| Course | FIN-3820 Risk Management |
|---|---|
| Module | Module 2 |
| Paper type | Written assignment 2: financial instruments and interest rate risk |
| Length | About 645 words, 5 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | B.S.B.A. in Finance |
| Updated | October 2026 |
Free sample paper for FIN 3820 Module 2
Short Deposits, Long Mortgages: Measuring and Hedging a Community Bank's Interest Rate Risk
Student Name
B.S.B.A. in Finance, Thomas Edison State University
FIN-3820: Risk Management
Mentor Name
Month Day, Year
Short Deposits, Long Mortgages: Measuring and Hedging a Community Bank's Interest Rate Risk
The Repricing Gap
The repricing gap compares assets and liabilities that will reprice within a period, here one year. Duration, first defined by Macaulay (1938), measures a bond's sensitivity to rates, and Stulz (1996) argues that risk management should focus on avoiding costly lower-tail outcomes rather than on removing all variance.
With a negative gap, more liabilities than assets reprice. A one-percentage-point rise in rates would raise interest expense on $560 million while raising income on only $420 million, cutting net interest income by about $140 million × 0.01 = $1.4 million a year, against current net interest income of about $38 million. A fall in rates would raise it by the same amount. Gap analysis is simple and intuitive, but it ignores timing within the period, assumes all rates move together and says nothing about the value of longer assets (Hull, 2023).
| One-year horizon | Amount |
|---|---|
| Rate-sensitive assets: variable loans, short securities, loans maturing | $420 million |
| Rate-sensitive liabilities: savings, money market and short certificates | $560 million |
| Repricing gap | −$140 million |
Duration and the Duration Gap
Duration measures the sensitivity of a security's value to interest rates. The community bank's duration gap compares how long its assets and liabilities are, weighting liabilities by their share of assets:
DGAP = DA − (L / A) × DL = 4.2 − (1.08 / 1.20) × 1.6 = 2.76 years,
where assets are $1.20 billion with a duration of 4.2 years and liabilities $1.08 billion with a duration of 1.6 years. For a rate shift, the bank's economic value of equity moves by roughly −DGAP × A × Δy / (1 + y). For a one-point rise from 5 percent:
ΔE ≈ −2.76 × $1.20 billion × 0.01 / 1.05 = −$31.5 million.
With equity of $120 million, a one-point rise would reduce the bank's economic value by about 26 percent, and a two-point rise by roughly half, beyond the 15 percent limit proposed in the board's risk appetite.
Two Views, One Problem
The gap and duration measures look at different horizons. Net interest income captures the next year's earnings; economic value captures the present value of all future cash flows. Both say the same thing: Pine Barrens loses when rates rise. Duration, like gap analysis, has limits. It is a linear approximation, so it misstates large rate changes because of convexity, and it ignores options embedded in the balance sheet: borrowers prepay mortgages when rates fall, and depositors move money when rates rise, both of which work against the bank.
Hedging With an Interest Rate Swap
An interest rate swap exchanges fixed-rate payments for floating-rate payments on a notional principal. By entering a pay-fixed, receive-floating swap, the bank effectively converts part of its fixed-rate mortgages into floating-rate assets: when rates rise, the floating payments it receives increase, offsetting the higher cost of deposits. A five-year pay-fixed swap has a duration of roughly −4.3 years for the fixed payer per dollar of notional. To cut the duration gap by about 1.5 years, the bank needs a swap reducing asset-weighted duration by 1.5 × $1.20 billion = $1.8 billion dollar-years, or a notional of about $1.8 billion / 4.3 ≈ $420 million.
A swap of that size would reduce the loss from a one-point rise to roughly $14 million, about 12 percent of equity, within the board's limit. The cost is that the bank gives up some gain if rates fall, and it takes on counterparty credit risk, reduced by clearing the swap through a central counterparty.
Recommendation
Pine Barrens should adopt economic value of equity as its primary long-term measure, with net interest income as a short-term check, run both under parallel and non-parallel rate shocks each quarter and enter pay-fixed swaps of about $400 million, phased in, to bring its exposure within the board's limit.
References
Hull, J. C. (2023). Risk management and financial institutions (6th ed.). Wiley.
Macaulay, F. R. (1938). Some theoretical problems suggested by the movements of interest rates, bond yields and stock prices in the United States since 1856. National Bureau of Economic Research.
