Chapter 1:
Interest Rate Risk (Part 1)
Reading materials
• Saunders, chapters 7&8
Content
• Interest Rate Risk
• Interest rate and Profit
• GAP
• Repricing Model
Interest Rate Risk
• The level of interest rate
• Loanable Funds Theory
• Movements of interest rate
Determination
of Equilibrium
Interest Rates
The Effect on Interest Rates
from a Shift in the Demand Curve for or Supply Curve of
Loanable Funds
Movements of interest rate
• Do interest rates stay the same?
• Why do interest rates change?
• Why do financial institutions care about the level and
volatility of interest rates?
Vietnam 10-Year Government Bond Yield
(https://tradingeconomics.com/vietnam/government-bond-yield)
Interest Rate Risk
• Interest rate risk exists when earnings are sensitive to the movements
of interest rates.
• A bank exposes to interest rate risk when its profit and net worth are
negatively impacted by interest rate movements.
• But how can interest rate movements impact a bank’s profit and net
worth?
• The risk incurred when the maturities of assets and liabilities are mismatched.
Interest rate and profit
How interest rate movements impact a bank’s profit?
• A bank’s assets and liabilities have maturities.
• Assets and liabilities bear interest rates during their life cycles.
• A mismatch in maturities between assets and liabilities lead to frequent
change in interest income and interest expense
→ Change in net interest income
Refinancing risk vs. reinvestment risk
• Refinancing risk
• The risk that the cost of rolling over or reborrowing funds will rise
above the returns being earned on asset investments.
• Reinvestment risk
• The risk that the returns on funds to be reinvested will fall below
the cost of the funds.
Example: Refinancing risk
Example: Refinancing risk
• At the end of 2023, a bank is having a 2-year loan of $100 million with
fixed interest rate of 6%
• The loan is financed with 1-year deposits worth $100 million, deposit
rate of 2%
• At the end of 2024, all market interest rates now increase by 1
percentage point.
→ How the bank’s net interest income can be impacted?
Example: Reinvestment risk
Example: Reinvestment risk
• At the end of 2023, a bank is having a 1-year loan of $100 million with
fixed interest rate of 6%
• The loan is financed with 2-year deposits worth $100 million, deposit
rate of 2%
• At the end of 2024, all market interest rates now increase by 1
percentage point.
→ How the bank’s net interest income can be impacted?
Interest rate GAPs
Interest rate gaps
Liquidity gap
• A projected liquidity gap generates an interest rate gap because
excess funds will be invested, or deficits will be funded, at future
dates at unknown interest rates.
• A projected deficit of funds = an interest-sensitive liability
• A projected excess of funds = an interest-sensitive asset
Rate-sensitive assets/liabilities
• Rate sensitivity means that the asset or liability is repriced at or near
current market interest rates within a certain time horizon (or
maturity bucket).
• A liability is rate-sensitive if it is repriced in a certain time frame
• The liability (e.g., deposit) matures, and the bank must raise new funds with
new interest rate
• The liability has float interest rate that will be changed during the time frame
• Similar for assets
Examples from hypothetical balance sheet
• RSAs
• Short-term consumer loans. Repriced at year-end, would just make one-year
cutoff
• Three-month T-bills repriced on maturity every 3 months
• Six-month T-notes repriced on maturity every 6 months
• 30-year floating-rate mortgages repriced (rate reset) every 9 months
• RSLs bucketed in same manner as RSAs
Simple balance sheet (in millions of dollars)
Maturity Buckets
• The central bank may require commercial banks to report quarterly
on their call reports for assets and liabilities with these maturities:
1. One day.
2. More than one day to three months.
3. More than three months to six months.
4. More than six months to twelve months.
5. More than one year to five years.
6. More than five years.
Example
Example
Determining Rate Sensitive Items for First National
Bank with a maturity bucket of one year.
Assets
Liabilities
• Assets with maturity less than one
• money market deposits
year
• variable-rate CDs
• variable-rate mortgages
• short-term CDs
• short-term commercial loans
• Federal funds
• portion of fixed-rate mortgages (20%) • short-term borrowings
• portion of checkable deposits (10%)
• portion of savings (20%)
Repricing GAP
• Difference between the book value of rate-sensitive assets and ratesensitive liabilities in a certain maturity bucket
RSAi : rate-sensitive assets in maturity bucket i
RSLi : rate-sensitive liabilities in maturity bucket i
GAP for different maturity buckets
Cumulative GAP
• Cumulative Gap of one year counts RSA and RSL from one day to 12 months.
Repricing model
When interest rates change, interests from RSA and RSL will change
∆NIIi: Change in net interest income in maturity bucket i
∆Ri: Change in the level of interest rates impacting assets and liabilities
in the ith bucket i
GAPi: Dollar size of the gap between the book value of rate-sensitive
assets and rate-sensitive liabilities in maturity bucket i
Maturity Adjusted GAP
Maturity Adjusted GAP
where GMA stands for the maturity-adjusted gap, i.e. the difference between ratesensitive assets and liabilities, each weighted for the time period from the date of
maturity or repricing to the end of the gapping period (here set at one year).
Example
Marginal vs. Cumulative GAPs
• cumulative gaps (Gt1, Gt2, Gt3): the difference between assets and liabilities that
call for renegotiation of interest rates by a set future date (t1, t2 > t1, t3 > t2, etc.)
• period or marginal gaps (G t1, G t2, G t3): the difference between assets and
liabilities that renegotiate rates in a specific period of time in the future (e.g. from
0 to t1, from t1 to t2, etc.)
Example: Marginal vs. Cumulative GAPs
Weighted Cumulative GAP
The repricing model
• The bank manager can estimate cumulative gaps (CGAPs) over various
repricing categories or maturity buckets. A common cumulative gap
of interest is the one-year repricing gap.
CGAP effect
• Assume equal change in interest rates on RSA and RSL
• How CGAP affects the relationship between interest rates and NII
CGAP effect
• In practice, we see unequal changes in in
interest rates on RSA and RSL (data)
• Change in interest rate spread affects NII
Unequal changes in rates on RSAs and RSLs: The spread effect
Unequal changes in rates
• If changes in rates on RSAs and RSLs are not equal, the spread
changes;
• The change in NII is
DNII = (RSA × DRRSA ) - (RSL × DRRSL )
Example: RSA rate rises by 1.2% and RSL rate rises by 1.0%
DNII = D interest revenue - D interest expense
= ($155 million × 1.2%) - ($155 million × 1.0%) = $310,000
The spread effect
Weakness of the repricing model
• Ignores market value effects of interest rate change: as interest
rates change, value of fixed-income instruments change too
(why?)
• Ignore runoff cashflows: Periodic payments/early payments the
bank received from insensitive assets that still has to be
reinvested.
Weakness of the repricing model
• Over-aggregative:
information within a
maturity bucket is lost
Summary: Interest rate risk management
Step 1: Measure exposure to interest rate risk
– Determine amount of A&Ls that are rate sensitive (income gap, also
called repricing / funding gap)
– Determine the average maturity of A&Ls (duration gap)
Step 2: Analyze what will happen if interest rates change
Step 3: Immunize the portfolio
– Increase / decrease amount of assets that are rate sensitive
– Increase / decrease average maturity of assets to immunize portfolio
Problem sets
• Chapter 8: 6, 7, 8, 9, 12, 14, 15, 16, 18, 19, 20, Minicase.