The authors introduce an expected return equation for high-frequency trading strategies. The hedge fund industry traditionally defines alpha in terms of absolute return. When a strategy is new, as in the case of high-frequency trading, these returns are often generated by a backtest or simulated trading. The authors break down the components of return in an effort to provide insight into the variability of profits and losses, the correlations between the components, and the impact of time (i.e., technological speed).

Algorithms started as tools for institutional investors in the beginning of the 1990s. Decimalization, direct market access, 100% electronic exchanges, reduction of commissions and exchange fees, and rebates contributed to fueling the growth of algorithmic trading to the point that more than 50% of all trades in the US equity markets are algorithmic. The authors contribute to an evolving body of research on high-frequency trading—in particular, whether high-frequency trading dynamics systematically affect the market in a way that disadvantages low-frequency traders. The authors’ comparison of high-frequency trading with its low-frequency counterpart should be enlightening to risk managers, strategy developers, and regulators. Algorithmic execution of block trades is an important tool that allows for systematic and disciplined execution of size, and studies like this one increase practitioners’ knowledge of how the strategy works and its impact on the market.

Algorithmic trading refers to the use of programs and computers to generate and execute large orders in markets with electronic access. The authors empirically test their model using data from the NASDAQ limit order book for Apple Inc. for 3 January 2012. High-frequency strategies are not based on price forecasts, so the authors address the components of alpha by examining four key trading components:

1. How much opportunity is available to be captured?
2. How much can be captured?
3. What is the cost of capturing it?
4. What is the effective rebate?

The size and consistency of alpha are equal to the product of the volatility multiplied by the information coefficient multiplied by the Z-score. Opportunity is measured by observing the standard deviation of changes in the bid–ask midpoint price. Capture is the percentage of the opportunity that the strategy can grab. It is often measured as the correlation of forecasted returns with the actual, realized returns. It is interesting to note that strategies based on providing liquidity may have a capture percentage that is less than zero. Firms that supply liquidity by placing limit orders in the limit order book are paid a fee by exchanges called a “rebate.” Incentivizing liquidity suppliers is thought to be good for the exchange.

The values of the components are dependent on each other. There are hidden interactions and a fundamental trade-off: Time is important, but if a strategy wants to execute immediately, then it will pay the spread. Passive limit orders earn the spread by waiting but take longer to execute, potentially sacrificing some captured opportunity. Whether a high-frequency trading strategy earns or pays the spread depends on the tactics used to implement it—in particular, whether the strategy uses market or limit orders. Market orders demand liquidity and take the market price.

In the new regulatory environment, certain high-frequency trading strategies may be illegal, but that does not mean they are unethical. The authors argue that high-frequency strategies seek to profit by removing inefficiencies from the marketplace. But a recent book by Michael Lewis, Flash Boys: A Wall Street Revolt (W.W. Norton & Company 2014), presents a case that high-frequency trades “front run” low-frequency trades, causing degradation in execution quality. An ethical trading strategy is one that promotes the societal interest in free markets that are transparent, efficient, and reliable. High-frequency traders provide a lot of volume but not necessarily a lot of liquidity when needed (i.e., they engage in nothing more than “hot potato” trading).