Case 037Stress testing and scenariosWarm up

A small cooperative bank holds a large government bond portfolio as held-to-maturity. Yields rise 200 basis points. How big is the hidden loss against capital, and why does the accounting label not make it go away?

The situation

Vedmora Cooperative Bank holds Rs 3,000 crore of government bonds with a modified duration of 4.5. They are classified as held to maturity (HTM), so they sit in the accounts at amortised cost and price changes do not flow through profit or capital. The bank's capital is Rs 400 crore.

Over a year, yields on similar bonds rise by 200 basis points. The bonds are government paper, so there is no default risk.

Your task

What is the unrealised loss, how does it compare with capital, and why is it still a loss if the accounts do not show it?

Quick check

Roughly how large is the unrealised loss on the bonds?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The bonds have lost about Rs 270 crore of value, 67.5% of the bank's Rs 400 crore of capital. Duration of 4.5 times a 2% rise gives a 9% fall. The HTM label keeps the loss out of the accounts, but the bank either realises it by selling or pays it slowly by earning below-market interest for years. If depositors withdraw and bonds must be sold, capital falls to about Rs 130 crore.

Step 1How big is the loss, and against what?

Buy a fixed deposit at 7%, and next month the bank offers 9% to new customers. Your deposit has not defaulted, but nobody would pay you full price for a 7% deposit when 9% is on offer. A bond's price falls by roughly its duration times the rise in yield: 4.5 times 2%, a 9% fall, Rs 270 crore on Rs 3,000 crore. Against capital of Rs 400 crore that is 67.5%. The duration estimate is a straight-line approximation; for a rise this size the true loss is slightly smaller, but the order of magnitude is what matters.

The accounts show Rs 400 crore of capital; the economics show Rs 130 crore400Capital in the accounts270Unrealised bond loss3,000 x 4.5 x 2%130lost if soldCapital if bonds are sold32% of the starting level
Vedmora's Rs 400 crore of capital sits against a Rs 270 crore unrealised loss on its held-to-maturity bonds, so if the bonds had to be sold its capital would fall to Rs 130 crore.
Step 2If the bank holds to maturity, is the loss real?

Yes, it just arrives differently. If the bank keeps the bonds, it earns their old, lower coupons while its depositors, sooner or later, must be paid rates closer to the new market level. That shortfall, roughly 2% on Rs 3,000 crore or Rs 60 crore a year over the bonds' remaining life, adds up to about the same loss, paid slowly through thinner margins instead of all at once. The held-to-maturityAn accounting category for bonds the bank intends and is able to keep until they mature. They are carried at cost, so market price changes do not appear in profit or capital. label decides when the loss is recognised, not whether it exists.

Step 3How much further could yields rise before capital is gone?

Each 100 basis points costs about 1% of the book times 4.5, Rs 135 crore. Capital of Rs 400 crore is used up at a rise of about 296 basis points. A small bank whose deposits are mostly local households may never have to sell, which is why the risk hides; but a cooperative bank facing a run, or a regulator requiring it to mark the book, would crystallise the loss at once.

Every 100 basis points costs about Rs 135 crore of a Rs 400 crore cushion2004006000100200300400Rise in yields, basis pointsUnrealised loss, Rs croreall of Vedmora's capital: 400+200 bp: loss 270+296 bp: capital gone
The unrealised loss grows by about Rs 135 crore for every 100 basis point rise in yields, reaching Rs 270 crore at 200 basis points and all of Vedmora's Rs 400 crore capital at about 296 basis points.

What a risk manager would ask for: an economic value of equity measure that marks every asset and liability to market regardless of accounting category, a limit on that measure, and a funding stress test that asks how many deposits could leave before bonds must be sold. Regulators set their own rules on how much a bank may hold as HTM; confirm the current limits before relying on a figure.

Where candidates lose it

The first trap is to answer that government bonds are safe, so there is no loss. They are safe from default, not from price moves, and duration measures exactly that exposure.

The second is to accept that holding to maturity makes the loss disappear. It only moves it into future net interest income, and a bank that cannot hold, because depositors leave, loses the choice.

What the interviewer asks next

  • How would the answer change if the bank's deposits also repriced slowly?
  • What would an interest rate swap do to this position, and what would it cost?
  • Why might a regulator cap the share of bonds a bank may hold as held-to-maturity?

Company names and figures are illustrative.