the stock price into a permanent component and a transitory component. The permanent component is often associated with information and the transitory component is typically associated with pricing errors. The state space model is estimated for each of the 23,400 one-second time intervals in a trading day for each stock using maximum likelihood estimation via the Kalman filter. The Kalman filter is a standard technique used to gain more precise estimates of variables when the inputs are noisy or incomplete.

The authors also examine the role of HFTs in price discovery during high-volatility days. They compare the results of a subsample of the highest-permanent-volatility days, which are denoted by days when the volatility of the stock is in the 90th percentile of the volatility of all days, with those of the remaining 90% of days in the sample.

The authors present empirical evidence that is inconsistent with the primarily anecdotal evidence reported in the news media and books that focuses on the purported negative effect of HFTs. In particular, they highlight the important role HFTs play in making prices more efficient on normal and high-volatility days. Also, although some HFTs may be profitable based solely on an analysis of their trading, it is important to be cognizant of the nontrivial costs required to set up and run an HFT firm, such as technology investment costs and data and collocation fees.