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044

Case 044Liquidity risk and ALMHard

A bank with concentrated uninsured deposits and underwater held-to-maturity bonds faces a social-media-driven run. Compute the funding hole, the loss realised selling bonds to fill it, and what the bank should have measured beforehand.

1The situation

Selvanar Bank has Rs 20,000 crore of deposits. 45% are above the deposit insurance limit, and most of those belong to technology start-ups and their investors, who know one another and share news fast. Liquid assets, cash and central bank balances, are 18% of deposits.

It also holds Rs 6,000 crore of government bonds as held to maturity, bought when rates were low and now worth 8% below book value. A post about the bank's bond losses spreads online, and in two days half the uninsured deposits are withdrawn.

2Your task

How big is the funding hole, what loss does the bank realise by selling bonds to fill it, what happens if the run continues, and what should the bank have measured before any of this?

Quick check

To raise the Rs 900 crore gap by selling bonds worth 92% of book, what loss does the bank realise?

Worked solution

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

30-second answerThe answer to give first

The run takes Rs 4,500 crore against Rs 3,600 crore of liquid assets, a Rs 900 crore hole; selling bonds to fill it realises about Rs 78 crore of loss. If the other half of uninsured deposits follows, the bank must sell about Rs 4,891 crore more and realises nearly all of the Rs 480 crore hidden loss. Deposit concentration, uninsured run-off speed and the unrealised bond loss were all measurable in advance, and none needed hindsight.

Step 1How big is the hole in the first two days?

A village moneylender who keeps some cash in the box and the rest lent out is fine until everyone who heard the same rumour arrives on the same morning. Half of Rs 9,000 crore of uninsured deposits, Rs 4,500 crore, leaves in two days, against Rs 3,600 crore of liquid assets, leaving a Rs 900 crore hole. The speed matters as much as the size: liquidity stress measures usually assume outflows over a month, and this one took two days.

Liquid assets cover 3,600 of a 4,500 run; bond sales cover the rest, at a lossOutflow in two days4,500: half of 9,000 uninsuredHow it is met3,600 liquid assets900bond salesBonds sold at book978 of book sold for 900 =loss 78Rs crore. Bonds sell at 92% of book value, so each Rs 100 of cash costs Rs 108.7 of book.
Selvanar loses Rs 4,500 crore of uninsured deposits in two days against Rs 3,600 crore of liquid assets; filling the Rs 900 crore gap means selling Rs 978 crore of bonds at book value and realising a Rs 78 crore loss.
Step 2What does selling the bonds cost, and why is it worse than it looks?

The bonds are worth 92% of book, so each Rs 100 of cash needs Rs 108.7 of book value. Raising Rs 900 crore means selling Rs 978 crore at book and realising a loss of Rs 78 crore. The larger problem is what the sale reveals: the whole book carries a hidden loss of Rs 480 crore, and selling part of a held-to-maturity book can, under many accounting rules, force the rest to be marked to market. Confirm the rule that applies. Either way, the market now knows the loss is real, which is what the depositors feared.

Step 3What if the run continues?

Runs rarely stop at half. If the remaining Rs 4,500 crore of uninsured deposits leaves, the bank has no liquid assets left and must sell about Rs 4,891 crore of bonds at book, realising another Rs 391 crore. Realised losses reach about Rs 470 crore, almost the whole hidden Rs 480 crore, and only about Rs 130 crore of bonds are left. At that point insured depositors start to worry too. This is the mechanism to describe: a run converts an accounting loss into a realised one, and the realised loss feeds the run.

The run turns the hidden Rs 480 crore into a realised one, sale by saleBook value6,000 held to maturity, at costMarket value5,520hidden 480Sold in the runwave 1wave 2 if the rest of the uninsured leave: 4,891Wave 1: sell 978 of book, realise 78. Wave 2: sell 4,891, realise 391.Realised in all: 470 of the 480, with 130 of bonds left to sell.
Selvanar's Rs 6,000 crore bond book is worth Rs 5,520 crore, a hidden Rs 480 crore loss; the first wave of the run realises Rs 78 crore of it, and a second wave would realise another Rs 391 crore, leaving about Rs 130 crore of bonds.
Step 4What should the bank have measured beforehand?

Four things, all available before the run. First, deposit concentration: 45% uninsured and in one networked industry is a single risk, not thousands of small ones. Second, a run-off assumption for uninsured deposits that matched their behaviour, days rather than a month. Third, the unrealised loss on held-to-maturity bonds against capital, reported to the board as if the bonds had to be sold. Fourth, contingent funding: bonds pre-positioned as collateral with the central bank or repo counterparties can be borrowed against, roughly Rs 5,244 crore at an illustrative 5% haircut on market value, without selling them and without realising the loss. The liquidity coverage ratioA regulatory measure comparing high-quality liquid assets with net cash outflows over a 30-day stress; its outflow rates for each deposit type are assumptions set by the regulator. would not have caught all of this, because its standard outflow rates assume a month, not two days.

Where candidates lose it

The first slip is to compute the loss as 8% of Rs 900 crore, Rs 72 crore. The discount applies to the book value sold, so the bank must sell more than Rs 900 crore of bonds, and the loss is about Rs 78 crore.

The second is to stop at the first wave. The case turns on the feedback: a realised loss makes remaining depositors more nervous, and the next wave empties the bond book and realises nearly the whole hidden loss.

What the interviewer asks next

  • How would you set a run-off rate for uninsured deposits concentrated in one industry?
  • Why is borrowing against the bonds better than selling them, and what could stop the bank from doing it?
  • Which single early warning indicator would you have put on the bank's risk dashboard?
← Case 043An underfunded pension fund must close its gap in ten years without risking a large loss in any one year. Set the return target and find the equity share that meets it inside the loss limit.Case 045 →A bank's fraud model flags 2% of transactions and catches 70% of fraud; a challenger flags half as many and catches 60%. Given the cost of a missed fraud and of reviewing an alert, which model should the bank run?

Company names and figures are illustrative.

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