On May 19, in Detroit, J.P. Morgan CEO Jamie Dimon and members of his longstanding board-level entourage will meet with shareholders. The bank’s investors should be asking if the top leaders are best suited to move the financial behemoth to a safer place.

Shareholders may want to start by asking Dimon and J.P. Morgan’s (JPM) board about the CEO’s annual letter to shareholders. Dimon, referring to the financial crisis, wrote: “What is most striking to me, in spite of all the turmoil, is that our company became safer and stronger.” He explains that “large does not necessarily mean complex” and “large does not necessarily mean more risky.”

Yet according to a Treasury report on the major banks issued in February, J.P. Morgan has more potential than any other bank to wreak havoc on the financial system. A look at the bank’s balance sheet shows that its trading assets grew at a faster pace than loans last year. (Trading businesses are more volatile than prudently managed lending operations.)

Here’s some background shareholders ought to consider when asking about the bank’s risk mitigation plans—and whether the CEO and board should stay or go.

CEO and chair. Dimon has been CEO since December 31, 2005 (and chair since December 2006), making his tenure much longer than the norm for the largest Wall Street banks and approaching the average for the Fortune 500. And that’s not counting his time as CEO at Bank One, which began in 2000. (Bank One was acquired by J.P. Morgan.)

The lead director and compensation chair. Lead director and compensation chair Lee Raymond has been a board member for 28 years stretching back to 1987. To its credit, J.P. Morgan discloses Raymond’s long-running connection to the company in its proxy statement, while proxy information provider Institutional Shareholder Services reports Raymond’s tenure at just 14 years, counting only the time since J.P .Morgan merged with Chase. Institutional Shareholder Services still gives J.P. Morgan poor governance marks, ranking the bank in the 90th percentile among companies with the highest governance risk.

Raymond’s been in charge of assessing Dimon’s performance and overseeing CEO succession throughout Dimon’s tenure as J.P. Morgan’s CEO. So, shareholders should be asking for his views on the high turnover of CEO succession candidates. And what would be the problem with J.P. Morgan having an independent chair?

The risk policy committee chair: Risk policy committee chair James Crown has been a board member for 24 years, since 1991, when he sat on the board of Bank One. So how does he think the bank should address the Treasury report and the bank’s never-ending operational and compliance problems?

The audit committee chair: In recent years, J.P. Morgan has experienced significant weaknesses in its accounting and internal controls. Audit chair Laban Jackson has been a board member since 1993, when he sat on the board of Bank One. That’s a 22 year run. Yet, Tim Flynn, former chair of KPMG, who joined the board in 2012, is absent from the bank’s audit committee. Why? And what has the audit committee been doing to ensure auditor independence? For 50 years, encompassing Dimon’s entire tenure and stretching back to 1965, PricewaterhouseCoopers has been the bank’s external auditor. Isn’t calling an audit firm independent after 50 years a stretch?

A spokesperson from J.P. Morgan pointed Fortune to the “significant space” in Dimon’s letter to shareholders devoted to “describing the meaningful steps that we have taken to simplify the company as well as an entire section about our fully engaged board, exceptional management team and strong corporate culture.”

Also in his annual shareholder letter, Dimon writes, “We always are prepared for the toughest of times.” He predicts we’ll have another crisis—and yet doesn’t seem particularly concerned about it.

Despite its travails, as of May 1, investors who bought shares in J.P. Morgan when Dimon became CEO would have more than doubled their money (equivalent to earning about 8% annualized returns). Clearly, shareholders are convinced that the bank is free to take on as much risk as it wants without consequence.

But it would be dangerous to assume that J.P. Morgan will have a soft landing in a future crisis. Regulators have criticized J.P. Morgan’s stress tests as overly optimistic. And Fortune recently reported that Federal Reserve Chair Janet Yellen is determined to cut the outsize risks that Wall Street banks pose to the economy and society. Shareholders would be wise to ask that J.P. Morgan’s board commit to facing the music regarding the bank’s riskiness and prevent the worst from, once again, happening to us all.

Eleanor Bloxham is CEO of The Value Alliance and Corporate Governance Alliance (http://www.thevaluealliance.com), an independent board education and advisory firm she founded in 1999. She has been a regular contributor to Fortune since April 2010 and has advised analysts, regulators, shareholders and banks of every size on the economics of financial services.