Duration Gap and Market Risk

Patrick Schubert
BMGT 445
Prof. Kiss
Duration Gap and Market Risk
Assets
Cash
Federal funds
Loans (floating)
Loans (fixed)
Total assets

$30
20
120
50
$220

Liabilities and Equity
Core deposits
$20
Federal funds
60
Euro CDs
120
Equity
20
Total liabilities & equity$220

A) What is the duration of the fixed-rate loan portfolio of Gotbucks
Bank?
Five-year Loan
Par value $1,000
=
YTM = 0.12

Coupon 0.1200
=
Maturity 5
=
PV of CF PV*CF*T

Tim Cash Flow PVIF
e
1
$120.00 0.89285 $107.14
7
2
$120.00 0.79719
$95.66
4
3
$120.00 0.71178
$85.41
0
4 $1120.00 0.63551 $711.78
8
Price = $1,000.00
Numerator
=

$107.14

Annual payments

PVIF = 1/
(1+YTM)^(Time)

$191.33
$256.24
$2847.12
$3401.83 Duratio = 3.401 =
n
Numerator/Price

B) If the duration of the floating-rate loans is 0.50 years and if the
duration of the fed funds sold is 0.30 years, what is the duration
of GBI’s assets?
Duration (30 + 50 (3.401) + 120(.5) +20 (.3)) = 266.05/220 =
1.209
c.
What is the duration of the core deposits if they
are priced at par?

Two-year Core
Deposits
Par value $1,000
=
YTM = 0.16
Tim Cash Flow PVIF
e
1
$160.00 0.86206
2

Coupon = 0.16

PV of CF

Maturity 2
=
PV*CF*T

$137.92

$137.92

Annual payments

PVIF = 1/
(1+YTM)^(Time)

$1,160.00 0.74316 $862.06 $1724.13
Price = $1,000.00
Numerator $1862.05 Duratio = 1.862 =
=
n
0
Numerator/Price

d. If the duration of the Euro CDs liabilities is 0.40 years and if
the duration of the Fed funds purchased liabilities is 0.20 years, what is
the duration of GBI’s liabilities?
Duration: (120(.4) + 60(.2) + 20 (1.8620)/200 = .4862
e. What is GBI’s duration gap?
GBIS Duration Gap = 1.209 – 200/220 X .4862 = .767
f. What is its interest rate risk exposure? What I am looking for
here is the answer to the question, “What may lead to a drop in equity,
interest rates rising or falling?” If equity falls when interest rates rise,
then the bank has an exposure to rising interest rates.
If interest rates rise then it will lead to a fall in equity around the level
of the duration gap in respect to its given assets.
g.
What is the impact on the market value of equity if the
relative change in all market interest rates is an increase of 1 percent
(100 basis points)? Note, the relative change in interest rates is {DR/
[1+(R/2)]} = 0.01.
Duration Gap being positive will lead to a decline in base worth if
interest rates increase.
.-.767 X .01 X 220 = -1,687,400
h.
What is the impact on the market value of equity if the
relative change in all market interest rates is a decrease of 0.5 percent
(-50 basis points)?
Duration Gap being positive will lead to an increase in base worth if
interest rates decrease.

-.767 X -.005 X 220 = .8437 = 843,700
Chapter 10: Bank Anchor has an inventory of AAA-rated, 12-year
zero-coupon Eurobonds with a face value of $500 million. The bonds
currently are yielding 6% in the over-the-counter market.
a. What is the modified duration of these bonds?
MODD = 12/1.06 = 11.3208
b. What is the price volatility if the potential adverse move in yield
is an increase of 25 basis points?
Price Volatility = 11.3208 X -.25% = %-2.8302
c. What is the DEAR?
DEAR= MV X Price V
=500,000,000/(1.06^12) X (-.028302) = -7032613.464
d. If the price volatility is based on a 90 percent confidence limit
(i.e, a right tail of 5% under the normal distribution curve) and a
mean historical change in daily yields of 0.0 percent, what is
the implied standard deviation of daily yield changes?
SD of daily yield changes = (1.65)
e. What is the 25-day VAR?
Square root 25 X 7032613.464 = -35163067.32