Not sure if this is the right place to ask this but I searched and didn't find this question already asked. I am having a lot of trouble conceptually understanding the formulas behind a rate / volume analysis for changes to a bank's balance sheet. I know this is just a specific application of a more general question (apportioning change to different factors) but this is the application within which I am working. Below is an example and then my question.
- Time Period 1: Balances = 100, Interest Rate = 1%, Income = 100 * 1% = 1
- Time Period 2: Balances = 200, Interest Rate = 2%, Income = 200 * 2% = 4
- Change in Income = 4 - 1 = 3
I am trying to explain how much of the increase in income is due to the balance increase and how much is due to the interest rate increase. The way I was taught to do this, and everything I've read in the last hour or so of googling, is below:
- Change due to volumes = (200 - 100) * 1% = 100 * 1% = 1
- Change due to rates = (2% - 1%) * 200 = 1% * 200 = 2
The math here works, and I understand what we're doing conceptually by calculating the change due to volumes (in the absence of any rate increase this is the income that is attributable to our observed volume increase), but I don't understand what we're doing conceptually by calculating the change due to rates; it seems like we should be multiplying the change in rates times the old balances i.e. calculating increased income in the absence of any balance increase. That math doesn't work, though.
Assuming these are the correct calculations for apportioning change (and if they aren't please let me know!), what is the conceptual explanation behind what we're doing to calculate rate change? And is my understanding of change due to volumes incorrect?