NEW YORK, June 24 (Reuters) - U.S. securities rules should be changed to allow stock exchanges to quote bids and offers in price increments of less than a penny so they can better compete with wholesale brokerages for retail orders, Robinhood Chief Executive Officer Vlad Tenev said on Thursday. Retail trading volumes have soared over the past year-and-a-half, fueled by the move to commission-free trading by most large online brokerages in November 2019 - a model Robinhood helped pioneer - and by the work-from-home environment during the coronavirus pandemic. But the vast majority of retail orders are sent to wholesale market makers, instead of exchanges, because the wholesalers can offer prices that are fractions of a cent better than the best prices available on exchanges, which are limited to penny increments. "In a nutshell, exchanges cannot fairly compete with off-exchange market makers in executing our customers" orders," Tenev, who also called for lower exchange fees, said in a blog post. To better enable exchanges to compete, the U.S. Securities and Exchange Commission should amend the so-called "sub-penny" rule that limits on-exchange quotes to one-cent increments, and allow them to quote prices up to four decimal places for all stocks, Tenev said. "If the sub-penny limitation is removed, and exchanges reduce fees for retail orders, we could see ... more transparency and perhaps more retail order flow executed on lit markets," he said, referring to exchanges which are considered "lit" because participants can see prices. SEC Chair Gary Gensler recently said he had asked his staff to recommend changes to minimum pricing increments on exchanges as part of a broader review of securities rules, because "wholesalers may operate on an unequal playing field when competing for order flow." read more In 2005, when the sub-penny rule was enacted, there were concerns sophisticated electronic traders might jump ahead of retail orders using the smaller pricing increments. Spokespeople for Nasdaq Inc (NDAQ.O) and Intercontinental Exchange Inc"s (ICE.N) New York Stock Exchange declined comment. Reporting by John McCrank; editing by David Evans