Gap Analysis: The Original IRR Tool

What Is Gap Analysis?

Gap analysis is the simplest tool for measuring interest rate risk. It answers one question: "At what times do my assets and liabilities reprice, and what's the net exposure?"

It's been around since the 1970s, and despite its simplicity, it's still the foundation of how most banks talk about IRR. Regulators use it, boards understand it, and it's the first model most new ALM analysts encounter.

How It Works

Gap analysis starts by organizing your balance sheet into repricing buckets — time periods when assets and liabilities are expected to change interest rates.

Typical buckets:

• 0–1 month


• 1–3 months


• 3–6 months


• 6 months–1 year


• 1–2 years


• 2–5 years


• 5–10 years


• >10 years

For each bucket, you calculate:

Rate Repricing Gap = Assets repricing in bucket - Liabilities repricing in bucket

If the gap is positive (more assets repricing than liabilities), you benefit when rates rise and are hurt when rates fall. If the gap is negative (more liabilities repricing than assets), you're hurt when rates rise.

Practical Example

Imagine this simplified balance sheet:

| Item | Amount | Repricing |
|------|--------|----------|
| Assets | | |
| Fixed-rate mortgages | $50B | >10 years |
| Floating-rate C&I loans (SOFR + 2.5%) | $20B | 3 months |
| Securities (2-5 year Treasuries) | $15B | 1-2 years |
| Cash | $5B | Daily (reprices immediately) |
| Liabilities | | |
| Deposits (non-interest-bearing) | $30B | Non-repricing |
| Money market deposits (~30bp to SOFR) | $30B | 1 month |
| CDs (1-year, fixed) | $20B | 1 year |
| Wholesale funding (3-month LIBOR + 90bps) | $15B | 3 months |
| Equity | $10B | — |

Now bucket the repricing:

| Repricing Bucket | Assets | Liabilities | Gap |
|---|---|---|---|
| 0-1 month | $5B (cash) + $30B (MMA) = $35B | $30B (NIB) = $30B | +$5B |
| 1-3 months | $20B (C&I) + (part of MMA) = ~$20B | $15B (wholesale) = $15B | +$5B |
| 3-6 months | — | (part of CDs) = ~$5B | -$5B |
| 6-12 months | — | (rest of CDs) = ~$15B | -$15B |
| 1-2 years | $15B (securities) | — | +$15B |
| 2-5 years | — | — | — |
| 5-10 years | — | — | — |
| >10 years | $50B (mortgages) | — | +$50B |

Cumulative gap (often presented for easy reading):

| Period | Cumulative Gap |
|---|---|
| 0-1 month | +$5B |
| 0-3 months | +$10B |
| 0-6 months | +$5B |
| 0-12 months | -$10B |
| 0-24 months | +$5B |
| 0-10 years | +$5B |
| 0-infinite | +$50B |

Interpretation: You have a positive gap at 3 months (+$10B) and a negative gap at 12 months (-$10B). In the near term, you benefit from rising rates. In the medium term (6-12 months), you're exposed to rising rates.

The NII Impact Calculation

Once you have the gap, you can estimate the NII impact of a rate change:

Change in NII = Gap × Change in interest rates

Using our example, under a +100bp shock:

| Period | Gap | Rate Change | NII Impact |
|---|---|---|---|
| 0-1 month | +$5B | +100bp | +$50M (annualized) |
| 1-3 months | +$5B | +100bp | +$50M |
| 3-6 months | -$5B | +100bp | -$50M |
| 6-12 months | -$15B | +100bp | -$150M |

Total 12-month NII impact: ~-$100M (negative, because the negative gap at 6-12 months dominates).

If the bank's annual NII is $2B, this is a 5% decline in NII — well within acceptable tolerances for most banks.

Why Gap Analysis Is Beautiful (and Why It's Limited)

Strengths

1. Intuitive: Anyone can understand a repricing gap. You don't need a PhD in finance.
2. Easy to calculate: You can build a gap analysis in Excel in a few hours.
3. Clear governance: Boards can set a simple target: "Gap at 12 months should be between -$10B and +$10B."
4. Foundation for other models: Gap analysis is the baseline; more sophisticated models build on it.
5. Regulatory comfort: Regulators understand gap analysis. It shows up in call reports and stress testing frameworks.

