Basis risk · RiskAtoms Academy

By the end you will be able to

1Map each line of a banking book to the index it reprices off: Bank Rate, SONIA, a rate the bank sets, or none.
2Measure basis risk as the change in NII when one index moves against another, using the book's own basis scenario.
3Explain why administered rates are a basis of their own, which no market instrument hedges.
4Size a basis swap that closes the SONIA and Bank Rate gap, and weigh its cost against the risk.

Why it matters

Two sterling overnight rates matter to a UK bank: Bank Rate, which the Bank of England sets, and SONIA, the average rate banks actually pay to borrow sterling overnight from other financial institutions. They track each other closely, but not exactly: for most of 2024 SONIA sat 5 basis points below Bank Rate. In October 2008, three-month sterling interbank rates were nearly 200 basis points above risk-free rates. A bank that lends at one rate and pays another can lose money without any move in "interest rates" at all. That is basis risk.

Core explanation

Same timing, different index

Illustrative dataRiskAtoms Bank plc's banking book

The same £67bn balance sheet as Module 3.5, on one made-up reporting date, in pounds, with how each line reprices (fixed, floating or administered), its customer rate, a SONIA curve with Bank Rate at 4.00%, a £19.2bn macro hedge on the fixed-rate mortgages and a £16bn structural hedge. Tier 1 capital is taken as £3.5bn. The figures are round illustrative values, not any bank's data. Every lesson in Module 3.6 uses this book, so the figures agree.

In this book SONIA overnight equals Bank Rate (in practice it fixes a few basis points below). Its NII calculation has a basis option that moves SONIA, and everything priced off it, against Bank Rate. The savings-rate move and the basis swap below are extras added for this lesson; they leave the book's totals unchanged.

L3.6.02: Where interest rate risk in the banking book comes from named four sources of rate risk. Gap risk is about when items reprice. Basis risk is about what they reprice to: two items can reset on the same day and still move by different amounts, because each follows a different index. RiskAtoms Bank uses three kinds of floating rate:

Bank Rate. Reserves at the Bank of England earn it; tracker mortgages are Bank Rate + 0.75%; the central bank term funding is charged at it.
SONIA. Corporate loans are SONIA + 1.8%, and every swap's floating leg is SONIA: the market's risk-free benchmark since the end of LIBOR.
Administered rates. The bank sets its savings, current account, standard variable mortgage and card rates itself, moving each by a beta times the change in Bank Rate, a month later.

Floating and administered positions only; fixed items do not depend on the index until they mature
Index	Gross amount	Net (assets − liabilities)	Year-1 ΔNII per +1bp
SONIA	£45.2bn	£13.2bn	+£1.155m
Bank Rate (floating)	£10.0bn	£8.0bn	+£0.774m
Administered (set by the bank)	£44.0bn	−£36.0bn	−£0.816m

The SONIA line is where the book's market basis sits. The bank earns SONIA on £10bn of corporate loans and on the £19.2bn floating legs of the macro hedge it received in exchange for paying fixed. It pays SONIA on the £16bn structural hedge. Net, it is long £13.2bn of SONIA, funded by deposits priced off Bank Rate. On Bank Rate itself it is long £8.0bn of floating items, and short £36.0bn of administered balances (£8.9bn once weighted by their betas).

The book's basis scenario

Suppose SONIA falls 25bp below Bank Rate and stays there for a year, while Bank Rate does not move. Only the SONIA-linked items change:

Year-1 NII falls by £28.9m, and by £94.9m over three years if the gap persists. The loss is symmetric: SONIA 25bp above Bank Rate would add £28.9m. None of the six standard shocks of L3.6.06: The standard shock scenarios captures it, because each moves one curve.

Administered rates: a basis the bank sets itself

The deposit beta of L3.6.04: Net interest income sensitivity is a promise about behaviour, not a contract. If competitors raise their instant-access rates, RiskAtoms Bank may have to follow with Bank Rate unchanged. A 25bp rise on the £10bn of savings costs £22.9m a year; on all £40bn of non-maturity deposits, £91.7m. No published index tracks that gap, so no swap can hedge it. Banks manage it through pricing decisions at ALCO and conservative deposit models (L3.6.09: Non-maturity deposits).

Sort itWhich index?

Sort each item of RiskAtoms Bank's book by what its rate follows.

Tracker mortgages at Bank Rate + 0.75%
Floating corporate loans reset quarterly
Standard variable rate mortgages
Reserves at the Bank of England
The floating leg of the structural hedge
Instant-access savings

ExploreWhere basis risk enters, and how ALM responds

Click a box to see what happens there.

Pricing

Products are priced off Bank Rate because customers understand it. That choice ties income to Bank Rate, whatever the bank's hedges reference.

The formal version

Write $N_i$ for the signed amount of position $i$ (positive if the bank receives the rate), $\tau_i$ for the time of its next reset in years and $b$ for the move of its index against Bank Rate. Each position earns the new rate from $\tau_i$ to the end of the year, so:

\begin{aligned} \Delta\text{NII}_1 &= \sum_{i \in \text{SONIA}} N_i\, b\, (1 - \tau_i) \\ &= b \Big(\sum_{i} N_i\Big)(1 - \bar\tau) \qquad \text{(all reset on the same quarterly cycle)} \\ &= -0.0025 \times 13{,}200 \times 0.875 = -\text{£}28.875\text{m} \end{aligned}

Here $1 - \bar\tau = 0.875$ , because quarterly resets spread over the first three months start on average 1.5 months in. In later years $\tau = 0$ and the loss is the full $0.0025 \times 13{,}200 = 33$ a year. For an administered rate moved by $m$ after a lag $L$ of a month:

\Delta\text{NII}_1 = -D\, m\, (1 - L) = -10{,}000 \times 0.0025 \times \tfrac{11}{12} = -\text{£}22.92\text{m}

A basis swap on notional $K$ , receiving Bank Rate and paying SONIA + $s$ , adds $-K\,b\,(1-\bar\tau) - K\,s$ . With $K = \sum_i N_i$ the $b$ terms cancel and only the spread is left.

