Valuation

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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

Part I

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 = (Duration A-LADuration L) * A / E

= (4.00-170200*2.18)*200/30

=14.33

Calculation of Duration Gap for the bank

Duration Gap = Duration A-LADuration L = 4.00-170200*2.18 = 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.

Scenario Analysis

According to △PP = -DMacaulay * (△y1+(y2)), 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...