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Duration Blue Stool Community Bank has the following market value balance shoot:
| Asset or Liability | Market value (in $ million) | Duration (in year) |
| Federal funds deposits | $ 31 | 0 |
| Accounts receivable | 540 | .20 |
| Short-term loans | 320 | .65 |
| Long-term loans | 98 | 5.25 |
| Mortgages | 435 | 12.85 |
| Checking and savings deposits | 615 | 0 |
| Certificates of deposit | 390 | 1.60 |
| Long-term financing | 285 | 9.80 |
| Equity | 134 | N/A |
- a. What is the duration of the assets?
- b. What is the duration of the liabilities?
- c. Is the bank immune to interest rate risk?
a.
To calculate: Duration of assets.
Duration:
It is an object used in bond valuation to determine the sensitivity of the bond. High duration comes with high probability of interest rate risk while in lower duration there is low risk of interest rate fluctuation.
Explanation of Solution
Calculation of duration of assets
| Assets |
Amount ($) |
Duration (in years) |
| Federal Fund deposits | 31 | 0 |
| Account receivables | 540 | 0.20 |
| Short term loans | 320 | 0.65 |
| Long term loan | 98 | 5.25 |
| Mortgage | 435 | 12.85 |
| Total | 1,424 |
Table (1)
Given,
Amount of federal fund deposit is $31.
Duration is 0 years.
Total amount of assets is $1,424.
Formula to calculate duration,
Duration=Number of year×Amount of assetTotal amount of assets
Substitute $31 for amount of federal fund deposit, 0 for number of years and $1,424 for total amount of assets.
Duration=0×$31$1,424=0 year
So, duration for federal fund deposit is 0 year.
Given,
Amount of account receivables is $540.
Duration is 0.20 years.
Total amount of assets is $1,424.
Formula to calculate duration,
Duration=Number of year×Amount of assetTotal amount of assets
Substitute $540 for amount of account receivables, 0.20 years for number of years and $1,424 for total amount of assets.
Duration=0.20×$540$1,424=0.07584 year
So, duration for account receivables is 0.07584 year.
Given,
Amount of short term loans is $320.
Duration is 0.65 years.
Total amount of assets is $1,424.
Formula to calculate duration is
Duration=Number of year×Amount of assetTotal amount of assets
Substitute $320 for amount of short term loans, 0.65 years for number of years and $1,424 for total amount of assets.
Duration=0.65×$320$1,424=0.14606 year
So duration for Short term loans is 0.14606 year.
Given,
Amount of long term loan is $98.
Duration is 5.25 years.
Total amount of assets is $1,424.
Formula to calculate duration,
Duration=Number of year×Amount of assetTotal amount of assets
Substitute $98 for amount of long term loan, 5.25 years for number of years and $1,424 for total amount of assets.
Duration=5.25×$98$1,424=0.36130 year
So, duration for long term loans is 0.36130 year.
Given,
Amount of mortgage is $435.
Duration is 12.85 years.
Total amount of assets is $1,424.
Formula to calculate duration,
Duration=Number of year×Amount of assetTotal amount of assets
Substitute $435 for amount of mortgage, 12.85 years for number of years and $1,424 for total amount of assets.
Duration=12.85×$435$1,424=3.9253 years
So, duration for mortgage is 3.9253 years.
Calculation of total duration of assets
Calculated values,
Duration of federal fund deposits 0 year.
Duration of account receivables is 0.07584 year.
Duration of short term loans is 0.14606 year.
Duration of long term loan is 0.36130 year.
Duration of mortgage is 3.9253 years.
Formula to calculate to total duration,
Total duration=(Duration of asset 1+Duration of asset 2+Duration of asset 3+Duration of asset 4)
Substitute 0 year for asset 1, 0.07584 year for asset 2, 0.14606 year for asset 3, 0.36130 year for asset 4, and 3.9253year for asset 5.
Total Duration=0+0.07584+0.14606+0.36130+3.9253=4.5085 years
So, total duration of assets is 4.5085 years.
b.
To calculate: Duration of liabilities.
Explanation of Solution
Calculation of duration of liabilities
| Liabilities |
Amount ($) |
Duration (in years) |
| Checking and saving deposit | 615 | 0 |
| Certificates of deposit | 390 | 1.60 |
| Long term financing | 285 | 9.80 |
| Equity | 134 | N/A |
| Total | 1,424 |
Table (2)
Given,
Amount of checking and saving deposit is $615.
Duration is 0 years.
Total amount of liabilities is $1,424.
Formula to calculate duration,
Duration=Number of year×Amount of liabilitiesTotal amount of liabilities
Substitute $615 for amount of checking and saving deposit, 0 for number of years and $1,424 for total amount of liabilities.
Duration=0×$615$1,424=0 year
So, duration for checking and saving deposit is 0 year.
Given,
Amount of certificates of deposit is $390.
Duration is 1.60 years.
Total amount of liabilities is $1,424.
Formula to calculate duration,
Duration=Number of year×Amount of liabilitiesTotal amount of liabilities
Substitute $390 for amount of certificates of deposit, 1.60 years for number of years and $1,424 for total amount of liabilities.
Duration=1.60×$390$1,424=0.43820 year
So, duration for certificates of deposit is 0.43820 year.
Given,
Amount of long term financing is $285.
Duration is 9.80 years.
Total amount of liabilities is $1,424.
Formula to calculate duration,
Duration=Number of year×Amount of liabilitiesTotal amount of liabilities
Substitute $285 for amount of long term financing, 9.80 years for number of years and $1,424 for total amount of liabilities.
Duration=9.80×$285$1,424=1.96 year
So, duration for long term financing is 1.96 year.
Calculation of total duration of liabilities
Given,
Duration of checking and saving deposit is 0 year.
Duration of certificates of deposit is 0.43820 year.
Duration of long term financing is 1.96 year.
Formula to calculate to total duration,
Total duration=(Duration of liability 1+Duration of liability 2+Duration of liability 3)
Substitute 0 year for liability 1, 0.43820 year for liability 2, and 1.96 year for liability 3.
Total Duration=0+0.43820+1.96=2.3982 years
So total duration of liabilities is 2.3982 years
c.
To explain: Whether the bank is immune to interest rate risk or not.
Answer to Problem 8QP
No, bank is not immune to interest rate risk.
Explanation of Solution
Since, the duration of assets and duration of liabilities is not the same, bank is not immune to the interest rate risk. It is mandating that the duration of assets and duration of liability to match for immune the interest rate of risk.
Therefore, bank is not immune to the interest rate of risk due the different duration of assets and liabilities.
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