Try it

Move SONIA against Bank Rate, then let competition push the savings rate up. Add a basis swap and find the notional that makes the SONIA line vanish. Does the swap help with the savings rate?

Try itPull the indices apart

SONIA against Bank Rate−25bp

Instant-access savings rate against Bank Rate0bp

Basis swap: receive Bank Rate, pay SONIA + 2bp (notional)£0.0bn

Year-1 ΔNII−£28.9m

Net SONIA position left unhedged£13.2bn

From SONIA-linked positions (book)−£28.9m

From the savings rate (extra)£0.0m

Basis swap, after its spread (extra)£0.0m

Bank Rateunchanged at 4.00%

SONIA-linked items and the swap reset quarterly, on average 1.5 months in; the savings rate moves after the book's one-month notice. A swap larger than £13.2bn over-hedges: the bank is then short SONIA. The swap and its 2bp cost are illustrative.

Worked example

Closing the SONIA basis with a swap

ALCO asks treasury to remove the SONIA and Bank Rate basis. The basis swap and its 2bp spread are illustrative.

From exposure to hedge

Step 1 of 5

1
Net SONIA position
$\begin{aligned} N_{\text{SONIA}} &= \underbrace{10{,}000}_{\text{loans}} + \underbrace{19{,}200}_{\text{macro hedge}} - \underbrace{16{,}000}_{\text{structural hedge}} = \text{£}13{,}200\text{m} \end{aligned}$

Not just sterling

Any bank with products on one index and hedges or funding on another has the same problem: US loans priced off the prime rate with hedges on SOFR, euro loans on Euribor funded or hedged at €STR, or loans in the LIBOR era priced off three-month rates and funded overnight.

Regulatory lens

The Basel standard (SRP31.2) lists basis risk as one of three kinds of interest rate risk in the banking book, alongside gap and option risk, and its application guidance (SRP98) notes that economic value methods can test it with scenarios in which the base rates a bank depends on diverge. The six standard shocks move one curve per currency, so basis risk sits in the bank's own measurement and in supervisors' review rather than in the outlier test. How supervisors assess it is in M4.5: Liquidity and IRRBB regulation; deposit pricing models are in M6.7: Liquidity, ALM and behavioural models.

Spark Atoms

Spark AtomOctober 2008

At a special meeting on 8 October 2008, the Bank of England's Monetary Policy Committee recorded that sterling and dollar three-month LIBOR had risen to nearly 200 and 300 basis points above risk-free rates. A lender with loans on Bank Rate funded at three-month LIBOR would have been paying away a margin it never priced for.

Spark AtomA flat line for most of a year

SONIA printed 5 basis points below Bank Rate for most of 2024, and by July 2025 the gap had narrowed to just over 3 basis points as reserves fell, according to the Bank of England. On RiskAtoms Bank's £13.2bn net position, each basis point of change is worth about £1.32m a year.

Key takeaways

Basis risk: items that reprice at the same time but follow different indices, so their rates move by different amounts.
RiskAtoms Bank prices customers off Bank Rate but hedges with SONIA swaps, leaving it long £13.2bn of SONIA.
SONIA 25bp below Bank Rate costs £28.9m in year 1 (resets start on average 1.5 months in) and £33m a year after that.
Administered rates are a basis the bank sets itself; competition can move them with Bank Rate still, and no swap hedges that.
A basis swap receiving Bank Rate and paying SONIA + spread on the net position removes the market basis for a known cost (£2.64m a year at 2bp).

Reaction

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Glossary

Basis risk: The risk that rates on instruments with similar repricing dates but different reference indices move by different amounts.
Index (reference rate): The published rate a floating item is tied to, such as Bank Rate or SONIA.
Bank Rate: The Bank of England's policy rate, paid on reserves held at the Bank.
SONIA: The Sterling Overnight Index Average: the average rate banks pay to borrow sterling overnight, unsecured, from other financial institutions and institutional investors, published by the Bank of England.
Administered rate: A rate the bank sets itself, such as a savings rate or a standard variable mortgage rate. It usually follows Bank Rate, but by how much and when is the bank's choice.
Deposit beta: The share of a change in Bank Rate the bank passes on to an administered rate.
Basis swap: A swap that exchanges one floating rate for another, for example Bank Rate for SONIA plus a spread.
Basis swap spread: The fixed add-on to one leg of a basis swap that makes it fair at the start.

Deep Dives & Origins

Deep Dives

Bank of England, Straight and narrow: recent changes in SONIA and why we care, Bank Overground, July 2025. Intermediate.
Basel Committee on Banking Supervision, Basel Framework, SRP98 Application guidance on interest rate risk in the banking book, BIS. Advanced.

Origins

Basel Committee on Banking Supervision, Basel Framework, SRP31.2 (gap, basis and option risk), version in force from 1 January 2026, BIS.
Basel Committee on Banking Supervision, Basel Framework, SRP98.15 and 98.49 (basis risk and how economic value measures test it), BIS.
Bank of England, Minutes of the Special Monetary Policy Committee Meeting held on 8 October 2008.
Bank of England, Straight and narrow: recent changes in SONIA and why we care, Bank Overground, 2025.

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