📘 FRR – 50 Important Numerical

 

📘 FRR – 50 Important Numerical

 

Credit Risk (Q1–Q17)

Q1.
A bank has granted a corporate term loan of USD 100 million. The internal risk model assigns a probability of default (PD) of 2%, while the loss given default (LGD) is estimated at 40%. Assuming the full exposure at default (EAD) is recognized, calculate the expected loss on this exposure.

Q2.
A commercial bank has extended a USD 50 million loan classified under the Basel I standardized approach with a 100% risk weight. Under regulatory requirements, banks must maintain capital equal to 8% of risk-weighted assets. What is the regulatory capital that must be held for this loan?

Q3.
A bank has an undrawn revolving credit line of USD 200 million provided to a corporate borrower. Under Basel rules, the Credit Conversion Factor (CCF) is 50%, and the exposure attracts a 100% risk weight. Compute the risk-weighted assets (RWA) for this facility.

Q4.
The inflation rate in the U.S. is 2% per year, while the inflation rate in the Eurozone is 5% per year. The current spot exchange rate is 1.10 USD/EUR.
According to Relative Purchasing Power Parity (PPP), what will be the expected exchange rate (USD/EUR) one year from now?

Q5.
The yield on a government bond is currently 3% while the yield on a corporate bond of similar maturity is 6%. Compute the credit spread for the corporate bond over the government bond.

Q6.
A securitization pool has a total regulatory capital requirement of USD 15 million. The pool is divided into three equal tranches. What is the capital charge allocated to each tranche, assuming equal distribution?

 

Q7.
Under the SA-CCR framework for derivatives, the exposure at default (EAD) is calculated as

where α = 1.4. If the current Replacement Cost (RC) is USD 5 million and Potential Future Exposure (PFE) is USD 10 million, compute the EAD.

Q8.
A bank has USD 400 million in off-balance sheet commitments. The Credit Conversion Factor (CCF) is 30%, and the risk weight for the exposure is 75%. Calculate the total RWA for these commitments.

Q9.
A portfolio has an Expected Loss (EL) of USD 3 million and an Unexpected Loss (UL) of USD 6 million. Under Basel rules, economic capital is defined as UL – EL. Compute the required economic capital.

Q10.
For a corporate bond, the expected loss based on PD and LGD is 2%. If investors require an additional risk premium of 1%, what is the total credit spread that should be charged?

Q11.
A bank has granted a term loan of USD 120 million secured by collateral worth USD 30 million. The probability of default (PD) is 5% and the loss given default (LGD) is 40%. Assuming collateral is already incorporated into the LGD estimate, calculate the expected loss.

Q12.
A credit risk model estimates the unexpected loss (UL) on a portfolio as USD 7 million, while the expected loss (EL) is USD 2 million. Compute the minimum regulatory capital requirement based on the IRB formula.

Q13.
A bank holds an exposure of USD 150 million with a 50% risk weight under Basel rules. Regulatory capital must be held at 8% of RWA. Calculate the capital required for this exposure.

Q14.
A corporate client has an undrawn facility of USD 100 million. The applicable credit conversion factor (CCF) is 40% and the exposure carries a 100% risk weight. What is the RWA for this facility?

Q15.
A bank assesses a loan with a probability of default (PD) of 3% and loss given default (LGD) of 40%. Investors require an additional 2% risk premium. Compute the minimum spread the bank should charge above the risk-free rate to compensate for credit risk.

Q16.
A bank funds its loan portfolio at a weighted average cost of funds (WACF) of 5%. A corporate loan is priced at 8% with an expected credit spread of 2%. Calculate the net profit margin for the bank on this loan.

Q17.
The Value-at-Risk (VaR) of a credit portfolio is estimated at USD 50 million, while the expected loss (EL) is USD 20 million. Compute the bank’s economic capital requirement.

Market Risk (Q18–Q33)

Q18.
A bond portfolio loses USD 50,000 in value when interest rates increase by 5 basis points. Compute the price value of a basis point (PVBP) for this portfolio.

Q19.
A bond has a modified duration of 6 years. If yields rise by 1%, estimate the percentage change in the bond’s price.

Q20.
A trading desk earns USD 12 million in profit while its Value-at-Risk (VaR) is estimated at USD 60 million. Compute the Risk-Adjusted Return on Capital (RAROC).

