Securities and Exchange Commission Chairman John S. R. Shad yesterday predicted more failures of independent government securities dealers if investors continue to desert them in favor of primary dealers.

The flight from the independent dealers, which is occurring as the result of what he termed "enormous publicity" and an "overreaction" following the failure of E.S.M. Government Securities Inc. and Bevill, Bresler & Schulman Asset Management Corp., may exacerbate the situation, Shad told a Senate subcommittee. Losses from the two failures -- excluding any recovery or insurance -- are estimated by the SEC to top $500 million.

There are approximately 300 government securities dealers. The annual dollar volume of government and agency securities trades is 15 times greater than that of all stock market activity. All but a fraction of the trading is transacted by 36 primary dealers that the Fed monitors, or by regulated banks and broker-dealers. Shad declined to comment on published reports that the SEC is now examining the records of up to a hundred companies registered with the SEC that deal in repurchase agreements backed by government securities.

The problem is the small, independent dealers that handle only government securities and, through a legal loophole, are not regulated at all. Sens. Alfonse D'Amato (R-N.Y.) and Alan Cranston (D-Calif.) announced separate bills to bring these dealers under the jurisdiction of a public securities rule-making board by expanding the board that currently oversees municipal bond dealers. A similar measure was introduced this week in the House.

The Treasury and the Federal Reserve Bank of New York, as well as some economists and industry groups, are not enthusiastic about regulation for fear it would reduce the liquidity of the important government securities market. Shad suggested that regulation on business conduct could increase financing costs. A one-tenth of 1 percent increase would raise federal interest costs by $2 billion a year, he noted.

On another controversial subject -- the increasing use of junk bonds to finance hostile takeovers -- Shad said that junk bonds had a good track record over the past 15 years as yielding more than enough to make up for occasional failures. But he added that the SEC does not have the power to approve financing plans ahead of time. Junk bonds are low-grade, high-yield obligations. The risk is that during an economic downturn, corporations saddled with large debt are more likely to succumb.

Last year the SEC supported legislation to end some abuses in the takeover process.