Limitations

1. Assumes static repricing: A 1-year CD is assumed to reprice on its maturity date. But in reality, if rates are attractive, you might lose the deposit before maturity (prepayment risk). If rates are unattractive, you might extend it (renewal risk). The "1-year" assumption is a simplification.

2. Ignores embedded options: A mortgage with a prepayment option isn't correctly modeled as repricing in 30 years. When rates fall, mortgagors refinance, and that 30-year asset becomes a 6-month liability. Gap analysis misses this.

3. Ignores deposit stickiness: A non-interest-bearing deposit is modeled as non-repricing, which is technically true. But in practice, if rates rise 200bp and you don't raise your offering (because you're lazy or profitable), depositors leave. The "non-repricing" assumption breaks down.

4. Doesn't capture basis risk: Your loans reprice off SOFR, but your deposits reprice off Fed funds. There's a 5–10bp basis spread that varies. Gap analysis assumes the basis is constant.

5. Misses convexity: A symmetric ±100bp shock doesn't produce symmetric NII results. But gap analysis treats both directions the same.

6. No duration perspective: A 2-year repricing period is not the same as a 2-year duration. Duration accounts for reinvestment risk and convexity. Gap analysis doesn't.

How Banks Actually Use Gap Analysis

As a Screening Tool

Most ALM teams use gap analysis as a first-pass sanity check. If your 12-month cumulative gap is -$50B in a $200B balance sheet, you've got a problem. Gap analysis catches obvious mismatches quickly.

In Regulatory Reporting

The Federal Reserve's call report (Form FR Y-9C) requires banks to disclose repricing schedules in Schedules HC-R and HC-RI. These are gap analysis tables. Regulators and investors use them to benchmark your IRR profile.

For Board Communication

Most boards prefer gap analysis to more complex models. A chart showing cumulative repricing gaps over time is clear and actionable. "We have a +$15B gap at 0-3 months, which means we earn the float if rates rise, but we're exposed from months 3–12." That's language a board understands.

As a Constraint

Many banks set explicit gap constraints:

• "0-3 month cumulative gap: +/- $10B maximum"


• "3-12 month gap: +/- $15B maximum"


• "Cumulative gap to infinity: balanced (near zero)"

These constraints then drive liquidity management, asset/liability pricing, and business line targets.

The Evolution to More Sophisticated Models

Gap analysis has obvious limitations, which is why modern ALM teams also use:

• NII simulation (Module 33): Projects actual NII under multiple rate paths and behavioral scenarios, moving beyond static repricing assumptions.
• Key rate duration (Module 37): Captures how non-parallel curve movements affect both assets and liabilities.
• Economic value of equity (Module 36): Measures the true present-value impact of rate changes, not just 12-month earnings.
• Duration and convexity (Module 39): Explains why duration is more accurate than gap analysis for longer-term positions.

But gap analysis remains the foundation. Even banks with sophisticated models use gap tables internally. It's the lingua franca of IRR.

Key Takeaways

• Gap analysis is simple: organize your balance sheet by repricing dates and calculate the net asset gap.
• Use it as a screening tool and for board communication.
• Understand its limitations: it ignores options, basis risk, behavioral dynamics, and convexity.
• Don't rely on it alone. Supplement gap analysis with NII simulation, duration analysis, and EVE modeling.
• When you see a peer bank's gap table in their 10-K, you should be able to quickly assess their IRR profile.

In the next modules, we'll build on gap analysis with the more sophisticated tools that handle its limitations.

Gap Analysis: The Original IRR Tool — Deep Dive

Part 1: The Mathematics of Gap Analysis

The Simple Gap Formula

The fundamental equation of gap analysis is:

Δ NII = GAP × Δ r

Where:

• Δ NII = change in net interest income


• GAP = repricing gap (assets repricing minus liabilities repricing in a given period)


• Δ r = change in interest rates

This assumes:
1. The repricing occurs exactly as scheduled
2. The interest rate change is instantaneous and permanent
3. All other variables (volumes, spreads, prepayment rates) are constant
4. The relationship is linear (a 100bp change produces exactly 100x the impact of a 1bp change)

For most banks, these assumptions are reasonable for small shocks (±25–50bp) over short horizons (1–3 months). They break down for large shocks (>100bp) or long horizons (>12 months).

Cumulative vs. Incremental Gap

There are two ways to present gap analysis:

Incremental Gap: The gap for a specific repricing bucket

• Example: "In the 3-6 month bucket, assets repricing are $15B, liabilities repricing are $10B. Incremental gap = +$5B."

