How it works
Illustrative dataCalderwick Bank plc, a new bank for the Lab Test
The lessons use RiskAtoms Bank's £67bn banking book. These problems apply the same curve, shocks, caps, multipliers and methods to a new, smaller bank: Calderwick Bank plc, with a £4,000m balance sheet, invented. The calculations are hand-sized: five gap bands, year-1 NII line by line with simple weights, EVE from a table of present values and durations. All its figures are made up, in £ millions. Customer rates are annual; the shocks are applied to them unchanged, as in the module.
Problem 1Calderwick's book and its repricing gap
L3.6.01 · L3.6.02 · L3.6.03ALM analyst, Calderwick Bank plc
Calderwick Bank plc (invented) is a UK retail and small-business bank with a £4,000m balance sheet, about a seventeenth the size of RiskAtoms Bank. Bank Rate is 4.00%, and SONIA fixes at the same level. Tier 1 capital is £250m: £300m of equity less £50m of intangibles and other deductions. Its balance sheet, used in every problem below:
| Asset | £m | Rate |
|---|---|---|
| Cash and central bank reservesBank Rate, moves at once | 600 | 4.00% |
| Gilts held to collect (amortised cost)Bought in 2021 at par; 6 years left | 400 | 1.25% |
| Covered bonds (FVOCI)3 years left | 100 | 3.90% |
| Two-year fixed-rate mortgagesEnds of fix spread evenly over 24 months | 1,200 | 4.80% |
| Five-year fixed-rate mortgagesEnds of fix spread evenly over 60 months | 600 | 4.20% |
| Tracker mortgagesBank Rate + 1.00%, reset a month after it moves | 300 | 5.00% |
| Loans to small businessesSONIA + 2.50%, reset monthly (next in a month) | 600 | 6.50% |
| Other assetsNo rate (includes £50m of intangibles) | 200 | – |
| Total assets | 4,000 |
| Liability or equity | £m | Rate |
|---|---|---|
| Personal current accountsSet by the bank; beta 0.1 | 1,400 | 0.10% |
| Instant-access savingsSet by the bank; beta 0.5 | 1,000 | 3.00% |
| Small-business depositsSet by the bank; beta 0.3 | 400 | 1.50% |
| One-year fixed-term depositsMaturities spread evenly over 12 months | 600 | 4.10% |
| Senior bondsFixed, 3 years left | 300 | 5.00% |
| EquityNo rate | 300 | – |
| Total | 4,000 |
For the gap, use five bands: up to 1 month, 1–3 months, 3–6 months, 6–12 months, over a year. On contract the three deposit lines reprice overnight. A line whose ends of fix are spread evenly over N months puts 1/N of its balance in each month (the 1–3 month band holds two months, 3–6 three, 6–12 six). Ignore prepayment. For the estimate, each band inside the year earns the rate move for the rest of the year after its mid-point (0.5, 2, 4.5 and 9 months).
Lessons: L3.6.01: What ALM does · L3.6.02: Where interest rate risk in the banking book comes from · L3.6.03: Repricing gap analysis
(a)What is Calderwick's net interest margin today: a year's NII at today's rates over total assets? Answer in %.
%(b)ALCO's risk pack lists four exposures: (1) the small-business loans reset to SONIA while the deposits are priced off Bank Rate; (2) the two- and five-year fixes are funded largely by instant-access savings; (3) borrowers on fixed rates can repay early when rates fall; (4) a steepener, short rates down and five-year rates up, cuts NII although the average rate barely moves. Which labels them right?
(c)What is the contractual cumulative repricing gap at one year? Answer in £m (negative if liabilities reprice first).
£m(d)Using that contractual gap, estimate the change in year-1 NII for a 100bp parallel rise, with each band weighted by the time left in the year. Answer in £m.
£m(e)Now count each deposit line at beta × its balance (the earnings view). What is the cumulative gap at one year? Answer in £m.
£m
Problem 2What a move in rates does to next year's NII
L3.6.04 · L3.6.07ALM analyst
Project Calderwick's year-1 NII on a constant balance sheet for an immediate parallel move Δ, with these rules (the module's, made hand-sized):
- Cash earns Bank Rate and moves with it at once: the whole year.
- Trackers and small-business loans reset a month after the move: 11 months.
- Fixes and term deposits that end inside the year are replaced by the same business at the new rate. A block repricing evenly through the year earns the move for half a year on average: half the two-year fixes, a fifth of the five-year fixes and all the term deposits reprice in year 1.
- The bank moves each deposit rate by beta × Δ a month after the market (11 months), and never below zero.
