Risk Management puzzles, solved step by step

Puzzles
100
Traced to a firm
17
Topics
13
Hard
30
Topic
All topicsCapital and leverage6Compounding and drawdowns8Correlation and diversification8Counterparty exposure and collateral7Credit risk arithmetic10Duration and rates7Liquidity and balance sheet7Logic, estimation and brainteasers7Operational loss and fraud7Options and Greeks7Probability and base rates8Statistics and estimation10VaR and expected shortfall8
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–2 of 2 · filtered from 100Clear filters
  1. 032A bank holds Rs 1,000 crore of liquid government bonds yielding 6.8% instead of lending the money at 10%, and it funds the whole amount at 6%. What does carrying this liquidity buffer cost the bank each year?Liquidity and balance sheetWarm upTreasury and ALM

    Try it first

    Which comparison gives the cost of the buffer?

    Show the worked solution

    About Rs 32 crore a year, before adjusting for credit losses on the loans. The money is funded at 6% either way, so funding drops out. The cost of the buffer is the income it gives up: lending would earn 10% and the bonds earn 6.8%, a 3.2 point gap on Rs 1,000 crore. The buffer still earns Rs 8 crore over funding; it just earns Rs 32 crore less than loans would.

    Why does the funding cost drop out of the answer?

    A family that keeps Rs 5 lakh in a savings account instead of prepaying a home loan pays the same salary-funded EMI either way. The cost of the emergency fund is the gap between the loan rate saved and the savings rate earned. The cost of any buffer is an opportunity cost: what the same rupees would have earned in their next-best use, with everything common to both uses cancelling out. Funding at 6% is common to both uses here, so the only number that matters is 10% minus 6.8%.

    The buffer's cost is what the same money would have earned as loans6.0%Funding cost6.8%Liquid bonds10.0%Lending3.2 pts+0.8 overfundingRs 1,000 crore x 3.2%Rs 32 crorea year: the insurancepremium for liquidityAfter a 1.2% expectedloss on the loans:Rs 20 crore
    Lending earns 10.0% and liquid bonds earn 6.8% on money funded at 6.0%, so holding Rs 1,000 crore of bonds instead of loans gives up 3.2 points, Rs 32 crore a year, even though the bonds still earn Rs 8 crore over funding.

    Is 3.2 points the true gap?

    Not quite, and saying why is the part interviewers listen for. A 10% loan yield is before credit losses and before the capital loans consume; government bonds need neither. If the loans carry an assumed expected loss of 1.2% a year, the like-for-like gap narrows to 2.0 points, and the buffer costs about Rs 20 crore rather than Rs 32 crore. Capital would narrow it further. The headline number is an upper bound; the risk-adjusted number is what the treasurer should defend.

    The relationship
    cost=size×(yloan−EL−yliquid)=1,000×(10.0%−1.2%−6.8%)=20\text{cost} = \text{size} \times (y_{\text{loan}} - EL - y_{\text{liquid}}) = 1{,}000 \times (10.0\% - 1.2\% - 6.8\%) = 20
    y_loanyield on the loans that could have been made, 10%
    ELan assumed annual expected credit loss on those loans, 1.2%
    y_liquidyield on the liquid bonds, 6.8%
    What it says in wordsCompare what the money earns in each use after the costs that differ between them.

    Close by naming what the premium buys. The buffer is insurance: in a deposit run it can be sold or pledged within days, while loans cannot. Liquidity coverageA regulatory measure comparing high-quality liquid assets with the net cash a bank could lose in a 30-day stress. rules make a floor of it compulsory; confirm the current requirement with the regulator rather than from memory. Above that floor, a bank is choosing how much insurance to buy, and Rs 20 to 32 crore a year is the price tag to weigh against the run it protects against.

    Where candidates lose it

    The common wrong answer is zero, because the bonds earn 6.8% against a 6% funding cost and so look profitable. Positive carry is not the same as no cost; the bank has given up a better use of the money.

