Duration

$billions (years)

Assets

PrimeRate Loans (rates set monthly) 160 1.0

2Year Car Loans 175 2.0

30Year Mortgages 170 7.0

Total Assets (A) 505 ?

Liabilities and Equity

Super Now Checking Accounts (rates set monthly) 200 1.0

6Month Certificates of Deposit 140 .5

3Year Certificates of Deposit 125 3.0

Total Liabilities (L) 465 ?

Equity (E) 40

Total Liabilities (L) and Equity (E) 505

a- What is the duration of assets, D_A, and liabilities, D_L ?

D_A =(160/505)*1.0+(175/505)*2.0+(170/505)*7.0=.3168+.6931+2.3564=3.36 yrs

D_L =(200/465)*1.0+(140/465)*.5+(125/465)*3.0=.4301+.1505+.8064=1.38 yrs

b-Given the duration imbalance of assets and liabilities, what is the loss in market value of assets, liabilities and equity as a result of an interest rate rise by 200 bp?

Compute the repricing gap for the bank using those assets and liabilities repricing, maturing in 2 years or less or with a duration of 2 years or less. From this information, will the bank benefit or be hurt by a 200 basis point rise in interest rates on assets and liabilities?

d. Find the duration of assets, assuming the duration of liabilities remains the same, that will fully net worth immunize the bank from interest rate changes? Define net worth immunization and state the advantages and disadvantages of using it and asset/liability duration as a means of mitigating interest rate risk. In the above balance sheet, which asset is most responsible for the duration mismatch? Define your terms.