Calculation of overall Macaulay Duration for1
Calculation of Duration Gap for the bank1
Estimation of magnitude of interest rate increase3
Market price (in US$) of the three T-notes/bonds4
Macaulay Duration values of the three T-notes/Bonds4
Convexity values of the three T-bonds5
Maximum Amount of Investment7
Estimation of magnitude of interest rate increase10
Calculation of overall Macaulay Duration for
i) The bank’s assets
Duration A=10.00% * 3.00 + 30.00% * 10.00 + 20.00% * 3.50 = 4.00
ii) The bank’s liabilities
Duration L = 82.35% * 2.00 + 17.65% * 3.00 = 2.18
iii) The bank’s net worth
Duration net worth =) * A / E
Calculation of Duration Gap for the bank
Duration Gap = = = 2.15
i) Duration Gap is positive.
ii) Positive duration gap indicates that this bank has more rate sensitive assets than rate sensitive liabilities.
If market interest rate increase, assets will lose more value than liabilities, thus reducing the value of the firm's equity.
If market interest rate decrease, assets will gain more value than liabilities, thus increasing the value of the firm's equity.
According to = - * (), where the interest is semi-annually compounded, we can firstly work out the change in market value for an individual item in both Asset and Liability sides. And then adding them up, we can calculate the value changes in total assets (△A) and total liabilities (△L). Finally, using the formula △E=△A-△L, we can obtain the change in market value of Equity.
For the given following interest rate changes △y= -2%,-1%, 0%, +1%, +2%, +3%, +4%, +5%, the corresponding changes in market value are demonstrated in following table.
We can also plot the following graph to show the variations of market values for assets, liabilities, and equity with respect to different interest rate changes. The vertical axis is the change in market value, while the horizontal axis is the change in interest rate.
From above scenario analysis, we can get following conclusions:
1. The change in asset value, liability value and equity value are negatively correlated with change in interest rate. That is, when change in interest rate is positive, variations of market values for assets, liabilities and equity would be negative and in larger magnitude for larger interest increase. For negative change in interest rate, all three values increase.
2. The impact of interest rate change on asset value is larger than that on liability and equity. This is reasonable as Asset = Liability + Equity. That is to say, assets value is more sensitive to interest rate change than liabilities and equity.
Estimation of magnitude of interest rate increase
From the above diagram, we can find out that when the market value of equity drops from $30B to $20B, the interest rate change is between +2% to 3% and around +2.5%. By trial and error, we can finally conclude that the interest rate increase is 2.42%. The result is as follows:
| |△y=2.42% | |change in asset value △A1 |-1.38 | |change in asset value △A2 |-14.10 | |change in asset value △A3 |-3.34 | |Change in Market Value of Total Assets △A |-18.83 | |change in Liability value △L1 |-6.70...