THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 369

CHAPTER 13 A PP LI CATI O N Banking and the Management of Financial Institutions 337 Duration Analysis Suppose that a bank s average duration of assets is 2.70 years and its average duration of liabilities is 1.03 years The bank manager wants to know what happens when interest rates rise from 10% to 11% The total asset value is $100 million, and the total liability value is $95 million Use Equation to calculate the change in the market value of the assets and liabilities Solution With a total asset value of $100 million, the market value of assets falls by $2.5 million ($100 million * 0.025 $2.5 million) %*P where DUR i i duration change in interest rate interest rate DUR 0.11 0.10 *i i 2.70 0.01 0.10 Thus %*P 0.01 0.10 2.70 0.025 2.5% With total liabilities of $95 million, the market value of liabilities falls by $0.9 million ($95 million * 0.009 $0.9 million) %*P where DUR duration i change in interest rate i interest rate Thus %*P 1.03 DUR 0.11 0.10 0.01 0.10 *i i 1.03 0.01 0.10 0.009 0.9% The result is that the net worth of the bank would decline by $1.6 million ( $2.5 million [ $0.9 million] $2.5 million $0.9 million $1.6 million)