White said she has numerous regulatory proposals in the works, including an "anti-disruptive trading" rule to rein in aggressive short-term trading by high-frequency traders during vulnerable market conditions, and a plan to force more proprietary trading shops to register with regulators and open their books for inspection.
White also said the SEC is working on a handful of transparency measures.
One such rule would require alternative trading venues such as dark pools and brokerage internalizers to disclose more to regulators and the public about how they operate.
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Dark pools allow investors to execute trades anonymously and do not make trading data available until after the trade is complete.
Another proposed measure would seek to mitigate potential conflicts of interest at brokerages by requiring more disclosure on how they handle orders for large institutional investors.
"Investors and public companies benefit greatly from robust and resilient equity markets," White said in prepared remarks. "I am recommending additional measures to further promote market stability and fairness."
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The SEC has been exploring potential equity market structure reforms since early 2010. The agency's review intensified later that year, after the May 2010 "flash crash" incident in which the Dow Jones Industrial Average plunged 700 points before it sharply rebounded.
Regulators traced the rapid plunge back to the trading strategies of a computer algorithm that started in the futures market and quickly spread to the equities markets.
Although no high-speed trading tactics were to blame for the incident, it sparked a worldwide debate about the impact high-speed trading has on the marketplace, and whether the SEC's major market rule changes in the early to mid-2000s have led to unintended consequences that gave some investors an edge over others.