JPMorgan Chase says that its potential losses related to Bernard L. Madoff, the man accused of engineering an immense global Ponzi scheme, are “pretty close to zero.” But what some angry European investors want to know is when the bank cut its exposure to Mr. Madoff  and why.

As early as 2006, the bank had started offering investors a way to leverage their bets on the future performance of two hedge funds that invested with Mr. Madoff. To protect itself from the resulting risk, the bank put $250 million of its own money into those funds.

But the bank suddenly began pulling its millions out of those funds in early autumn, months before Mr. Madoff was arrested, according to accounts from Europe and New York that were subsequently confirmed by the bank. The bank did not notify investors of its move, and several of them are furious that it protected itself but left them holding notes that the bank itself now says are probably worthless.

A spokeswoman, Kristin Lemkau, said the bank withdrew from the Madoff-linked funds last fall after “a wide-ranging review of our hedge fund exposure.” Ms. Lemkau acknowledged, however, that the bank also “became concerned about the lack of transparency to some questions we posed as part of our review.”