Stulz, R. M. (1996). Rethinking risk management. Journal of Applied Corporate Finance, 9(3), 8-25. https://doi.org/10.1111/j.1745-6622.1996.tb00295.x
FIN 3820 Module 2 instructions, in plain terms
Interest rate risk is the second module's subject. Expect problems on repricing gaps, duration and convexity, the duration gap, how rate moves hit net interest income and economic value, and the use of swaps, futures or other instruments to hedge. Macaulay's original work on duration underlies the measures. The bank's balance sheet here is a composite with round figures; your problems will supply their own. Expect repricing gap and duration gap calculations for a bank balance sheet and questions on how swaps can change its exposure. Expect to compute repricing gaps and duration, estimate the effect of a rate change on net interest income and economic value, and explain how a bank can hedge with swaps or futures.
Inside the FIN 3820 Module 2 example
The paper computes the one-year repricing gap in a table and its effect on net interest income, then notes the method's limits. The duration section computes the duration gap and the change in economic value of equity, expressed as a share of equity and compared with the board's limit. A section reconciles the two measures and their shared limitations, including convexity and embedded options. The swap section explains how a pay-fixed swap works and sizes the notional needed to narrow the gap, and the recommendation sets out measures and a hedge. The gap results are translated into the change in net interest income and in equity value for a stated rate move. The swap recommendation is sized to the gap.
FIN 3820 Module 2 rubric: what earns full marks
Gap and duration figures for the community bank carry this grade. Mentors look for correct gap and duration calculations, interpretation of the results relative to equity and earnings and an accurate explanation of how a swap changes the exposure. Recognizing the limits of each measure and sizing a hedge with stated assumptions show the depth expected. Clear presentation of formulas and inputs helps the mentor credit each step. Answers that compute both gaps correctly and explain what each measures, earnings or economic value, show understanding. A swap recommendation that matches the size of the gap earns credit.
Common FIN 3820 Module 2 mistakes, and how to avoid them
Interest rate risk answers lose points for computing the duration gap without the liabilities-to-assets ratio, for stating losses in dollars without comparing them with equity and for recommending a swap without saying which side the bank should take. Show every input. Express results as a share of earnings and equity. Explain why the bank pays fixed or receives fixed. Say where gap and duration measures break down. A free first sample of your own FIN-3820 Module 2 problems is available on request. State which assets and liabilities reprice within the gap period, and show the duration of each item used. Explain whether the bank gains or loses when rates rise, in one sentence.
Write yours, or have the desk draft it
This paper is an original model document written by our desk, not a submitted student paper and not an official Thomas Edison State University document. Read it for the moves, then write your own to the instructions in your classroom. If you want one built to your exact prompt and rubric, the first custom sample is free and arrives in 24 to 48 hours.
More FIN 3820 and B.S.B.A. in Finance sample papers
- FIN 3820 Module 1: Written Assignment: Why Firms and Banks Manage Risk
- FIN 3820 Module 3: Written Assignment: Volatility, Correlation and Value at Risk
- FIN 3820 Module 4: Midterm Project: Describing and Evaluating Value at Risk
- FIN 3820 Module 5: Written Assignment: Measuring Credit Risk in a Loan Portfolio
- FIN 3820 Module 6: Written Assignment: The Credit Crunch and a Bank Stress Test
- FIN 3820 Module 7: Written Assignment: Operational, Liquidity and Model Risk
- FIN 3820 Module 8: Final Project: Fuel, Liquidity and Risk Management at Southwest Airlines
- FIN 3140 Module 3: Written Assignment: Profitability Ratios and Seasonal Working Capital
- FIN 3210 Module 3: Written Assignment: Diversification, the Efficient Frontier and the CAPM
- FIN 3340 Module 3: Written Assignment: Forwards, Futures and Options on the Peso
- FIN 3310 Module 5: Written Assignment: Mortgage Markets and Foreign Exchange
FIN 3820 Module 2 questions, answered
Where can I find a free FIN 3820 Module 2 sample paper?
The community bank paper above computes a repricing gap, a duration gap and the change in economic value of equity, and sizes an interest rate swap hedge.
What is the duration gap?
The duration of assets minus the duration of liabilities times the ratio of liabilities to assets, measuring equity's sensitivity to rates.
What does a negative repricing gap mean?
More liabilities than assets reprice within the period, so rising rates reduce net interest income.
How does a pay-fixed interest rate swap reduce risk for a bank?
It converts fixed-rate assets into floating-rate exposure, so the bank receives more when rates rise, offsetting higher funding costs.
What are the limits of duration?
It is a linear approximation that misstates large rate moves and ignores embedded options such as prepayments.