Q21.
A portfolio worth USD 100 million has a volatility of 3%. Compute the 1-day 95% Value-at-Risk (VaR) using a Z-value of 1.65.

Q22.
Using historical simulation, the 5th worst daily return in a 250-day period is –2%. For a portfolio worth USD 200 million, calculate the 95% daily VaR.

Q23.
A bond’s value decreases by USD 20,000 when yields rise by 2 basis points. Compute the PV01 (price value of one basis point).

Q24.
If 3-month LIBOR is 3% and the 3-month T-bill yield is 1%, compute the TED spread.

Q25.
A portfolio has two bonds: Bond A with 40% weight and duration 5, and Bond B with 60% weight and duration 8. Compute the portfolio duration.

Q26.
A bond has a modified duration of 6 years and a yield to maturity of 5%. Compute the Macaulay duration.

Q27.
A futures contract has a notional of USD 20 million and requires a margin deposit of 5%. Compute the margin requirement.

Q28.
The floating leg of a swap is valued at USD 10 million while the fixed leg is valued at USD 9.7 million. What is the market value of the swap?

Q29.
A business unit reports USD 15 million profit. The economic capital allocated is USD 100 million. Compute the RAROC.

Q30.
A bank has Tier 1 capital of USD 10 million and total exposures of USD 400 million. Compute the leverage ratio and state whether it meets Basel III minimum requirements of 3%.

Q31.
The daily standard deviation of portfolio returns is USD 1 million. Compute the 10-day 95% VaR using the square-root-of-time rule.

Q32.
A trader is long USD 200 million and short USD 190 million. Compute the gross exposure and the net exposure.

Q33.
Two corporate borrowers each have a probability of default (PD) of 4%. The defaults are assumed to be independent.
What is the probability that both borrowers default simultaneously?

ALM (Q34–Q50)

Q34.
A bank’s balance sheet shows present value of assets = USD 500 million and present value of liabilities = USD 450 million. Compute the Economic Value of Equity (EVE).

Q35.
The average duration of assets is 6 years and liabilities is 2 years. Assets = USD 400 million, Liabilities = USD 360 million. Compute the duration gap using:

Q36.
Tier 1 capital = USD 20m, Tier 2 = USD 10m, RWA = USD 300m. Compute the Capital Adequacy Ratio (CAR).

Q37.
A bank has Tier 1 capital of USD 15m and total exposure of USD 500m. Compute the leverage ratio and check against the Basel minimum.

Q38.
A bank funds itself using three sources: Deposits of ₹1,000 Cr @ 3%, Interbank borrowings of ₹500 Cr @ 5%, and Bonds of ₹500 Cr @ 6%. Compute the Weighted Average Cost of Funds (WACF).

Q39.
If a bank lends at 7% and its WACF is 5%, compute the spread under Funds Transfer Pricing (FTP).

Q40.
Available Stable Funding (ASF) = 800m, Required Stable Funding (RSF) = 1,000m. Compute the Net Stable Funding Ratio (NSFR).

Q41.
High-Quality Liquid Assets (HQLA) = 120m, Net 30-day cash outflows = 100m. Compute the Liquidity Coverage Ratio (LCR).

Q42.
Total capital = 25m, RWA = 400m. Compute the Capital Adequacy Ratio (CAR) and state if it meets the 8% minimum.

Q43.
A bank has a duration gap of 4 years, total assets = 500m. If interest rates rise by 1%, compute the change in Economic Value of Equity (EVE).

Q44.
Deposits = 200m at 2% interest. Compute the annual cost of deposit funding.

Q45.
A bank enters into a repo transaction of USD 50m with a 10% haircut. How much cash does the bank receive?

Q46.
A repo haircut is 20%. Compute the leverage the bank can achieve using this collateral.

Q47.
If the risk-free rate is 3% and the required credit spread is 2%, compute the fair loan rate a bank should charge.

Q48.
A bank has a capital ratio of 9%. The regulatory requirement is 8% plus a 2.5% capital conservation buffer. Compute the shortfall in the capital ratio.

Q49.
A liability-sensitive bank faces a rise in interest rates. What will be the impact on its Net Interest Income (NII)?

Q50.
A bank’s short-term (<30 days) maturing assets = 80m, liabilities maturing = 100m. Compute the liquidity gap.

