A bank has hired you as a consultant to advise it on its interest rate exposure.

Question

A bank has hired you as a consultant to advise it on its interest rate exposure. The bank has an asset portfolio of $1,000,000 with a duration of five years, and the portfolio is currently yielding 12%. This asset portfolio is funded by a liability portfolio, also worth $1,000,000 with a duration of 1.5 years and which is yielding 10.5%. Your problem is to advise the bank on its risk exposure in case interest rates change by 1% in either direction. Analyze the resulting position of the bank for both of these cases.

Explanation / Answer

Duration is a measure of risk exposure to interest rate movements. In this case we want the modified duration which is equal to Duration/1+yield Modified duration measures price fall/increase for a 1% increase/decrease in yield. Duration for assets: = 5/1.12 = 4.46 Duration for liabilities: 1.5/1.105 = 1.35 If yields rise by 1% the asset portfolio will fall by: 1,000,000 *4.46*1% = 44,600 Thus it will be worth: 950,000 The liabilities would fall by: 1,000,000 *1.36*1% = 13,600 Thus it will be worth 986,400 If yields fall by 1% the asset portfolio will increase by: 1,000,000 *4.46*1% = 44,600 Thus it will be worth: 1,044,600 The liabilities would increase by: 1,000,000 *1.36*1% = 13,600 Thus it will be worth 1,013,600 So the bank is vulnerable to a yield increase because it will make their liabilities worth more than they assets.

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