Greenlight Capital Inc., the hedge-fund firm led by billionaire David Einhorn, gained 2.2 percent in its main hedge fund in October, when peers on average posted losses amid violent market swings.

The gain brings returns since the start of the year to 4.9 percent, according to an e-mail to investors obtained by Bloomberg News. The HFRX Global Hedge Fund Index, which measures asset-weighted performance of hedge funds across various strategies, fell 1.7 percent in October, resulting in a year-to-date loss of 0.5 percent.

The $10 billion Greenlight, which mainly invests in U.S. equities, told clients last month that it plans to accept new money for the first time in more than two years to take advantage of recent market turmoil. The Standard & Poor’s 500 Index fell 5.6 percent from the start of the month through Oct. 15, led by stocks that were hedge-fund favorites. The S&P reversed losses to end October 2.3 percent higher.

Jonathan Gasthalter, a spokesman for Greenlight, declined to comment on the returns, which were previously reported by Institutional Investor’s Alpha Magazine.

“While we have been fully invested for some time, it has been hard to find new opportunities,” the firm wrote in an Oct. 16 letter to investors. “Given the current turmoil in the markets, this is changing quickly.”