Assuming ROA is less than one and an increase in the fair value of a trading security, why ROA is higher when both numerator and denominator from ROA increase (Net Income / Assets)?
Simple arithmetic.
Try an example:
- NI = 10
- A = 100
- ROA = 10 / 100 = 10.0%
- FV increase = 5
- New NI = 10 + 5 = 15
- New A = 100 + 5 = 105
- New ROA = 15 / 105 = 14.3%
When ROA is less than 1.0, adding the same amount to both the numerator and the denominator increases the numerator by a greater percentage than the increase in the denominator.
Taking your example makes it more clear : (10 + 50%*10)/ (100+5%*100) = 10/100 * 1,5/1,05 -> New ROA = Old ROA * 1,5/1,05 => higher
Thanks
My pleasure.
I always find it helpful to write out a numerical example for these and see what’s really happening. It’s then easier to understand the general idea.