Tutorial 1
Chapter 8
14.
A bank manager is quite certain that interest rates are going to fall within the
next six months, but the fall will be different on RSAs versus RSLs. How should
the bank manager adjust the bank’s six-month repricing gap and spread to take
advantage of this anticipated rise? What if the manger believed rates would rise
in the next six months.
When interest rates are expected to fall, a bank should set its repricing gap to a
negative position. Further, the manager would want to increase the spread
between the return on RSAs and RSLs. In this case, as rates fall, interest income
will fall by less than interest expense. The result is an increase in net interest
income. When interest rates are expected to rise, a bank should set its repricing
gap to a positive position. Again, the manager would want to increase the spread
between the return on RSAs and RSLs. In this case, as rates rise, interest income
will rise by more than interest expense. The result is an increase in net interest
income.
16.
Use the following information about a hypothetical government security dealer
named M.P. Jorgan. Market yields are in parenthesis, and amounts are in
millions.
Assets Liabilities and Equity
Cash $10 Overnight Repos $170
1 month T-bills (7.05%) 75 Subordinated debt
3 month T-bills (7.25%) 75 7-year fixed rate (8.55% 150
2 year T-notes (7.50%) 50
8 year T-notes (8.96%) 100
5 year munis (floating rate)
(8.20% reset every 6 months) 25 Equity 15
Total Assets $335 Total Liabilities & Equity $335
a. What is the funding or repricing gap if the planning period is 30 days? 91
days? 2 years? Recall that cash is a noninterest-earning asset.
Funding or repricing gap using a 30-day planning period = 75 - 170 = -$95
million.
Funding gap using a 91-day planning period = (75 + 75) - 170 = -$20 million.
Funding gap using a two-year planning period = (75 + 75 + 50 + 25) - 170
= +$55 million.
, b. What is the impact over the next 30 days on net interest income if all
interest rates rise 50 basis points? Decrease 75 basis points?
Net interest income will decline by $475,000. NII = FG(R) = -95(.005) =
$0.475m.
Net interest income will increase by $712,500. NII = FG(R) = -95(.0075)
= $0.7125m.
c. The following one-year runoffs are expected: $10 million for two-year T-
notes, and $20 million for eight-year T-notes. What is the one-year
repricing gap?
Funding or repricing gap over the 1-year planning period = (75 + 75 + 10 +
20 + 25) - 170 = +$35 million.
d. If runoffs are considered, what is the effect on net interest income at
year-end if interest rates rise 50 basis points? Decrease 75 basis points?
Net interest income will increase by $175,000. NII = FG(R) = 35(0.005)
= $0.175m.
Net interest income will decrease by $262,500, NII = FG(R) = 35(-
0.0075)
= -$0.2625m.
Chapter 9
13.
You have discovered that the price of a bond rose from $975 to $995 when the
yield to maturity fell from 9.75 percent to 9.25 percent. What is the duration of
the bond?
P 20
D P 975 4.5 years D 4.5 years
R .005
(1 R) 1.0975
We know
18.
Suppose you purchase a five-year, 13.76 percent bond that is priced to yield 10
percent.
a. Show that the duration of this annual payment bond is equal to four years.
(Annual payments)
Five-year Bond
Par value $1,000 Coupon = 0.1376
=
YTM = 0.10 Maturity = 5
Tim Cash PVIF PV of CF PV*CF*T
e Flow
1 $137.60 0.90909 $125.09 $125.09 PVIF = 1/
Chapter 8
14.
A bank manager is quite certain that interest rates are going to fall within the
next six months, but the fall will be different on RSAs versus RSLs. How should
the bank manager adjust the bank’s six-month repricing gap and spread to take
advantage of this anticipated rise? What if the manger believed rates would rise
in the next six months.
When interest rates are expected to fall, a bank should set its repricing gap to a
negative position. Further, the manager would want to increase the spread
between the return on RSAs and RSLs. In this case, as rates fall, interest income
will fall by less than interest expense. The result is an increase in net interest
income. When interest rates are expected to rise, a bank should set its repricing
gap to a positive position. Again, the manager would want to increase the spread
between the return on RSAs and RSLs. In this case, as rates rise, interest income
will rise by more than interest expense. The result is an increase in net interest
income.
16.
Use the following information about a hypothetical government security dealer
named M.P. Jorgan. Market yields are in parenthesis, and amounts are in
millions.
Assets Liabilities and Equity
Cash $10 Overnight Repos $170
1 month T-bills (7.05%) 75 Subordinated debt
3 month T-bills (7.25%) 75 7-year fixed rate (8.55% 150
2 year T-notes (7.50%) 50
8 year T-notes (8.96%) 100
5 year munis (floating rate)
(8.20% reset every 6 months) 25 Equity 15
Total Assets $335 Total Liabilities & Equity $335
a. What is the funding or repricing gap if the planning period is 30 days? 91
days? 2 years? Recall that cash is a noninterest-earning asset.
Funding or repricing gap using a 30-day planning period = 75 - 170 = -$95
million.
Funding gap using a 91-day planning period = (75 + 75) - 170 = -$20 million.
Funding gap using a two-year planning period = (75 + 75 + 50 + 25) - 170
= +$55 million.
, b. What is the impact over the next 30 days on net interest income if all
interest rates rise 50 basis points? Decrease 75 basis points?
Net interest income will decline by $475,000. NII = FG(R) = -95(.005) =
$0.475m.
Net interest income will increase by $712,500. NII = FG(R) = -95(.0075)
= $0.7125m.
c. The following one-year runoffs are expected: $10 million for two-year T-
notes, and $20 million for eight-year T-notes. What is the one-year
repricing gap?
Funding or repricing gap over the 1-year planning period = (75 + 75 + 10 +
20 + 25) - 170 = +$35 million.
d. If runoffs are considered, what is the effect on net interest income at
year-end if interest rates rise 50 basis points? Decrease 75 basis points?
Net interest income will increase by $175,000. NII = FG(R) = 35(0.005)
= $0.175m.
Net interest income will decrease by $262,500, NII = FG(R) = 35(-
0.0075)
= -$0.2625m.
Chapter 9
13.
You have discovered that the price of a bond rose from $975 to $995 when the
yield to maturity fell from 9.75 percent to 9.25 percent. What is the duration of
the bond?
P 20
D P 975 4.5 years D 4.5 years
R .005
(1 R) 1.0975
We know
18.
Suppose you purchase a five-year, 13.76 percent bond that is priced to yield 10
percent.
a. Show that the duration of this annual payment bond is equal to four years.
(Annual payments)
Five-year Bond
Par value $1,000 Coupon = 0.1376
=
YTM = 0.10 Maturity = 5
Tim Cash PVIF PV of CF PV*CF*T
e Flow
1 $137.60 0.90909 $125.09 $125.09 PVIF = 1/
