Banking / ALM

Interest-rate risk in the banking book

The calculation that failed at Silicon Valley Bank. A balance sheet funded with short deposits and invested in long fixed-rate bonds looks solvent at book value and is deeply insolvent at market value the moment rates rise. Basel measures it two ways — economic value of equity and net interest income — and they can point in opposite directions.

Worst scenario-16.7%Outlier testBreachedEVE sensitivity-62.9%

EVE

79.7

present value of the banking book

ΔEVE at 200 bp

-50.2

-16.7% of capital

ΔNII

-8.0

-320.0% over twelve months

One-year gap

-400

assets repricing inside a year minus liabilities

Repricing schedule and scenarios

The gap schedule first, then every standardised shock against the same book.

-16.7%

Repricing schedule and scenarios
Bucket	Assets	Liabilities	Gap	PV gap
0.5y	150	400	-250	-249.7
1.0y	200	350	-150	-152.7
3.0y	250	120	130	102.9
5.0y	300	60	240	180.7
10.0y	350	20	330	198.5
Total	1250	950	-400	79.7
Parallel up				-16.7%
Long up				-13.4%
Steepener				-10.1%
Short down				-0.3%
Short up				1.2%
Flattener				11.0%
Long down				15.3%
Parallel down				20.1%

EVE and NII answer different questions and can disagree. A book that is asset-sensitive earns more NII when rates rise but loses EVE, because its long assets fall in value by more than its short liabilities.

EVE against a parallel shock

Concave, because the discount factors are convex in the rate. The asymmetry is the whole risk.

ΔEVE by Basel scenario

As a percentage of Tier 1 capital. The supervisory outlier test trips at 15%.

Canonical equations

The exact relationships implemented by this engine.

EVE = Σ A_t/(1+r_a)^t − Σ L_t/(1+r_l)^t · The economic value of the banking book.

EVE(shock) − EVE(base) · Scaled by Tier 1 for the supervisory test.

ΔNII = Σ_{t≤1} gap_t × Δr · Only the buckets that reprice inside the year.

D = −(ΔEVE/EVE)/Δr · The equity duration implied by the shock.

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

Step-by-step methodWorked exampleAssumptions explained

Worked example

A bank that borrows short and lends long

Inputs

Assets 150/200/250/300/350 across 0.5 to 10 years at 5%.
Liabilities 400/350/120/60/20 at 2%.
Tier 1 capital 300, parallel shock +200 bp.

Calculation path

1
The present value of the assets is 1002.9 and of the liabilities 923.2, so EVE is 79.7.
2
A 200 bp parallel rise discounts the long assets much harder than the short liabilities.
3
EVE falls to 29.5, a change of −50.2.
4
That is −16.7% of Tier 1 capital, which breaches the 15% supervisory outlier test.
5
The one-year gap is −400, so net interest income also falls by 8.0 over the next twelve months.

Result

EVE 79.7 · ΔEVE −50.2 (−16.7% of capital) · ΔNII −8.0.

Interpreting the result

Both measures move the same way here, which happens when the book is short-funded and long-invested: rising rates hurt the balance sheet and the income statement at once. The more common case is that they disagree, and the standard asks for both precisely so that a bank cannot flatter one by optimising the other.

Assumptions & limitations

Cash flows are slotted by repricing date into five buckets, with no optionality.

A single flat discount rate per side, not a curve.

The standardised shocks are applied with a five-year linear ramp between the short and long ends.

Behavioural assumptions for non-maturity deposits are not modelled.

Frequently asked questions

Why did SVB fail on this measure?

Because its assets were long-dated and its deposits were short and, in practice, flighty. The EVE calculation showed the loss; the liquidity run is what made it fatal.

Why do EVE and NII disagree?

EVE is a present value over the whole life of the book; NII is a one-year flow. A book can gain income from higher rates while losing value.

What is the 15% outlier test?

A supervisory threshold: if the worst standardised scenario moves EVE by more than 15% of Tier 1, the bank is an outlier and faces additional scrutiny.

Are deposits really that short?

Core deposits behave much longer than their contractual repricing. The modelling assumption for them is the single most consequential judgement in an IRRBB calculation.