Duration-Gap and Leverage-Adjusted Gap Calculations - Article

Introduction

Traditional Gap Analysis examines how interest-rate changes affect Net Interest Income.

Duration Gap Analysis looks at a different question:

How will an interest-rate change affect the economic value of the bank’s equity?

Under the RBI Commercial Banks – Asset Liability Management Directions, 2025, Interest Rate Risk from the economic-value perspective is measured through the Duration Gap Approach (DGA). Banks calculate the Modified Duration of Rate-Sensitive Assets (MDA), Modified Duration of Rate-Sensitive Liabilities (MDL) and the resulting Modified Duration Gap (MDG).

The current 2026 CAIIB BFM syllabus includes Interest Rate Risk Management under Module D, covering the sources, effects, measurement techniques and control of Interest Rate Risk.

Learning Objectives

After studying this topic, you should be able to:

• understand why duration is used to measure economic-value sensitivity;

• calculate weighted Modified Duration of assets and liabilities;

• distinguish a simple duration difference from a leverage-adjusted duration gap;

• calculate RBI’s Modified Duration Gap;

• determine the direction and amount of change in Market Value of Equity; and

• avoid common CAIIB errors involving signs, basis points and the liability-to-asset adjustment.

Why Duration Matters

Interest rates and the value of fixed future cash flows generally move in opposite directions.

When market rates rise:

• the present value of fixed future asset cash flows falls; and

• the present value of fixed future liability cash flows also falls.

When rates decline, their values generally increase.

The bank’s economic exposure therefore depends on the difference between the interest-rate sensitivity of its assets and liabilities.

Duration provides a way to measure this sensitivity.

RBI defines Modified Duration as the approximate percentage change in the value of an asset or liability for a 100-basis-point change in the interest rate.

Modified Duration of Assets and Liabilities

A bank normally has many types of Rate-Sensitive Assets and Liabilities with different durations.

Therefore, it first calculates:

• MDA – weighted Modified Duration of RSA; and

• MDL – weighted Modified Duration of RSL.

RBI states that MDA and MDL are the weighted averages of the Modified Durations of the relevant RSA and RSL positions.

MDA = Σ(RSA Amount × Modified Duration) ÷ Total RSA

This determines the weighted Modified Duration of the bank’s Rate-Sensitive Assets.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

Similarly:

MDL = Σ(RSL Amount × Modified Duration) ÷ Total RSL

This determines the weighted Modified Duration of the bank’s Rate-Sensitive Liabilities.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

Weighting Is Important

Do not simply average the durations.

A large asset must influence MDA more than a small asset.

Therefore:

Amount-weighted duration ≠ Simple arithmetic average of durations

This is a frequent numerical trap.

Simple Duration Difference

At the most basic conceptual level, a learner may initially compare:

Asset Duration − Liability Duration

If asset duration is greater, asset value is generally more sensitive to interest-rate movements than liability value.

However, this comparison is incomplete because:

Assets and liabilities are normally not equal in amount.

A bank is funded partly by liabilities and partly by equity.

Therefore, liability duration must be adjusted for the relative size of liabilities compared with assets.

This leads to the leverage-adjusted duration gap.

Why the Leverage Adjustment Is Needed

Suppose:

• asset duration and liability duration are identical; but

• liabilities finance only part of the assets.

Simply subtracting the two durations would produce zero.

But this ignores the fact that the amount of liabilities whose value changes may be different from the amount of assets whose value changes.

The duration gap must therefore incorporate the liability-to-asset relationship.

In RBI’s current framework, this adjustment uses:

RSL ÷ RSA

This factor should not be confused with the Basel regulatory leverage ratio. It is simply the relative amount of Rate-Sensitive Liabilities compared with Rate-Sensitive Assets in the MDG calculation.

RBI Modified Duration Gap

The current RBI formula is:

MDG = MDA − [MDL × (RSL ÷ RSA)]

This calculates the leverage-adjusted Modified Duration Gap between Rate-Sensitive Assets and Liabilities.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

The expression:

MDL × (RSL ÷ RSA)

adjusts liability duration for the relative size of liabilities.

Therefore, RBI’s MDG is more informative than simply calculating:

MDA − MDL

Interpreting a Positive MDG

A positive MDG means the adjusted duration of assets is greater than that of liabilities.

Therefore, assets are economically more sensitive to interest-rate movements.

When Interest Rates Rise

Asset values generally fall more than liability values.

Result:

Market Value of Equity tends to fall.

When Interest Rates Fall

Asset values generally rise more than liability values.

Result:

Market Value of Equity tends to rise.

Therefore:

Positive MDG + Rate Rise → Negative impact on MVE

Interpreting a Negative MDG

A negative MDG means the leverage-adjusted liability-duration effect is greater than asset duration.

When Interest Rates Rise

Liability values may fall more than asset values.

Result:

MVE tends to increase.

When Rates Fall

Liability values may rise more than asset values.

