Question

Bank 2 Rate Sensative Fixed Rate Non Earning Assets Yield 600 250 150 Liabilities Rate 600 220 11% ON 100 Equity Total 1000 1000 32. Calculate the Gap 33. Calculate Net Interest income 34. Calculate Net Interest Margin 35. Recalculate Net Interest Income and Net Interest margin when interest rates increase by 1% 36. Calculate a the Duration and Modified Duration of the following Bond Current Price $1,026.24 Face Value 1000 Coupon Rate 8% Maturity 3 years Annual Bond 37. If Interest rates increase by 1 %, what will be the percentage change in the Bond's price?

Answer 1

32)  There is no gap in rate sensitive assets and liabilities but there is a positive gap between the fixed rate assets and liabilities of 250- 220= 30.

33)Net interest income

#interest income

Rate sensitive assets 600x8%= 48

Fixed rate assets 250x11% =27.5

total interest income = 75.5

#Interest payment

Rate sensitive liability 600x4%= 24

Fixed rate liability 220x6%= 13.2

total interest payment= 37.2

Net interest income= 75.5 - 37.2= 38.3

34. Net interest margin

= (Interest income - interest expenses)/ Average earning assets

38.3/850= 0.045

35. When interest increases by 1%

Income from rate sensitive assets =600x9%= 54

Expense on rate sensitive liability = 600x5%= 30

The income and expense on fixed assets and liabilities will remain the same.

New interest income = 54+27.5= 81.5

New interest expense = 30+13.2 = 43.2

New net interest income = 81.5 - 43.2= 38.3

New interest margin = 38.3/850 = 0.045

36.

Duration

year	coupon+maturity value	pvf	pv
1	80	0.926	74.08
2	80	0.857	68.56
3	80+1000	0.794	857.52

we will calculate weights as per the different present values.

Total pv is 1000.16

W1 = 74.08/1000.16= 0.07

W2= 68.56/1000.16=0.07

W3= 857.52/1000.16=0.86

Multiplying each weight with subsequent time period

0.07x1= 0.07

0.07x2= 0.14

0.86x3= 2.58

Duration is 0.07+0.14+2.58 = 2.79 years

Modified duration = (-) Duration/ 1+ yield

2.79/0.08 = 34.87

37. If interest rate rises by 1%, the bond price will decrease by 34.87%.