When it comes to bank stress tests, there is a fine line between theory and practice.

The Federal Reserve last week released results of these tests, a theoretical exercise gauging how banks would weather a financial storm. Given they are hypothetical, the tests have obvious shortcomings. Yet there are two very practical implications.

First, they are a starting point for Fed decisions on bank capital-return requests, due this week. Second, banks are increasingly trying to manage their businesses to meet the stress tests, rather than other measures of capital.

So the difference between how the Fed saw banks performing and how banks themselves thought they did is notable for investors. Among the biggest banks, Citigroup  and Bank of America  were the furthest off on this front. Citigroup saw itself as having a minimum Tier 1 capital ratio of 10% under stress, 2.8 percentage points above the Fed's view. BofA's assumption was 2.7 percentage points higher. J.P. Morgan Chase's estimate, by contrast, was nearly in line with the Fed.

The variance stems partly from differing assumptions regarding loan losses. Also playing a role were banks' view that assets would decline during a crisis. The Fed, which for the first time did its own calculation of bank balance sheets for the tests, assumed banks would end up taking more assets onto their books.

The immediate outcome of this difference probably isn't dire. Most banks should still be able to return capital in line with market expectations. That said, analysts expressed concern that BofA may have less room for maneuver than initially thought and could have to resize its return request.

In the longer term, Citi and BofA may have to keep in mind an old adage when viewing the risks in their businesses: Don't fight the Fed.