A bank has $500 millionin rate-sensitive assetsand, 400million in rate-sensitive liabilities

within a one-year time horizon. If interest rates increase by 1.5% (150 basis points), what is

the predicted change in annual net interest income?

Question

A bank has $500 millionin rate-sensitive assetsand, 400million in rate-sensitive liabilities

within a one-year time horizon. If interest rates increase by 1.5% (150 basis points), what is

the predicted change in annual net interest income?

BlackTom AI · Accepted Answer

We start by identifying how net interest income (NII) responds to a one-year change in interest rates when focusing on rate-sensitive assets (RSA) and rate-sensitive liabilities (RSL).

First, consider what happens to RSA: if rates rise by 1.5%, the income from RSA increases by 1.5% of the RSA amount. Here, RSA = $500 million, so the change in income from assets is 500 million × 0.015 = $7.5 million.

Next, consider RSL: with rates rising by 1.5%, interest costs on liabilities also increase. The rate-sensitive liabilities amount is $400 million, so the change in interest expense on liabilities is 400 million × 0.015 = $6.0 million.

Net interest income (NII) change is the difference between the asset-related increase and the liability-related increase: $7.5 million − $6.0 million = $1.5 million.

Now, evaluate each answer option against this calculation:
- Decrease by $6.0 million: This would imply NII falls when rates rise, which contradicts the positive impact on assets outweighing the liability costs.
- Decrease by $1.5 million: This would require assets to rise less or liabilities to rise more than our computed amounts; the math here does not fit the given RSA and RSL figures.
- Increase by $7.5 million: This ignores the concurrent rise in funding costs (RSL), overstating the net effect by assuming no liability cost increase.
- Increase by $1.5 million: This matches the net result from the asset increase ($7.5M) minus the liability increase ($6.0M).

In summary, the correct interpretation is that the net interest income increases by the difference between the asset and liability sensitivity, which equals $1.5 million. The option that reflects this outcome is the one stating an increase of $1.5 million.

BU.231.710.51.FA25 The Final Exam

A bank has $500 millionin rate-sensitive assetsand, 400million in rate-sensitive liabilities within a one-year time horizon. If interest rates increase by 1.5% (150 basis points), what is the predicted change in annual net interest income?

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