Cumulative Gap: The sum of all gaps up to and including a given bucket

• Example: "Through the 6-month bucket, cumulative gap = +$20B."

Cumulative gap is more useful for IRR because it captures the net exposure to parallel shifts in the entire yield curve up to that point.

Multi-Period Weighted Gap

A more sophisticated version of gap analysis uses weighted gaps to account for timing within a bucket:

Weighted Gap = Σ (Gap_i × Time_i)

Where Time_i is the midpoint of repricing bucket i (in years).

Example:

| Bucket | Gap | Midpoint (Years) | Weighted Gap |
|---|---|---|---|
| 0-1 month | +$5B | 0.042 | +$0.21B |
| 1-3 months | +$5B | 0.167 | +$0.84B |
| 3-6 months | -$5B | 0.375 | -$1.88B |
| 6-12 months | -$15B | 0.75 | -$11.25B |
| 1-2 years | +$15B | 1.5 | +$22.50B |
| 2-5 years | $0 | 3.5 | $0 |
| Total Weighted Gap | — | — | +$9.42B-years |

This weighted gap (measured in "dollar-years") gives you a rough duration-like measure. A weighted gap of +$9.42B-years on a $100B balance sheet implies roughly +0.09 years of duration risk.

The Assumption: Linear Repricing

Gap analysis assumes that an asset or liability reprices on a fixed date. In reality, repricing is a process:

Example: C&I Loan

• Original terms: $10M, SOFR + 250bps, repricing quarterly


• Current quarter: SOFR is 5.25%, so the rate is 7.75%


• In 3 months: SOFR reprices (unknown today; assume 5.50%), rate becomes 8.00%

Gap analysis says: "This loan reprices in 3 months." Correct, but the size of the repricing is uncertain because SOFR is unknown.

Example: Fixed-Rate Mortgage

• Original terms: $250K, 6.5% fixed, 30-year


• Gap analysis says: "This reprices in 30 years."


• Reality: If rates fall to 4% in 5 years, the borrower refinances, and you lose the asset entirely.

Gap analysis misses this prepayment risk entirely.

Part 2: The Behavioral Complications

Deposit Repricing and the Beta Problem

This is where gap analysis becomes tricky and requires judgment.

Definition: A deposit beta is the percentage of a market rate change that is passed through to the customer.

Example:

• You offer a savings account paying 4.50% when SOFR is 5.25%


• SOFR rises to 5.50% (25bp increase)


• You raise the savings rate to 4.70% (20bp increase)


• Beta = 20bp / 25bp = 0.80

Deposit betas are not constant. They depend on:

1. Competitive environment: In a tight labor market with tech companies raising money, betas can be 100%+. In a slack environment, they can be 10–20%.

2. Rate level: At zero or near-zero rates, betas are near-zero (you can't go lower). At high rates, betas are higher as customers have alternatives.

3. Direction of rates: In a rising-rate environment, betas on deposits are typically 50–80% (you gradually raise rates to retain deposits). In a falling-rate environment, betas are 20–40% (you cut rates slowly; depositors don't demand all the benefit).

4. Deposit type:
- Non-interest-bearing deposits: Beta ~0% (they earn nothing regardless)
- Money market deposits: Beta ~80–100% (competitive, rate-sensitive)
- Savings deposits: Beta ~40–60%
- CDs: Beta = 100% (they're fixed at origination; at maturity, the new rate is whatever the market is)

5. Customer type: Institutional deposits have higher betas (they monitor rates closely). Consumer deposits have lower betas.

How Beta Affects Gap Analysis

Consider a $30B deposit base:

• $10B non-interest-bearing (beta 0%)


• $10B savings deposits (beta 50%)


• $10B money market deposits (beta 90%)

Under a +100bp shock in a rising-rate environment:

• Non-interest-bearing: 0bp increase (you keep earning the float)


• Savings: 50bp increase (you lose $50M/year)


• Money market: 90bp increase (you lose $90M/year)

Effective beta = (0 + 50 + 90) / 3 / 100bp = 46.7%

Now, for gap analysis, you need to decide: "When does this $30B of deposits 'reprice'?"

The problem: The $10B non-interest-bearing never reprices (beta 0%). The $10B in savings reprices partially and gradually (beta 50%, repricing over months). The $10B in money market reprices quickly (beta 90%, repricing over weeks).

