NEW YORK (Reuters) – A University of Michigan doctoral candidate has estimated the potential annual profit from “latency arbitrage” on the S&P 500, a trading tactic at the heart of Michael Lewis’ claim in his book “Flash Boys” that markets are rigged, at about $3 billion.

The research is the first empirical study on the extent of latency arbitrage, a trading strategy that harnesses technology and an in-depth understanding of the market’s architecture to reduce the time, or latency, for orders to execute.

The study provides evidence that high-frequency traders have numerous opportunities to profit when prices in the same security differ among U.S. stock exchanges, said author Elaine Wah, a computer sciences doctoral candidate who did the analysis of the 2014 trading.

The high cost of technology and alleged abuse of marketplace latencies have led to cries that the playing field for investors is not level and helped spur the success of IEX, an alternative trading venue that has applied to be an exchange.

Wah examined instances when quotes for the best bid to buy, which typically are lower than quotes for the best offer to sell, actually cross – an arbitrage opportunity because the bid on one exchange is higher than the offer on another exchange.

Wah acknowledged the prevalence of the exploitable price differentials is not entirely clear. She counted approximately 69 arbitrage opportunities per security per day in 495 stocks in the S&P 500, and the median duration of these opportunities was 0.87 seconds.

The study also said the metric used to measure duration is highly sensitive to extreme values, leading to a result that most likely overestimates the measure.

Wah’s estimate of $3.03 billion in potential profit did not take into account transaction costs or execution risk – the possibility of no profit or a loss. She was unable to determine how often the arbitrage opportunities became trades.

Bill Harts, who leads Modern Markets Initiative, an advocacy group for electronic markets, was dismissive of the study, saying, “Only someone who has never traded would hypothesize that there is $3 billion of free money lying around.”

Wah analyzed order and quote data in 495 S&P 500 stocks and 46 small-cap stocks that are part of the Russell 2000 index. The data, from both direct feeds and the consolidated tape, came from the MIDAS system at the U.S. Securities and Exchange Commission, where she was an intern in the summer of 2014 and fall of 2015.

Wah used data from the 11 U.S. stock exchanges that were open throughout 2014. She did not examine data from alternative venues.