Question

suppose a bank finds its ROA climbing by 50%, with its ROE unchanged. ehat happened to its equity multiplier? why?

Answer 1

ROE (Return on equity) = Net income/Shareholders equity
ROA (Return on assets) = Net income/Total assets
Equity multiplier = total assets/shareholders equity
Equity multiplier = ROE/ROA
The ROA is increasing 50% and the ROE is remaining unchanged.
Let say the equity multiplier is 100/25 or 4.
ROA is increasing by 50%, so the new equity multiplier will be
100/(25*(1.5))
the new equity multiplier is 2.67.
In other words, the equity multiplier will decrease by 33%
because the ROA is increasing by 50%.