a)

maturity of asset= (0.5*50,000+1*50,000)/100,000=0.75

maturity of liability= 1*100,000/100,000=1

maturity gap=0.75-1=-0.25 year

If interest rates rise, net worth will increase because the average maturity of the assets is lower than the average maturity of the liabilities. The opposite holds true if interest rates fall. That is, net worth will decrease.

b)

liability

FV=100,000, PMT=0, N=1

1 i=7%   PV1=93,457.94

2 I=10%  PV2=90.909.09

The cash flow of liability is decrease.

ASSEET

PMT=50,000  N=2  FV=0

1 I=7%  PV1=94987.71

2I=10% PV2=92970.52

The cash flow of asset is decrease.

Net interest income at 7%

NII=(50,000*0.5*7%+50,000*7%)-(100,000*7%)=-1.75

Net interest income at 10%

NII=(50,000*0.5*10%+50,000*10%)-(100,000*10%)=-2.5

The net interest income is decrease.

c)

liability

FV=100,000, PMT=0, N=1

1 i=7%   PV1=93,457.94

2 I=4%  PV2=96153.85

The cash flow of liability is increase.

ASSEET

PMT=50,000  N=2  FV=0

1 I=7%  PV1=94987.71

2I=4% PV2=97078.05

The cash flow of asset is increase.

Net interest income at 7%

NII=(50,000*0.5*7%+50,000*7%)-(100,000*7%)=-1.75

Net interest income at 10%

NII=(50,000*0.5*4%+50,000*4%)-(100,000*4%)=-1

The net interest income is increase.

d)

Yes. The value of asset and liability will decrease when the interest rate increase. However, the value of longer maturity will decrease less than the value shorter maturity. Hence, net worth will increase.

e)

DURATION=101,170.96/100,000=1.012 years

f)

The expected change in price = – dollar duration × ∆R

=-(1.012/1.55)*(0.001)*103360.74=-67.48

g)

103360.74-103350.9=9.84

1. h)

Convexity led to the difference of the price change. Because the relationship between bond price and yield is not linear. which is not considered in the duration elasticity measure.