Gap analysis forces you to pick a single repricing date for the entire $30B. Options:

1. Conservative: Model all $30B as repricing in 1 month (assume worst-case beta of ~100%). This overstates your exposure but is prudent.

2. Realistic: Split the deposits by type and model each with its own repricing date and beta. $10B at 0% beta in "never" bucket, $10B at 50% beta in "6-month" bucket, $10B at 90% beta in "1-month" bucket. But now you're adding complexity.

3. Simple: Model an effective beta of 47%, so the $30B is assumed to reprice at 47% of the rate change in 3 months. Again, adding complexity.

Most banks do option 2: split deposits by category and apply category-specific betas and repricing dates. This is documented in the gap schedule.

Non-Interest-Bearing Deposits: The Thorny Issue

Non-interest-bearing (NIB) deposits are a huge part of a bank's liability base (15–30% for large banks). How do you model them in gap analysis?

The standard approach: NIB deposits have a beta of ~0%, so they don't technically "reprice." But that's not quite right. Here's what actually happens:

• When rates rise 100bp: You don't raise the rate on NIB deposits (they earn 0%). But implicitly, you should model the cost of these deposits as rising because depositors are tempted to move the money elsewhere. The "true" cost is the opportunity cost: what they could earn in a money market fund (now 5.25%+). So the economic cost of the deposit rises by 100bp, even though the explicit rate is 0%.

• When rates fall 100bp: You still pay 0% on NIB deposits, so the cost stays 0%. Depositors can't move the money to get something better; they're stuck. The economic cost of the deposit falls, but you don't capture that benefit.

This asymmetry is huge for EVE analysis but is often ignored in simple gap analysis.

Practical approach: For NIB deposits, most banks use an implicit beta of 30–50%, modeling the assumption that in a rising-rate environment, you lose some of the balances to alternatives. This is a judgment call and varies by bank.

The Mortgage Prepayment Problem

Mortgages are usually your largest asset class. Gap analysis models them as repricing in 30 years. But this is wildly inaccurate.

Example:

• You originate a $100M portfolio of 30-year, 6.5% fixed-rate mortgages


• Gap analysis says: "This reprices in 30 years"


• One year later, rates fall to 4.5%


• 80% of borrowers refinance. Your $100M portfolio becomes $20M.


• Effective repricing date: 1 year, not 30 years

The prepayment function: The probability of refinancing depends on:

• Refi incentive: (Current rate - Mortgage rate) / Mortgage rate. If current 30-year rate is 4.5% and the mortgage is 6.5%, the incentive is +2.0%. Refinancing is attractive.


• Age of loan: Older loans have fewer refinancing opportunities (shorter remaining life). Newer loans are more likely to refi.


• Economic conditions: Tight labor markets increase refi velocity (people are mobile, they move, they refi). Recessions decrease it.


• Origination channel: Loans originated through wholesale are more likely to refi than loans originated through branches (inertia).

A reasonable prepayment model might look like:

| Refi Incentive | CPR (Conditional Prepayment Rate) |
|---|---|
| < -2% | 0.3% (some people refi for other reasons) |
| -2% to 0% | 5% |
| 0% to +1% | 15% |
| +1% to +2% | 35% |
| > +2% | 70% |

Where CPR is the annualized prepayment rate.

Using this, if rates fall and the refi incentive jumps to +2.5%, the CPR becomes 70%, and your 30-year mortgage asset has an effective life of roughly 2 years (most of it prepays).

Gap analysis can't capture this because it assumes fixed repricing dates.

Part 3: How Real Banks Implement Gap Analysis

The Gap Report Template

Here's a simplified version of what a bank's gap report looks like:

| Repricing Period | Assets ($000s) | Liabilities ($000s) | Gap ($000s) | Cum Gap |
|---|---|---|---|---|
| 0-1 month | 12,500 | 10,000 | 2,500 | 2,500 |
| 1-3 months | 8,000 | 5,000 | 3,000 | 5,500 |
| 3-6 months | 5,500 | 8,000 | (2,500) | 3,000 |
| 6-12 months | 6,000 | 12,000 | (6,000) | (3,000) |
| 1-2 years | 8,500 | 4,000 | 4,500 | 1,500 |
| 2-5 years | 12,000 | 3,000 | 9,000 | 10,500 |
| 5-10 years | 18,000 | 2,000 | 16,000 | 26,500 |
| >10 years | 128,000 | 6,000 | 122,000 | 148,500 |
| Total | 198,500 | 50,000 | — | — |

Reading This Report

• Strong near-term positive gap (0-3 months: +$5.5B): Benefits from rising rates in the near term. If rates rise 50bp, you gain ~$27.5M in NII.
• Negative gap at 6-12 months (-$3M cumulative through 12 months): You're vulnerable to rising rates in the medium term because liabilities reprice faster.
• Positive gap beyond 1 year: You have a long-duration asset base (mortgages, securities) that doesn't reprice. This is the core of your duration risk.
• Cumulative gap to infinity (~$148.5B = equity): This is just a sanity check. Assets minus liabilities equals equity.