- No prepayment. Gilts, covered bonds and senior bonds do not reprice in year 1.
For part (c), Bank Rate does not move. Instead SONIA fixes 20bp below Bank Rate from the small-business loans' next reset and stays there, and competition forces Calderwick to raise its instant-access savings rate by 25bp, a month from now.
Lessons: L3.6.04: Net interest income sensitivity · L3.6.07: Basis risk
(a)What is the change in year-1 NII for a 100bp parallel rise? Answer in £m.
£m(b)What is the change in year-1 NII for a 275bp parallel fall, with the zero floor on deposit rates? Answer in £m.
£m(c)What do the two basis moves of part (c) do to year-1 NII together? Answer in £m.
£m
Problem 3How long do the deposits stay?
L3.6.09Treasury, behavioural modelling
Calderwick's deposit history gives each line a stable share. As in the module, core share = stable share × (1 − beta), capped at the Basel share for its category; core balances are slotted in equal monthly cohorts over Y years (an average maturity of Y/2, which must stay within the Basel cap); the rest is non-core and counts as overnight.
| Deposit | £m | Beta | Stable | Category | Core cap | Maturity cap | Slotted over |
|---|---|---|---|---|---|---|---|
| Personal current accounts | 1,400 | 0.1 | 80% | Retail transactional | 90% | 5.0 years | 3 years |
| Instant-access savings | 1,000 | 0.5 | 70% | Retail non-transactional | 70% | 4.5 years | 2 years |
| Small-business deposits | 400 | 0.3 | 85% | Wholesale | 50% | 4.0 years | 1 year |
Lessons: L3.6.09: Non-maturity deposits
(a)How much of the deposits is core in total? Answer in £m.
£m(b)What is the longest horizon over which the core savings could be slotted in equal monthly cohorts within the Basel cap? Answer in years.
years(c)ALCO considers slotting the core current accounts over five years instead of three. What does that do?
Problem 4What the book is worth, and how fast that changes
L3.6.05Market risk, banking book
The ALM system values every rate-sensitive cash flow on today's SONIA curve (the module's curve): interest at today's customer rates (commercial margins included), principal at repricing, core deposits at their slots from Problem 3, fixes prepaying at a base CPR of 9%. Equity and other assets have no cash flows and are left out. Present values (liabilities shown as positive amounts) and durations:
| Assets | PV £m | D years |
|---|---|---|
| Cash and central bank reserves | 600.0 | 0.00 |
| Gilts held to collect (amortised cost) | 336.7 | 5.76 |
| Covered bonds (FVOCI) | 99.3 | 2.84 |
| Two-year fixed-rate mortgages | 1,207.7 | 0.93 |
| Five-year fixed-rate mortgages | 600.1 | 2.05 |
| Tracker mortgages | 300.3 | 0.08 |
| Loans to small businesses | 601.3 | 0.08 |
| Liabilities | PV £m | D years |
|---|---|---|
| Personal current accounts | 1,342.3 | 1.04 |
| Instant-access savings | 996.4 | 0.34 |
| Small-business deposits | 397.5 | 0.25 |
| One-year fixed-term deposits | 600.3 | 0.50 |
| Senior bonds | 307.2 | 2.81 |
Durations are with respect to a parallel shift of the continuously compounded zero curve, so ΔPV ≈ −D × PV × Δ, and dollar durations (PV × D) add up.
(a)What is Calderwick's EVE, the PV of the assets less the PV of the liabilities? Answer in £m.
£m(b)What is the duration of equity, D_E? Answer in years.
years(c)Using D_E, estimate the change in EVE in the +275bp parallel up shock. Answer in £m.
£m
Problem 5The six shocks and the two tests
L3.6.06 · L3.6.01ALCO secretary
The standard shocks for sterling are 275bp parallel, 425bp short and 250bp long, with the short shock scaled by e−t/4 and the long by 1 − e−t/4; the steepener is −0.65 × short + 0.9 × long. The system's full revaluation of the book (scenario CPR, 0% floor), £m:
| Parallel up | Parallel down | Steepener | Flattener | Short up | Short down |
|---|---|---|---|---|---|
| −42.5 | +48.6 | −25.0 | +13.4 | −9.9 | +8.9 |
The board's limits (illustrative): in the parallel shocks, year-1 NII may not fall by more than 20% of today's NII; in any shock, EVE may not fall by more than 12% of Tier 1. The supervisor's outlier test is 15% of Tier 1; for comparison, the EU's NII test flags a year-1 NII fall in the parallel shocks of more than 5% of Tier 1.
