Question

Suppose Bank Z has ROE of 12% and ROA of 1%. If capital-to-asset ratios (simply called capital ratios) above 9% are considered to be well capitalized, is this bank well or poorly capitalized? Please support your answer with numbers.

Answer 1

For Bank Z,

Return on Equity = 12%

Return on Assets = 1%

Now, suppose that the absolute value of returns is R

Thus, R/E = 0.12            -- 1)

R/A = 0.01                       -- 2)

From 1), R = 0.12E

Substitute in 2)

0.12E/A = 0.01

Thus, E/A = 0.01/0.12 = 0.0833

Or in other words,

The Equity to Assets ratio (Capital to Assets ratio) = 8.33%

As per the criteria of 9%, this bank's equity capital is not enough to be considered as well capitalized.