 

📘 FRR – 50 Important Numericals (Solutions)

🔹 Credit Risk (Q1–Q17)

 

Q1. Expected Loss = PD × LGD × EAD = 0.02 × 0.40 × $100m = $0.8m.

Q2. Regulatory Capital = (EAD × RW) × 8% = (50m × 1.0) × 0.08 = $4m.

Q3. RWA = Notional × CCF × RW = 200m × 0.50 × 1.0 = $100m.

Q4. Formula (Relative PPP):

Here:

  • St=1.10 USD/EURS
  • Domestic inflation (U.S.) = 2% = 0.02
  • Foreign inflation (Eurozone) = 5% = 0.05

Substitute:

1.10×0.9714= 1.10 \times 0.9714=1.10×0.9714 =1.0686= 1.0686=1.0686

 Expected rate after 1 year = 1.07 USD/EUR (approx.)

 

Q5. Credit Spread = 6% – 3% = 3%.

Q6. In real Basel securitization, capital is not allocated equally across tranches (equity absorbs most). But in our simplified question: 15m ÷ 3 = $5m per tranche.

Q7. EAD = 1.4 × (5m + 10m) = 1.4 × 15m = $21m.

Q8. RWA = 400m × 0.30 × 0.75 = $90m.

Q9. Economic Capital (per our set) = UL – EL = 6m – 3m = $3m.

Q10. Credit Spread = EL (2%) + Risk Premium (1%) = 3%.

Q11. EL = 0.05 × 0.40 × 120m = $2.4m.

Q12. Capital = UL – EL = 7m – 2m = $5m.

Q13. Capital = (150m × 0.50) × 0.08 = $6m.

Q14. RWA = 100m × 0.40 × 1.0 = $40m.

Q15. Spread = (0.03 × 0.40 = 1.2%) + 2% = 3.2%.

Q16. Net Profit Margin = 8% – 5% – 2% = 1%.

Q17. Economic Capital = VaR – EL = 50m – 20m = $30m.

🔹 Market Risk (Q18–Q33)

Q18. PVBP = 50,000 ÷ 5 = $10,000 per bp.

Q19. ΔP% = –6 × 0.01 = –6%.

Q20. RAROC = 12m ÷ 60m = 20%.

Q21. VaR = 100m × 0.03 × 1.65 = $4.95m.

Q22. VaR = 200m × 0.02 = $4m.

Q23. PV01 = 20,000 ÷ 2 = $10,000.

Q24. TED Spread = 3% – 1% = 2%.

Q25. Portfolio Duration = 0.40×5 + 0.60×8 = 6.8 years.

Q26. Macaulay = 6 × (1 + 0.05) = 6.3 years.

Q27. Margin = 20m × 0.05 = $1m.

Q28. Swap Value = 10m – 9.7m = $0.3m.

Q29. RAROC = 15m ÷ 100m = 15%.

Q30. Leverage Ratio = 10m ÷ 400m = 2.5% (<3%, fails).

Q31. 1-day VaR = 1m × 1.65 = 1.65m. 10-day = 1.65 × √10 = $5.22m.

Q32. Gross = 200m + 190m = 390m; Net = 200m – 190m = 10m.

Q33. P(Both Default)=PD1​×PD2​ =0.04×0.04=0.0016

 

🔹 ALM (Q34–Q50)

Q34. EVE = 500m – 450m = $50m.

Q35. DG = 6 – 2×(360/400) = 6 – 1.8 = 4.2 yrs.

Q36. CAR = (20+10)/300 = 30/300 = 10%.

Q37. Leverage = 15/500 = 3% (meets).

Q38. WACF = 4.25%.

Q39. FTP Spread = 7% – 5% = 2%.

Q40. NSFR = 800/1000 = 80% (<100%).

Q41. LCR = 120/100 = 120% (>100%).

Q42. CAR = 25/400 = 6.25% (<8%).

Q43. ΔEVE = –4 × 500m × 0.01 = –$20m.

Q44. Cost = 200m × 2% = $4m.

Q45. Cash = 50m × 0.9 = $45m.

Q46. Leverage = 1/0.20 = 5×.

Q47. Rate = 3% + 2% = 5%.

Q48. Shortfall = 10.5% – 9% = 1.5%.

Q49. Liability-sensitive → rates ↑ → NII decreases.

Q50. Gap = 80m – 100m = –$20m.

 

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