Part I 1
Calculation of overall Macaulay Duration for 1
Calculation of Duration Gap for the bank 1
Scenario Analysis 2
Estimation of magnitude of interest rate increase 3
Part II 4
Market price (in US$) of the three T-notes/bonds 4
Macaulay Duration values of the three T-notes/Bonds 4
Convexity values of the three T-bonds 5
Part III 7
Maximum Amount of Investment 7
Investment Selection 7
Scenario Analysis 9
Estimation of magnitude of interest rate increase 10
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%,