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I've been analyzing banks balance sheet. However, I am getting confused regarding definition of ratios. For instance, some authors state

Net Profit Margin = (Net profit)/Net interest income others as Net Profit Margin = (Net profit)/total income i.e. some of interest income and other income.

Similarly, some authors define ROA= Net profit/Total assets while others define it as ROA= Net profit/Average Total assets

Is there any comprehensive source/reference for ratio analysis of banks?

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You can look at the contents of the CFA institute : https://blogs.cfainstitute.org/insideinvesting/2013/01/23/how-much-does-apple-make-a-dupont-analysis/ . As there are more and more candidates and CFA charteholders, we could say that their views are becoming or are already the mainstream views.

I would add that accounting and corporate finance is not a "pure science". Sometimes, you will use a formula with the average assets and in others case the current assets. For instance, just after a merger or an acquisition, it does not make sense to take the average assets as the company you study has dramaticaly changed recently. Conversely, if you suspect dubious accounting, taking the average is a way to eliminate some sensibilities of the last report.

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