Mr. Kirilenko’s study focused on one corner of the financial markets that the C.F.T.C. oversees, contracts that are settled based on the future value of the Standard & Poor’s 500-stock index. He and his co-authors, professors at Princeton and the University of Washington, chose the contract because it is one of the most heavily traded financial assets in any market and is popular with a broad array of investors.

Using previously private data, Mr. Kirilenko’s team found that from August 2010 to August 2012, high-frequency trading firms were able to reliably capture profits by buying and selling futures contracts from several types of traditional investors.

The study notes that there are different types of high-frequency traders, some of which are more aggressive in initiating trades and some of which are passive, simply taking the other side of existing offers in the market.

The researchers found that more aggressive traders accounted for the largest share of trading volume and made the biggest profits. The most aggressive scored an average profit of $1.92 for every futures contract they traded with big institutional investors, and made an average $3.49 with a smaller, retail investor. Passive traders, on the other hand, saw a small loss on each contract traded with institutional investors, but they made a bigger profit against retail investors, of $5.05 a contract.

Large investors can trade thousands of contracts at once to bet on future shifts in the S.& P. 500 index. The average aggressive high-speed trader made a daily profit of $45,267 in a month in 2010 analyzed by the study.

Industry profits have been falling, however, as overall stock trading volume has dropped and the race for the latest technological advances has increased costs.

Mr. Kirilenko, who is about to leave the C.F.T.C. for an academic position at the Massachusetts Institute of Technology, presented a draft of the paper at a C.F.T.C. conference last week. He said that the markets were a “zero sum game” in which the high-speed profits came at the expense of other traders.