This is a big week for Citigroup (C -0.48%) and its investors.

On Wednesday, the Federal Reserve will announce whether the nation's third-biggest bank by assets can increase its dividend for the first time since the financial crisis of 2008-2009.

Generally speaking, most companies are free to adjust their quarterly distributions at the discretion of the board of directors. But this isn't the case for the nation's largest lenders.

Legislation and regulations passed in the wake of the financial crisis require that changes in capital plans at banks -- specifically, banks with more than $50 billion in assets -- pass a two-step regulatory approval process.

The first step consists of stress tests administered by the central bank at the beginning of every year. These tests are intended to determine whether the so-called too-big-to-fail banks have enough capital to sustain an economic cataclysm akin to the last crisis. Notably, this step assumes that participating banks make no adjustments to their existing capital plans.

Below are the results the Fed released last week. By the looks of it, at least, Citigroup passed this step with flying colors. Even at the nadir of the Fed's "severely adverse" economic scenario, Citigroup's pivotal Tier 1 common capital ratio only declined to 8.2%, which is well in excess of the 5% regulatory minimum.

The second step, known as the Comprehensive Capital Analysis and Review, takes these results and incorporates the banks' requests to increase its dividends and/or share buybacks over the next 12 months. If the changes to the capital plans cause a bank's capital ratios to dip below the regulatory minimum at the trough of the Fed's severely adverse economic scenario, then the Fed will presumably deny the request.

This is what happened to Citigroup last year. Or, more specifically, a variation of this happened to Citigroup last year, as the real issue was with the New York-based bank's "capital planning practices."

As the Fed explained at the time:

While Citigroup has made considerable progress in improving its general risk-management and control practices over the past several years, its 2014 capital plan reflected a number of deficiencies in its capital planning practices, including in some areas that had been previously identified by supervisors as requiring attention, but for which there was not sufficient improvement. Practices with specific deficiencies included Citigroup's ability to project revenue and losses under a stressful scenario for material parts of the firm's global operations, and its ability to develop scenarios for its internal stress testing that adequately reflect and stress its full range of business activities and exposures. Taken in isolation, each of the deficiencies would not have been deemed critical enough to warrant an objection, but, when viewed together, they raise sufficient concerns regarding the overall reliability of Citigroup's capital planning process to warrant an objection to the capital plan and require a resubmission.

The outcome this year is widely expected to be different. In the first case, passing both rounds of this year's stress test has been a top priority at Citigroup over the past 12 months, with most analysts assuming CEO Michael Corbat's job hangs in the balance. One can only assume, in turn, that the bank has addressed the systemic concerns that impeded a dividend increase in 2014.

In the second case -- according to CLSA bank analyst Mike Mayo's analysis of Citigroup's balance sheet, at least -- the bank holds as much as $20 billion in excess Tier 1 capital. If that's true, it seems reasonable to conclude that the Fed would allow at least some of it to be returned to shareholders.

At the end of the day, of course, the proof is in the pudding. The signs point in the positive direction, but we'll know for sure on Wednesday afternoon.