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What was Roosevelt's goal in creating the SEC and FDIC?
The SEC and FDIC were created to create stability in the US banking system and capital markets for the average consumer.
During the 1920s, the stock market boomed. Money flowed in and out of the stock market. The market was largely unregulated. You could borrow up to 90 percent of a stock's price to buy stock. Further, practices like "churning" - conspiring to trade with the intent of raising a stock's price and then getting out after artificially raising it - were common. There were no reporting requirements about who owned the stock or what profits were actually made (or not made). It was "buyer beware."
In late 1929, stock prices began to fall as large investors pulled money out of the market. People who had borrowed money to buy stocks were forced to sell, which sent prices lower, which forced more selling and thus a crash.
The SEC was created to both regulate the market by prohibiting churning and other practices that hurt small investors and benefited large investors. At the same time, the SEC created mechanisms to prevent market panics.
The stock market collapse was part of a worldwide contraction of credit that led to creditors calling in many loans. As the money supply shrank, more and more banks failed even as the stock market recovered it's value. By 1933, there was a full blown banking crisis as many banks failed, further shrinking the money supply.
FDIC guaranteed deposits in certain types of banks up to a pretty large amount. Even if a bank failed, depositors were guaranteed to get their money out when another bank took over the failed bank, assisted by the federal government.
The result was renewed confidence in the financial system and a long period of economic stability in the US, lasting into the late 1990s.