WASHINGTON—The Federal Reserve over the last three months has flooded money markets with hundreds of billions of dollars in cash to avoid a repeat of volatility that roiled cash markets in September.

The success of the moves—which reversed roughly half of the Fed’s shrinkage of its asset portfolio over the prior two years—will encounter a test around Dec. 31. That is when some financial institutions could face incentives from regulations to limit their lending, which could cause supply and demand imbalances for cash.

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