Lessons: L3.6.06: The standard shock scenarios · L3.6.01: What ALM does
(a)How large is the steepener at 5 years? Answer in bp (negative for a fall).
bp(b)What is the worst fall in EVE as a share of Tier 1? Answer in %.
%(c)What is the worst year-1 NII fall in the parallel shocks (Problem 2) as a share of Tier 1? Answer in %.
%(d)How much of ALCO's NII limit does that fall use? Answer in %.
%(e)What is the right reading for ALCO?
Problem 6The borrowers' options
L3.6.08Mortgage pricing and ALM
Calderwick's fixed-rate mortgages prepay at a base CPR of 9% a year. In the standard shocks the CPR is multiplied by 0.8 when rates rise and 1.2 when they fall.
Treasury hedged one £200m cohort of five-year fixes, with four years of fix left, with a pay-fixed swap whose notional amortises on the base-CPR schedule: (1 − CPR) to the power of the years gone.
One borrower owes £180,000, interest only, on a five-year fix at 4.20%. They are in year 4, with 2 years of fix left. Calderwick's early repayment charge falls 4%, 4%, 3%, 2%, 1% in years 1 to 5. Rates have fallen, and a new two-year fix costs 3.00%. Take £1 a year for two years as worth £1.94 today.
Lessons: L3.6.08: Optionality in loans
(a)What monthly prepayment rate (SMM) matches the base CPR? Answer in %.
%(b)In the parallel down scenario, what share of a fixed-rate cohort is still on the book after three years? Answer in %.
%(c)If prepayment runs at the parallel down CPR for two years, what is the hedge ratio of the cohort (swap notional over mortgages)? Answer in %.
%(d)What does the borrower gain, in today's money, by repaying and refixing (negative if it does not pay)? Answer in £.
£
Problem 7A swap, a ladder, and who carries the risk
L3.6.10 · L3.6.11Treasurer and FTP desk
ALCO's paper proposes a £250m five-year swap: Calderwick pays 4.29% fixed (today's five-year swap rate) and receives SONIA, reset quarterly in three monthly cohorts (on average a month and a half to the first reset). Both legs are worth about £250m; the fixed leg has a duration of 4.53 years and the SONIA leg 0.125.
Calderwick's FTP credits the core current accounts with the yield of a replicating portfolio: a notional five-year ladder of 60 equal monthly tranches, rolled for years, each written at the five-year swap rate of its month. It is internal (no swaps), so it is not in Problems 1 to 5. The tranches earn, by years left to run:
| Years left | Under 1 | 1–2 | 2–3 | 3–4 | 4–5 |
|---|---|---|---|---|---|
| Fixed rate | 1.10% | 3.90% | 4.40% | 3.70% | 4.20% |
A new £50m three-year fixed-rate loan to a small business is priced at 6.60%; the three-year swap rate is 4.22% and Bank Rate 4.00%.
Lessons: L3.6.10: Hedging the banking book · L3.6.11: Funds transfer pricing
(a)With the swap, what is the duration estimate of the change in EVE in the +275bp parallel up shock? Answer in £m.
£m(b)With the swap, what is the change in year-1 NII for a 275bp parallel fall (Problem 2's figure plus the swap)? Answer in £m.
£m(c)Rates fall 275bp at once and stay there. What is the replicating ladder's yield a year later? Answer in %.
%(d)With matched-maturity transfer pricing, what margin does the business keep on the new loan in a year? Answer in £m.
£m(e)If treasury funds the loan overnight and does not hedge, what is its year-1 result on it after an immediate 275bp rise? Answer in £m.
£m
Problem 8Spreads, accounting and an SVB-style loss
L3.6.12Finance and risk, the capital plan
Calderwick's £400m of gilts were bought at par in 2021 at 1.25% and are held to collect at amortised cost, so their value changes do not reach the accounts. The £100m of covered bonds are at fair value through OCI (FVOCI), so theirs reach equity and CET1. Use the present values and durations of Problem 4, and take a covered bond's spread duration as its duration. Tax is 25%.
Lessons: L3.6.12: Credit spread risk in the banking book and the SVB case
(a)What is the unrealised loss on the gilts as a share of Tier 1? Answer in %.
%(b)Covered bond spreads widen 60bp, risk-free rates unchanged. What loss goes through OCI? Answer in £m.
£m(c)Deposits run and Calderwick must sell the whole gilt book. What is Tier 1 after the realised loss, after tax (nothing else changing)? Answer in £m.
£m(d)Why is the gilt book an SVB-style risk?