# 99 econ 350 us financial systems markets and

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Econ 350 U.S. Financial Systems, Markets and Institutions Class 10 As an example, suppose that RateBank has the following simplified balance sheet: RATEBANK assets liabilities Rate-sensitive assets \$20 mil Rate-sensitive liabilities \$50 mil Fixed-rate assets \$80 mil Fixed-rate liabilities \$50 mil \$100 mil \$100 mil Given the bank’s financial position, suppose that interest rates rise by 5%. This increase in interest rates will affect the value of rate-sensitive assets and liabilities. If interest rates rise by 5% income on assets increases by \$1 million (5% x \$20 mil) payments on liabilities increases by \$2.5 million (5% x \$50 mil) bank profits decline by \$1.5 million (\$1 mil - \$2.5 mil) So if interest rates increase by 5%, then bank profits will decline by \$1.5 million. Conversely, if interest rates decrease by 5%, then bank profits will increase by \$1.5 million. The moral of the story is this: If a bank has more rate-sensitive liabilities than rate-sensitive assets, then a rise in interest rates will reduce bank profits. Gap Analysis Gap analysis: is a tool to measure the effects of interest rate changes by measuring the difference between rate-sensitive assets and rate-sensitive liabilities. Gap analysis is a fairly simple, straightforward model. First, we define the Gap: Gap = Rate sensitive assets – Rate-sensitive liabilities . The change in bank profit is then given by the change in interest rate times the gap. ∆Π = i x Gap In our example, Gap = \$20 mil - \$50 mil = - \$30 mil So ∆Π = 5% x (-\$30 million) = -\$1.5 million, as shown above. 100
Econ 350 U.S. Financial Systems, Markets and Institutions Class 10 Once again, we show that an increase in interest rates of 5% leads to a decline in bank profits of \$1.5 million. Duration Analysis Another measure of the sensitivity of bank profits is known as duration analysis. Duration analysis: is a tool to measure interest rate risk by examining the sensitivity of the market value of assets and liabilities to changes in interest rates. Let V = market value of security i = interest rates DUR = duration. Where Duration : is the average lifetime of a security’s stream of payments. It consists of the average weighted duration of an institution’s assets and liabilities. It measures how net worth responds to changes in interest rates. Then % V - % i x DUR Duration analysis provides a way to measure the effects of changes in interest rates on the market value of a bank’s assets and liabilities, and in consequence, the effects of changes in interest rates on a bank’s net worth. For example, suppose that for RateBank above, the average duration of its assets is 4 years, while the average duration of its liabilities is 2 years. Then if interest rates increase by 5%, the following changes occur: Assets: the value of assets changes by % V - % i x DUR = -5% x 4 = -20% So the value of assets changes by -20% x 100 = -20 million.

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