* Group profits and revenues fall
* Equities trading weaker than rivals
* Shares fall sharply (Updates with comments from executives, fund manager, details)
PARIS, Aug 2 (Reuters) - Societe Generale reported lower second-quarter profits on Wednesday, missing out on an equities trading surge that benefited rivals including BNP Paribas and Natixis.
SocGen's equity trading revenue fell more than 3 percent while BNP Paribas last week reported a 25.7 percent rise in its equities and prime services business which serves hedge funds and Natixis's revenue from equity trading was up 33 percent.
"Figures speak for themselves, they have done better than us, that's it," Didier Valet, head of SocGen's investment bank, told reporters, referring to the performance of SocGen's French rivals. "It's clear that we want to do better," he said.
SocGen's shares fell more than four percent, underperforming the broader European banking index which was down 0.9 percent.
France's second biggest bank said volatility in global markets had moved "ever lower" in the second quarter and there was a widespread "wait-and-see" attitude among investors. Its equity derivatives perform strongly when markets are volatile.
Valet said volatility would not remain low forever and that it would pick up later on, given that some market-moving events, such as elections, or monetary policy decisions, were on the horizon.
SocGen, more focused on equities than its rivals, has shaken up management and invested more in fixed income and prime services, aimed at hedge fund clients, in the past few years.
"We have a model which has as an objective a resilient revenue contribution," Chief Executive Frederic Oudea said in a video presentation.
Rival Natixis said on Tuesday that it had outperformed rivals in equities trading and derivatives, as its business does not depend on trading volumes or flows, but on specific products for clients on their transactions.
SocGen's investment bank, which accounts for about a third of group revenue, is bigger than that of Natixis and depends more on flows, meaning fees from clients, such as asset managers.
"Flow products continued to experience limited activity, in conjunction with very low volatility, leading to a drop in volumes, primarily on flow derivatives and cash," the bank said.
In Germany, Commerzbank on Wednesday also pointed to weak markets as a reason for its bigger-than-expected net loss in the second quarter.
SocGen fared better in fixed income trading, where it reported a 6.8 percent fall in second-quarter sales versus a 16 percent drop at BNP Paribas.
"SocGen's results were a bit worse than those of their French peers due to a weaker performance in corporate and investment banking, even if there was a positive surprise on their risk provisions," Keren Finance fund manager Benoit de Broissia. His firm does not own SocGen shares but holds BNP Paribas shares.
SocGen continued to cut costs in the investment bank in the second quarter, which helped to offset lower revenue from trading and financing and advisory to bring net profit up 11 percent to 499 million euros.
As well as cutting costs, French banks in general are aiming to win market share from European rivals, such as Credit Suisse and Deutsche Bank which are cutting jobs and exiting businesses.
SocGen's second-quarter group net income fell to 1.06 billion euros from 1.46 billion euros a year earlier, in line with the average of estimates from five analysts in a Reuters poll.
Group revenues fell 26 percent to 5.20 billion euros, below 5.39 billion euros expected by the analysts. A recovery in retail banking in eastern Europe and Africa helped partly to offset pressure on margins in French retail banking from low interest rates, and a decrease in trading sales.
($1 = 0.8472 euros)
(Reporting by Maya Nikolaeva, Julien Ponthus and Sudip Kar-Gupta. Editing by Jane Merriman)