Dr. Sudhakar Raju
FN 6700
ASSIGNMENT 5 -ASSET LIABILITY MANAGEMENT (ALM)
1.) What is the repricing gap? In using this model to evaluate interest rate risk, what is
meant by rate sensitivity? On what financial performance variable does the repricing
model focus?
2.) What is a maturity bucket in the repricing model? Why is the length of time selected
for repricing assets and liabilities important when using the repricing model?
3.) Calculate the repricing gap and the impact on net interest income of both a 1%
increase and a 1% decrease in interest rates for each of the following positions:
a. Rate-sensitive assets = $200 million; Rate-sensitive liabilities = $100 million.
b. Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million.
c. Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million.
4.) What is the gap ratio? What is the value of this ratio to interest rate risk managers
and regulators?
5.) What is the difference between book value accounting and market value accounting?
How do interest rate changes affect the value of bank assets and liabilities under the
two methods? What is marking to market?
6.) Why is it important to use market values as opposed to book values when evaluating
the net worth of an FI? What are some of the advantages of using book values as
opposed to market values?
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7.) The following is a simplified FI balance sheet:
Assets
Loans
Total Assets
$1,000
0
$1,000
Liabilities and Equity
Deposits
Equity
Total Liabilities & Equity
$850
$150
$1,000
The average maturity of loans is four years, and the average maturity of deposits is
two years. Loan and deposit balances are reported as book value, zero-coupon
items.
a.) Assume that interest rates on both loans and deposits are 9%. What is the
market value of equity?
b.) What must be the interest rate on deposits to force the market value of equity
to be zero? What economic market conditions must exist to make this situation
possible?
c.) Assume that interest rates on both loans and deposits are 9%. What must be the
average maturity of deposits for the market value of equity to be zero?
8.) The following is a simplified FI (Financial Institution) balance sheet:
Assets
Total Assets [5]
$100
Total Assets
$100
Liabilities and Equity
Liabilities [3]
Equity
Total Liabilities & Equity
$90
$10
$100
The Macaulay duration of the assets and liabilities is within parentheses. Assume that
assets are fixed rate assets and liabilities are fixed rate liabilities. Initially, interest rates
are at 10%. Suppose rates rise to 11%.
a.) What is the dollar change in TA? TL? What is the form of the new balance sheet?
What is the new value of TE? What is the change in TE (∆Equity)?
b.) What is the Duration Gap? Confirm the value you got for the change in TE from part
(a) by using the Duration Gap approach.
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9.) The balance sheet for GBI Bank is presented below ($ millions):
Assets
Cash
Federal funds
Loans (floating)
Loans (fixed)
Total assets
Liabilities and Equity
Core deposits
Federal funds
Euro CDs
Equity
Total liabilities & equity
$30
20
105
65
$220
$20
50
130
20
$220
NOTES TO THE BALANCE SHEET: The Fed funds rate is 8.50%, the floating loan rate is
LIBOR + 4%, and currently LIBOR is 11%. Fixed rate loans have five-year maturities,
are priced at par, and pay 12% annual interest. Core deposits are fixed-rate for 2 years
at 8% paid annually. Euros currently yield 9%. .
a.) What is the duration of the fixed-rate loan portfolio of GBI Bank?
b.) If the duration of the floating-rate loans and fed funds is 0.36 years, what is the
duration of GBI’s assets?
c.) What is the duration of the core deposits if they are priced at par?
d.) If the duration of the Euro CDs and Fed funds liabilities is 0.401 years, what is the
duration of GBI’s liabilities?
e.) What is GBI’s duration gap? What is its interest rate risk exposure?
f.) What is the impact on the market value of equity if the relative change in all market
interest rates is an increase of 1% (100 basis points)?
g.) What is the impact on the market value of equity if the relative change in all market
interest rates is a decrease of 0.50% (-50 basis points)?
h.) What variables are available to GBI to immunize the bank? How much would each
variable need to change to get the Duration GAP to equal 0?
10.) Hands Insurance Company issued a $97.20 million face value, 1-year, zero-coupon
note at 8% per annum. The proceeds were used to fund a $100 million, 2-year bond at
10% p.a. Immediately after these transactions were simultaneously closed, all market
interest rates increased by 1.50% (150 basis points).
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a.) What is the true market value of the loan investment and the liability after the
change in interest rates?
b.)What impact did these changes in market value have on the market value of the
equity?
c.) What was the modified duration of the loan investment and the liability at the time
of issuance? (i.e. before rates increased)
d.) Use these modified duration values to calculate the expected change in the value of
the loan and the liability for the predicted increase of 1.50% in interest rates.
e.) What was the modified duration gap of Hands Insurance Company after the issuance
of the asset and note? (i.e. before rates went up).
f.) What was the change in equity value predicted by the duration gap for the 1.50%
increase in interest rates?
g.) If the interest rate prediction had been available during the time period in which the
loan and the liability were being negotiated, what suggestions would you offer to
reduce the possible effect on the equity of the company? What are the difficulties in
implementing your ideas?
11.) Two banks are being examined by the regulators to determine the interest rate
sensitivity of their balance sheets. Bank A has assets composed solely of a 10-year, 12%,
$1 million loan with an estimated Macaulay duration of 6.33. The loan is financed with a
10-year, 10%, $1 million CD with an estimated duration of 6.76. Bank B has assets
composed solely of a 7-year, 12% zero-coupon bond with a current market value of
$894,006.20 and a maturity/principal value of $1,976,362.88. The bond is financed with
a 10-year, 8.275% coupon, $1,000,000 face value CD with an YTM of 10% and an
estimated Macaulay duration of 7. The loan and the CDs pay interest annually, with
principal due at maturity.
a). If market interest rates increase 1% (100 basis points), how do the market values of
the assets and liabilities of each bank change? That is, what will be the net affect on the
market value of the equity for each bank?
b). What accounts for the differences in the changes of the market value of equity
between the two banks?
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c). Estimate the changes in asset, liability and equity value for the expected change in
interest rates using the Duration approach.
12.) The following balance sheet information is available (amounts in $ thousands and
duration in years) for a financial institution:
T-bills
T-notes
T-bonds
Loans
Deposits
Federal funds
Equity
Amount
$90
55
176
2,274
2,092
238
715
Duration
0.50
0.90
4.39
7.00
1.00
0.01
Treasury bonds are 5-year maturities paying 6% semiannually and selling at par.
a.) What is the duration of total assets?
b.) What is the duration of total liabilities?
c.) What is the leverage-adjusted duration gap? What is the interest rate risk exposure?
d.) What is the impact on the market value of equity caused by an interest rate increase
of 0.50% (50 bp)?
e.) What is the impact on the market value of equity caused by an interest rate decrease
of .50% (50 bp)?
f.) What variables are available to the financial institution to immunize the balance
sheet? How much would each variable need to change to attain a duration GAP of zero?
13.) Discuss three criticisms of using the duration based GAP model as a device to
immunize the portfolio of a financial institution.
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