When rates rise, and the economy’s growth is strong, NIMs compress because competition for deposits rises and CoF increases. Floating rate loans are quickly repriced but fixed rate loans are not and thus NIMs contract. This is what happened with Equitas because as you said they are a majority fixed rate book.
When rates fall, this usually happens in a slowing economy, as the CB may have overtightened, the lender’s need for deposit growth is not as high as credit demand may not be as high as in the scenario above, thus lenders are quick to reprice deposits, CoF reduces. However, the lenders are in no hurry to reprice the loans and pass on the falling rate benefit 1:1. Thus NIMs usually expand in this scenario.
So the default state in a rate cut environment is NIMs expanding and not falling as you have mentioned.
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