Result:

MVE tends to decline.

The broad direction is therefore:

Change in Market Value of Equity

RBI evaluates the economic-value effect of an interest-rate shock using:

ΔE = −MDG × RSA × Δi

This estimates the change in the value of equity resulting from the assumed interest-rate movement.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

The minus sign is extremely important.

For a positive MDG:

• positive rate shock → negative ΔE;

• negative rate shock → positive ΔE.

In other words, a bank with a positive duration gap generally loses economic value when rates rise.

Converting the Equity Change into a Percentage

The economic-value impact is commonly related to the bank’s equity or Net Worth.

Change in MVE % = (ΔE ÷ Equity) × 100

This expresses the economic-value impact as a percentage of the bank’s equity.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

Under the RBI framework, Equity for this purpose means Net Worth as defined in the Directions.

Interest-Rate Shock Conversion

A common CAIIB error occurs when basis points are converted incorrectly.

Remember:

• 1 bp = 0.01%

• 25 bps = 0.25% = 0.0025

• 50 bps = 0.50% = 0.005

• 100 bps = 1.00% = 0.01

• 200 bps = 2.00% = 0.02

RBI specifically states that a 1% change should be written as 0.01 when calculating ΔE.

Direction of the Interest-Rate Shock

The sign of Δi must also be handled correctly.

Rate Increase

Δi is positive.

For example conceptually:

Rate rises → Δi positive

Rate Decrease

Δi is negative.

Therefore, the sign of:

−MDG × Δi

determines whether equity value increases or decreases.

A learner should not automatically write the economic-value change as negative merely because an interest-rate shock is mentioned.

First identify:

1. sign of MDG; and

2. direction of the rate shock.

Numerical Calculation Sequence

For a CAIIB numerical, use the following order.

Step 1: Identify Rate-Sensitive Assets

Determine the amount and Modified Duration of each RSA category.

Step 2: Calculate Weighted MDA

Use amount-weighted Modified Durations.

Step 3: Identify Rate-Sensitive Liabilities

Determine the amount and Modified Duration of each RSL category.

Step 4: Calculate Weighted MDL

Again, use amount weighting.

Step 5: Determine Total RSA and Total RSL

These totals are required for the adjustment factor.

Step 6: Calculate the Adjustment Factor

Use:

RSL ÷ RSA

Step 7: Calculate MDG

Apply the leverage-adjusted RBI formula.

Step 8: Convert the Interest-Rate Shock

Convert basis points into decimal form.

Step 9: Calculate ΔE

Determine the absolute change in economic equity.

Step 10: Compare ΔE with Equity

Where required, express the change as a percentage of Net Worth.

This sequence is safer than attempting to combine all calculations in one step.

Market Value or Book Value?

RBI states that for assessing changes in MVE, market values of RSA and RSL should be used.

However, for simplicity, book values—including the notional value of rate-sensitive OBS positions—may be used as an approximation. Banks capable of using market values should determine them using discounted cash-flow methods.

For an examination numerical:

• use the values specifically provided in the question;

• do not invent market values; and

• follow the stated assumptions.

Time Buckets and Modified Duration

RBI requires RSA, RSL and rate-sensitive OBS positions to be placed in the prescribed Interest Rate Sensitivity buckets according to residual maturity or repricing dates.

Where individual Modified Duration cannot be calculated directly, the benchmark framework allows banks to:

• group exposures into time buckets;

• use the midpoint of the bucket as a proxy for maturity;

• determine appropriate coupon and yield assumptions; and

• calculate Modified Duration for each category.

The resulting durations are then weighted to obtain:

• MDA; and

• MDL.

Off-Balance-Sheet Positions

Duration Gap is not restricted to physical loans, investments and deposits.

RBI requires rate-sensitive OBS positions to be included.

Under the prescribed process, the absolute notional amount of a rate-sensitive OBS item in a time bucket is included:

• as RSA when positive; and

• as RSL when negative.

Examples may include:

• interest-rate swaps;

• Forward Rate Agreements;

• futures; and

• other rate-sensitive derivatives.

Ignoring these positions can materially distort MDG.

Higher Absolute MDG Means Higher Sensitivity

RBI specifically states that a higher absolute value of MDG indicates greater exposure to interest-rate shocks.

This means:

• +2.0 has greater first-order duration exposure than +0.5;

• −2.0 also has greater exposure than −0.5.

For measuring the size of exposure, look at the absolute value.

For determining the direction of the MVE effect, look at the sign.

Therefore:

Magnitude → |MDG|

Direction → Sign of MDG + Sign of Rate Shock

Zero MDG Does Not Mean Zero Interest-Rate Risk

If MDG is zero or close to zero, the first-order duration mismatch is limited.

But this does not mean that all IRR has disappeared.

The bank can still face:

• basis risk;

• yield-curve risk;

• convexity effects;

• option risk;

• behavioural changes; and

• non-parallel movements in rates.

