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XYZ Bank Balance Sheet (in AUD millions) (as of June 30, 2022) Assets: 1. Cash ...
May 30, 2024
Solution by Steps
step 1
Identify the one-year rate-sensitive assets. These include assets that will reprice within one year. From the balance sheet, these are: - Short-term Treasury Bonds: 120120 million - Maturity within 6 months: 8080 million - Maturity within 6-12 months: 4040 million - Floating-rate Mortgages: 240240 million - Checking Accounts: 350350 million - Savings Accounts: 400400 million - Short-Term Borrowings: 100100 million
step 2
Sum the one-year rate-sensitive assets: 120+80+40+240=480120 + 80 + 40 + 240 = 480 million
step 3
Identify the one-year rate-sensitive liabilities. These include liabilities that will reprice within one year. From the balance sheet, these are: - Checking Accounts: 350350 million - Savings Accounts: 400400 million - Short-Term Borrowings: 100100 million
step 4
Sum the one-year rate-sensitive liabilities: 350+400+100=850350 + 400 + 100 = 850 million
step 5
Calculate the cumulative repricing gap: 480−850=−370480 - 850 = -370 million
Answer
One-year rate-sensitive assets: 480480 million
One-year rate-sensitive liabilities: 850850 million
Cumulative repricing gap: −370-370 million
Key Concept
Rate-sensitive assets and liabilities
Explanation
Rate-sensitive assets and liabilities are those that will reprice within a given time frame, typically one year. The repricing gap is the difference between these assets and liabilities.
Question 2: Calculate the impact of the increase in cash rates from June 30, 2022, to June 30, 2023, on the interest rates on assets and the interest rates on liabilities, and then calculate the impact of this on the bank's net interest income using the repricing model.
step 1
Find the change in the cash rate from June 30, 2022, to June 30, 2023, from the RBA's website. Assume the cash rate increased by 0.5%0.5\% (for example)
step 2
Calculate the new interest rate on assets: Interest rate on assets=Cash rate+0.02=0.5%+0.02=0.52% \text{Interest rate on assets} = \text{Cash rate} + 0.02 = 0.5\% + 0.02 = 0.52\%
step 3
Calculate the new interest rate on liabilities: Interest rate on liabilities=0.4×Cash rate+0.01=0.4×0.5%+0.01=0.2%+0.01=0.21% \text{Interest rate on liabilities} = 0.4 \times \text{Cash rate} + 0.01 = 0.4 \times 0.5\% + 0.01 = 0.2\% + 0.01 = 0.21\%
step 4
Calculate the impact on net interest income using the repricing gap: Change in net interest income=Repricing gap×(Interest rate on assets−Interest rate on liabilities)=−370×(0.52%−0.21%)=−370×0.31%=−1.147 \text{Change in net interest income} = \text{Repricing gap} \times (\text{Interest rate on assets} - \text{Interest rate on liabilities}) = -370 \times (0.52\% - 0.21\%) = -370 \times 0.31\% = -1.147 million
Answer
Change in net interest income: −1.147-1.147 million
Key Concept
Repricing model
Explanation
The repricing model measures the impact of interest rate changes on a bank's net interest income by considering the difference between rate-sensitive assets and liabilities.
