1. You are asked to determine the market value(mark-to-market) balance sheet for Angus State Bankand loan duration (amounts in $ thousands and duration in years):
Book Value Market Value
Assets Amount Amount Duration
T-bills $ 180 $ 180 0.50
Loans* 5,000 ______ _____
Total Assets 5,180 ______
Deposits 4,184 4,184 0.50
Total Liabilities 4,184 4,184
Equity 996 ______
Total Lia and NW 5,180 ______
*Since this is a simple bank, it has only one type of loan. The loan has a $5,000 book value (current outstanding principal), amortized loan with annual payments, an interest rate of 6.5 percent, and 20-years to maturity. Similar amortized loans today (market interest rate for similar loans) have an interest rate of 7 percent which, is the market yield.
a.Using Excel, determine the market value and duration of the loan and fill in the blanks in the balance sheet above. Please include a copy of your Excel Spreadsheet with your completed exam (you can copy and paste as a picture).
b. What is the average duration of all the assets and what is the average duration of all the liabilities?
Average Duration of Assets: = ______ years
Average Duration of Liabilities:[4,184*0.5]/4184 = 0.50 years
c.What is the leverage-adjustedduration gap? Is Angus State Bank exposed to interest rate risk? Is it exposed if interest rate increase or decrease?
Leverage-adjusted duration gap (DG) = -[DA – kDL]= = ___________ years
The duration gap is _______ years, indicates that an increase in interest rates will lead to an increaseor decrease in net worth. Circle the correct change in net worth
d. What is the forecasted impact on the market value of equity caused by a relative 1.5 percent upward shift in the entire yield curve? [i.e.,Dr/(1+r) = 0.0150]?
The market value of the equity will change by the following:
MVE = -DG * (A) * r/(1 + r) = ______ (_________)(0.015)= $______________.
e.What variables are available to the financial institution to immunize or at least reduce interest rate risk exposure on the balance sheet? Taking one variable at a time, how much would each variable need to change to get DGAP equal to 0?
To immunize the institution for interest rate risk, the Leverage Adjusted DG needs to be zero:
DG = DA–kDL= 0
The choice is to make the duration of assets equal to:
DA= (4184/4987.37)0.50=0.42 years
or the duration of liabilities equal to:
DL= _______________ = ____________ years
Or some combination thereof. Obviously, for any depository institution, this cannon occur, thus the next most cost effect way to reduce interest rate risk is using interest rate swaps.