One can often see bank tiers 1-3 being mentioned, yet sometimes there are also tiers 4 to 6.
So, how many bank tiers are there really?
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Here is a reference that seems to cover it, at least for Gartner: https://www.gartner.com/it-glossary/bank-tier
Bank tier or size — that is, the size of the bank in relation to other banks — depends on the relative size to the overall banking market in terms of total banking assets as provided by the balance sheet of the bank. This type of comparison – across tiers – makes sense in relation to a particular country or region that define that specific banking marketplace. For this reason Gartner has preferred to adopt a localized definition of bank tiers that depends on 11 different regions that cluster together countries of similar economic and business homogeneity and avoid a generic global definition of bank tiers that would not allow proper comparison between the largest banks of different regions.
Investopedia references bank tiers, https://www.investopedia.com/ask/answers/043015/what-difference-between-tier-1-capital-and-tier-2-capital.asp, but they are internal to the bank itself.
Under the Basel Accord, a bank's capital consists of tier 1 capital and tier 2 capital, and the two types of capital are different. Tier 1 capital is a bank's core capital, whereas tier 2 capital is a bank's supplementary capital. A bank's total capital is calculated by adding its tier 1 and tier 2 capital together. Regulators use the capital ratio to determine and rank a bank's capital adequacy