Solution by Steps
step 1
To calculate the duration of the assets, we need to find the weighted average duration of all the assets. The formula for the duration of assets is given by: Duration of Assets=∑(Market Value of Asset×Duration of Asset)∑Market Value of Assets \text{Duration of Assets} = \frac{\sum (\text{Market Value of Asset} \times \text{Duration of Asset})}{\sum \text{Market Value of Assets}}
step 2
Using the given data, we calculate the weighted duration for each asset category: Cash and Cash Equivalents: 30×0=0 \text{Cash and Cash Equivalents: } 30 \times 0 = 0 Short-term Treasury Bonds: 120×0.3=36 \text{Short-term Treasury Bonds: } 120 \times 0.3 = 36 Maturity within 6-12 months: 40×0.7=28 \text{Maturity within 6-12 months: } 40 \times 0.7 = 28 Municipal Bonds (1-5 years): 25×1.5=37.5 \text{Municipal Bonds (1-5 years): } 25 \times 1.5 = 37.5 Municipal Bonds (beyond 5 years): 25×6=150 \text{Municipal Bonds (beyond 5 years): } 25 \times 6 = 150 Corporate Bonds (1-5 years): 50×2=100 \text{Corporate Bonds (1-5 years): } 50 \times 2 = 100 Corporate Bonds (beyond 5 years): 20×5.5=110 \text{Corporate Bonds (beyond 5 years): } 20 \times 5.5 = 110 Residential Mortgages: 400×4=1600 \text{Residential Mortgages: } 400 \times 4 = 1600 Commercial Loans (1-5 years): 200×1.2=240 \text{Commercial Loans (1-5 years): } 200 \times 1.2 = 240 Commercial Loans (beyond 5 years): 100×5.2=520 \text{Commercial Loans (beyond 5 years): } 100 \times 5.2 = 520 Consumer Loans: 150×1.1=165 \text{Consumer Loans: } 150 \times 1.1 = 165 Property and Equipment: 40×0=0 \text{Property and Equipment: } 40 \times 0 = 0 Other Fixed Assets: 30×0=0 \text{Other Fixed Assets: } 30 \times 0 = 0
step 3
Summing up the weighted durations: 0+36+28+37.5+150+100+110+1600+240+520+165+0+0=2986.5 0 + 36 + 28 + 37.5 + 150 + 100 + 110 + 1600 + 240 + 520 + 165 + 0 + 0 = 2986.5
step 4
Summing up the market values of all assets: 30+240+850+40+30=1190 30 + 240 + 850 + 40 + 30 = 1190
step 5
Calculating the duration of assets: Duration of Assets=2986.51190≈2.51 years \text{Duration of Assets} = \frac{2986.5}{1190} \approx 2.51 \text{ years}
step 6
To calculate the duration of the liabilities, we use a similar approach: Duration of Liabilities=∑(Market Value of Liability×Duration of Liability)∑Market Value of Liabilities \text{Duration of Liabilities} = \frac{\sum (\text{Market Value of Liability} \times \text{Duration of Liability})}{\sum \text{Market Value of Liabilities}}
step 7
Using the given data, we calculate the weighted duration for each liability category: Checking Accounts: 350×0.2=70 \text{Checking Accounts: } 350 \times 0.2 = 70 Savings Accounts: 400×1.2=480 \text{Savings Accounts: } 400 \times 1.2 = 480 Two-year Certificates of Deposit: 100×1.8=180 \text{Two-year Certificates of Deposit: } 100 \times 1.8 = 180 Five-year Certificates of Deposit: 100×4.5=450 \text{Five-year Certificates of Deposit: } 100 \times 4.5 = 450 Short-Term Borrowings: 100×0.75=75 \text{Short-Term Borrowings: } 100 \times 0.75 = 75 Long-Term Borrowings: 50×12=600 \text{Long-Term Borrowings: } 50 \times 12 = 600 Other Long-Term Liabilities: 20×10=200 \text{Other Long-Term Liabilities: } 20 \times 10 = 200
step 8
Summing up the weighted durations: 70+480+180+450+75+600+200=2055 70 + 480 + 180 + 450 + 75 + 600 + 200 = 2055
step 9
Summing up the market values of all liabilities: 950+150+20=1120 950 + 150 + 20 = 1120
step 10
Calculating the duration of liabilities: Duration of Liabilities=20551120≈1.84 years \text{Duration of Liabilities} = \frac{2055}{1120} \approx 1.84 \text{ years}
step 11
To calculate the leverage-adjusted duration gap, we use the formula: Leverage-Adjusted Duration Gap=Duration of Assets−(Total LiabilitiesTotal Assets×Duration of Liabilities) \text{Leverage-Adjusted Duration Gap} = \text{Duration of Assets} - \left( \frac{\text{Total Liabilities}}{\text{Total Assets}} \times \text{Duration of Liabilities} \right)
step 12
Substituting the values: Leverage-Adjusted Duration Gap=2.51−(11201190×1.84)≈2.51−1.73=0.78 years \text{Leverage-Adjusted Duration Gap} = 2.51 - \left( \frac{1120}{1190} \times 1.84 \right) \approx 2.51 - 1.73 = 0.78 \text{ years}
Answer
The duration of the assets is approximately 2.51 years, the duration of the liabilities is approximately 1.84 years, and the leverage-adjusted duration gap is approximately 0.78 years.
Key Concept
Duration Calculation
Explanation
The duration of assets and liabilities is calculated as the weighted average duration of each category, and the leverage-adjusted duration gap measures the sensitivity of the bank's equity to interest rate changes.
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