Systems and Data

Most large banks build gap analysis in their ALM information system, which feeds from the core banking system. The pipeline:

1. Core banking system (Fiserv, Jack Henry, etc.) provides daily balances and terms for all deposits, loans, and borrowings
2. ALM system (Murex, Integrex, etc.) ingests this and classifies each balance into a repricing bucket based on:
- Contractual repricing date (maturity, rate reset date)
- Assumed behavioral repricing (beta assumptions for deposits, prepayment assumptions for mortgages)
3. Gap analysis engine aggregates into buckets and calculates gaps
4. Reporting layer publishes daily/weekly/monthly gap reports to ALM, risk, treasury, and board

The classification rules are crucial and often become a source of disagreement. Should a 3-month CD that's likely to renew be modeled as repricing in 3 months or 12 months? Should a non-interest-bearing deposit be modeled as repricing in 6 months (if you lose it) or never (if you keep it)?

Each choice changes the gap and the risk profile.

Board Governance

Most boards set gap limits as part of the ALM policy:

Example ALM Policy:

• "Cumulative gap at 0-3 months: +/- $15B maximum"


• "Cumulative gap at 0-12 months: +/- $20B maximum"


• "Cumulative gap to infinity: +/- $5B maximum"

Why these limits?

• 0-3 month limit: Protects against near-term repricing shocks. A large positive gap means you're betting on rising rates; a large negative gap means you're betting on falling rates.


• 0-12 month limit: Captures your medium-term exposure, which is material for earnings.


• Infinity limit: Captures your long-term duration risk. Ideally, you want to be roughly duration-matched to your equity base (long-term, stable value).

If the gap exceeds these limits, ALM must take action: adjust deposit pricing, shift loan origination mix, adjust security purchases, or issue/repay debt.

Part 4: Limitations and the Path to Better Models

The Gap Doesn't Tell You Everything

Example 1: Basis Risk
Your assets reprice off SOFR, your liabilities reprice off Fed funds. These aren't the same; there's a 5–10bp basis that varies. A 100bp SOFR move might be a 95bp Fed funds move. Gap analysis assumes perfect correlation and can overstate or understate your risk.

Example 2: Correlation Risk
Your loans reprice off SOFR, your deposits reprice off Fed funds. In a normal rate move, the correlation is high (>0.95). But in a crisis, when the Fed injects liquidity, Fed funds can move differently from SOFR. Gap analysis assumes they move together.

Example 3: Convexity
A -100bp shock on a bank with a long asset duration doesn't produce the same NII impact as a +100bp shock. Deposits have a floor (you can't go below 0%), so downside beta is lower than upside beta. Gap analysis treats both as identical.

Where Gap Analysis Is Insufficient

Gap analysis is sufficient for:

• Quick screening of obvious mismatches


• Board communication about the balance sheet's basic repricing profile


• Regulatory reporting

Gap analysis is insufficient for:

• Projecting actual earnings under different rate scenarios (needs NII simulation)


• Capturing the impact of embedded options (prepayments, deposit flight, renewals)


• Measuring the true economic value impact of rate changes (needs EVE analysis)


• Assessing non-parallel curve risk (needs key rate duration analysis)


• Understanding why a 50bp shock produces different outcomes than a 100bp shock (needs convexity analysis)

Part 5: The Evolution from Gap to Simulation

Modern ALM teams use gap analysis as a foundation but layer on more sophisticated tools.

The progression:
1. Gap analysis (Module 32): "When do things reprice?"
2. NII simulation (Module 33): "What does my earnings actually look like under different rates?"
3. Key rate duration (Module 37): "Which maturity buckets am I most exposed to?"
4. Economic value (Module 36): "What's the true economic impact of a rate move?"

In the next module, we'll move from static gaps to dynamic NII simulation, where behavioral assumptions come alive and the real complexity begins.