Duration is primarily a first-order approximation of price sensitivity.

Therefore, perfect duration matching does not guarantee perfect economic-value immunisation under every possible rate scenario.

Duration Gap vs Repricing Gap

These two calculations serve different purposes.

RBI requires banks to carry out both TGA and DGA because the earnings and economic-value perspectives provide complementary information.

Supervisory 200-basis-point Shock

Under the current RBI ALM Directions, a bank is treated as an outlier from the Pillar II supervisory perspective if the economic value of its banking book declines by more than 20% of MVE under a standardised interest-rate shock of 200 basis points.

This creates an important numerical sequence:

MDG → 200 bp Shock → ΔE → ΔE as % of MVE → Compare with 20%

The percentage is based on the decline relative to MVE, not relative to total assets.

The RBI Directions also distinguish this banking-book outlier test from the calculation of a 200-basis-point shock applied to the entire balance sheet.

Estimated MVE Loss Is Not an Accounting Loss

RBI clarifies that a fall in MVE estimated under the duration-gap shock represents the economic impact on equity if the scenario occurs.

It should not automatically be interpreted as an identical accounting loss because the banking book is not simply marked to market in that manner.

This distinction is frequently misunderstood.

Economic sensitivity ≠ Immediate P&L loss

Practical Banking Application

Consider two balance-sheet structures.

Structure A: Long-Duration Assets, Shorter-Duration Liabilities

The bank holds:

• long-term fixed-rate loans and securities; and

• relatively short-duration deposits and borrowings.

Asset duration is high relative to leverage-adjusted liability duration.

MDG is likely to be positive.

If rates rise sharply:

• asset economic value tends to fall more;

• liability economic value falls by a smaller adjusted amount; and

• MVE tends to decline.

Structure B: Shorter-Duration Assets, Longer-Duration Liabilities

The reverse structure can produce a negative MDG.

If rates rise:

• the adjusted value of liabilities may decline more than assets; and

• MVE may increase.

ALCO therefore uses duration information to consider actions such as:

• changing asset duration;

• changing funding maturity;

• altering fixed/floating mix; or

• using permitted interest-rate derivatives.

CAIIB Exam Focus

1. DGA Measures Economic-Value Risk

Do not confuse it with NII sensitivity.

2. RBI Uses Modified Duration

MDA and MDL are weighted Modified Durations of RSA and RSL.

3. Do Not Simply Calculate MDA − MDL

RBI adjusts MDL using:

RSL ÷ RSA

4. Positive MDG + Rate Rise = MVE Decline

The minus sign in the ΔE relationship is important.

5. Negative MDG Reverses the Direction

A rising-rate shock can increase MVE when MDG is negative.

6. Weight Durations by Amount

Never use an ordinary arithmetic average where exposures differ.

7. Convert Basis Points Correctly

200 bps = 2% = 0.02.

8. Use Equity for the Percentage Impact

Do not divide ΔE by RSA or RSL when the question asks for percentage change in MVE.

9. Absolute MDG Shows Exposure Size

The sign shows direction; absolute value indicates the degree of duration mismatch.

10. Remember the RBI Outlier Test

A banking-book economic-value decline of more than 20% of MVE under the standardised 200 bp shock triggers the supervisory outlier criterion under the current framework.

Common Exam Traps

Trap 1: Using a Simple Average for MDA or MDL

Wrong. Modified Durations must be weighted by the corresponding exposures.

Trap 2: Calculating MDG as MDA − MDL

Incomplete. RBI’s MDG adjusts liability duration by RSL/RSA.

Trap 3: Treating RSL/RSA as the Basel Leverage Ratio

Wrong. It is an adjustment factor within the duration-gap calculation.

Trap 4: Entering 200 bps as 200

Wrong. In the ΔE calculation, 200 bps is 0.02.

Trap 5: Ignoring the Minus Sign in ΔE

Wrong. It reverses the direction of the equity effect.

Trap 6: Assuming Positive MDG Is Always Good

Wrong. A positive MDG is vulnerable to rising rates.

Trap 7: Assuming Negative MDG Means No Risk

Wrong. It represents exposure in the opposite direction.

Trap 8: Dividing ΔE by Total Assets

Wrong when calculating percentage change in MVE. Use Equity/Net Worth.

Trap 9: Ignoring OBS Positions

Wrong. Relevant rate-sensitive OBS positions form part of the RBI DGA framework.

Trap 10: Treating an Estimated MVE Fall as an Immediate Accounting Loss

Wrong. RBI treats it as an economic-value impact, not automatically the same accounting loss.

Memory Technique

Remember:

A − Adjusted L = Gap

So:

MDG = Asset Duration − Adjusted Liability Duration

Then remember:

Positive Gap + Rates Up = Equity Down

The numerical sequence is:

Amounts → Weighted MDA/MDL → RSL/RSA → MDG → Rate Shock → ΔE → ΔE/Equity