    The second miss is quoting Rs 32 crore as if loans were risk-free. Mention expected loss and capital in one sentence and you show you compare like with like.

    What the interviewer asks next

    • Rates on liquid bonds rise to 7.5% with everything else fixed. What happens to the cost?
    • Why might a bank hold more liquidity than the regulatory minimum?
    • How would you allocate this cost to the business lines that create the liquidity need?
  2. 057A bank has loans of Rs 95 crore and deposits of Rs 100 crore. Deposits fall 10%. If the bank keeps its loan-to-deposit ratio at 95%, by how much must its loans shrink?Liquidity and balance sheetWarm upTreasury and ALMBank credit risk

    Try it first

    Quick answer: how much lending goes?

    Show the worked solution

    Loans must shrink by Rs 9.5 crore, from Rs 95 crore to Rs 85.5 crore. Deposits fall 10% to Rs 90 crore, and 95% of Rs 90 crore is Rs 85.5 crore. The Rs 10 crore that leaves is met by Rs 9.5 crore of loans running off and Rs 0.5 crore of liquid assets, so the bank's lending falls by the same 10% as its deposits.

    Why does a deposit outflow become a lending cut?

    A household that lives on its salary and lends a cousin money every month has to stop lending if the salary is cut. The cousin has done nothing wrong; the money simply is not there. A bank funding its loans from deposits is in the same position. Holding the loan-to-deposit ratio fixed means every rupee of deposit flight passes straight into less lending, scaled by the ratio.

    Keep the ratio fixed and a 10% deposit fall becomes a 10% loan shrinkBeforeDeposits100Loans + liquidLoans 95AfterDeposits90Loans + liquidLoans 85.5-10 out-9.5 loans-0.5 liquidliquid 5Loans / deposits: 95 / 100 = 95% and 85.5 / 90 = 95%
    Deposits fall from Rs 100 crore to Rs 90 crore. Keeping loans at 95% of deposits takes loans from Rs 95 crore to Rs 85.5 crore, so Rs 9.5 crore of lending runs off and liquid assets fall by Rs 0.5 crore to cover the rest of the outflow.

    What makes this harder in practice than on paper?

    Loans do not shrink on command. Term loans run off only as they repay, and calling them early harms the borrower and the bank's franchise. In the short run the bank has to meet the outflow from liquid assets or new funding, and a buffer of Rs 5 crore against a Rs 10 crore outflow is not enough. That gap is why liquidity rules ask banks to hold enough high quality liquid assets to survive a stressed outflow without selling loans.

    The relationship
    ΔL=LDR×ΔD=0.95×(−10)=−9.5\Delta L = \text{LDR} \times \Delta D = 0.95 \times (-10) = -9.5
    \Delta Lthe change in loans, Rs crore
    \text{LDR}the loan-to-deposit ratio held fixed at 95%
    \Delta Dthe change in deposits, a fall of Rs 10 crore
    What it says in wordsWith the ratio fixed, loans change by the ratio times the change in deposits.

    Say the limitation: a real bank also has equity and wholesale funding on the liability side, and it could replace lost deposits with borrowing at a higher cost. The puzzle shuts that door deliberately, to show how directly a deposit run reaches lending when no other funding is available.

    Where candidates lose it

    The quick wrong answer is Rs 10 crore, matching the deposit fall one for one. That ignores that the ratio is 95%, not 100%, so only 95 paise of lending goes for every rupee of deposits.

    The more costly miss is stopping at the arithmetic. The interviewer wants to hear that loans cannot shrink overnight, so the outflow is met first from liquid assets, which is what a liquidity buffer is for.

    What the interviewer asks next

    • If the bank instead keeps loans unchanged, what does its ratio become?
    • How much liquid asset buffer would it need to meet a 20% outflow without shrinking loans?
    • Why do regulators care about the speed at which different deposits can leave?