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 **______**

**Liabilities**

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-adjusted**duration 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.**