Download Managing Interest Rate Risk: Duration GAP and Economic

Prof. Dr. Rainer Stachuletz
Banking Academy of Vietnam
Based upon: Bank Management, 6th edition.
Timothy W. Koch and S. Scott MacDonald
Managing Interest Rate Risk:
Duration GAP and Economic
Value of Equity
Chapter 6
Prof. Dr. Rainer Stachuletz – Banking Academy of Vietnam - Hanoi
Measuring Interest Rate Risk with Duration
GAP
 Economic Value of Equity Analysis
 Focuses
on changes in stockholders’
equity given potential changes in
interest rates
 Duration GAP Analysis
 Compares
the price sensitivity of a
bank’s total assets with the price
sensitivity of its total liabilities to
assess the impact of potential changes
in interest rates on stockholders’
equity.
Recall from Chapter 4
 Duration is a measure of the effective
maturity of a security.
 Duration
incorporates the timing and
size of a security’s cash flows.
 Duration measures how price sensitive
a security is to changes in interest
rates.

The greater (shorter) the duration, the
greater (lesser) the price sensitivity.
Duration and Price Volatility
 Duration as an Elasticity Measure
 Duration
versus Maturity
Consider the cash flows for these two
securities over the following time line
0
5
10
15
20

01
900
5
10
15
$1,000
20
$100
Duration versus Maturity
 The maturity of both is 20 years

Maturity does not account for the differences in
timing of the cash flows
 What is the effective maturity of both?

The effective maturity of the first security is:


(1,000/1,000) x 1 = 20 years
The effective maturity of the second security is:

[(900/1,000) x 1]+[(100/1,000) x 20] = 2.9 years
 Duration is similar, however, it uses a weighted
average of the present values of the cash flows
Duration versus Maturity
Duration is an approximate measure of
the price elasticity of demand
% Change in Quantity Demanded
Price Elasticity of Demand  % Change in Price
Duration versus Maturity
 The longer the duration, the larger the
change in price for a given change in
interest rates.
P
Duration  - P
i
(1  i)
 i 
P  - Duration 
P

 (1  i) 
Measuring Duration
 Duration is a weighted average of the
time until the expected cash flows
from a security will be received,
relative to the security’s price
 Macaulay’s
k
Duration
n
CFt (t)
CFt (t)


t
t
(1
+
r)
(1
+
r)
t =1
D = t=k1

CFt
Price of the Security

t
t =1 (1 + r)
Measuring Duration
 Example
 What
is the duration of a bond with a
$1,000 face value, 10% annual coupon
payments, 3 years to maturity and a
12% YTM? The bond’s price is $951.96.
100  1 100  2 100  3 1,000  3
+
+
+
1
2
3
2,597.6
(1.12)
(1.12)
(1.12)
(1.12) 3
D

= 2.73 years
3
100
1000
951.96
+

t
(1.12) 3
t =1 (1.12)
Measuring Duration
 Example
 What
is the duration of a bond with a
$1,000 face value, 10% coupon, 3 years
to maturity but the YTM is 5%?The
bond’s price is $1,136.16.
100 * 1 100 * 2 100 * 3 1,000 * 3
+
+
+
1
2
3
3,127.31
(1.05)
(1.05)
(1.05)
(1.05) 3
D

= 2.75 years
1136.16
1,136.16
Measuring Duration
 Example
 What
is the duration of a bond with a
$1,000 face value, 10% coupon, 3 years
to maturity but the YTM is 20%?The
bond’s price is $789.35.
100 * 1 100 * 2 100 * 3 1,000 * 3
+
+
+
1
2
3
2,131.95
(1.20)
(1.20)
(1.20)
(1.20) 3
D

= 2.68 years
789.35
789.35
Measuring Duration
 Example
 What
is the duration of a zero coupon
bond with a $1,000 face value, 3 years
to maturity but the YTM is 12%?
1,000 * 3
2,135.34
(1.12) 3
D

= 3 years
1,000
711.78
(1.12) 3

By definition, the duration of a zero
coupon bond is equal to its maturity
Duration and Modified Duration
 The greater the duration, the greater
the price sensitivity
 Modified Duration gives an estimate of
price volatility:
Macaulay' s Duration
Modified Duration 
(1  i)
P
 - Modified Duration  i
P
Effective Duration
 Effective Duration
 Used
to estimate a security’s price
sensitivity when the security contains
embedded options.
 Compares a security’s estimated price in
a falling and rising rate environment.
Effective Duration
Pi- - Pi
Effective Duration 

P0 (i - i )
 Where:
Pi- = Price if rates fall
Pi+ = Price if rates rise
P0 = Initial (current) price
i+ = Initial market rate plus the increase in rate
i- = Initial market rate minus the decrease in rate
Effective Duration
 Example
 Consider
a 3-year, 9.4 percent semiannual coupon bond selling for $10,000
par to yield 9.4 percent to maturity.
 Macaulay’s Duration for the option-free
version of this bond is 5.36 semiannual
periods, or 2.68 years.
 The Modified Duration of this bond is
5.12 semiannual periods or 2.56 years.
Effective Duration
 Example
 Assume,
instead, that the bond is
callable at par in the near-term .
If rates fall, the price will not rise much
above the par value since it will likely
be called
 If rates rise, the bond is unlikely to be
called and the price will fall

Effective Duration
 Example
 If
rates rise 30 basis points to 5%
semiannually, the price will fall to
$9,847.72.
 If rates fall 30 basis points to 4.4%
semiannually, the price will remain at
par
$10,000 - $9,847.72
Effective Duration 
 2.54
$10,000( 0.05 - 0.044)
Duration GAP
 Duration GAP Model
 Focuses
on either managing the
market value of stockholders’ equity

The bank can protect EITHER the
market value of equity or net interest
income, but not both

Duration GAP analysis emphasizes the
impact on equity
Duration GAP
 Duration GAP Analysis
 Compares
the duration of a bank’s
assets with the duration of the bank’s
liabilities and examines how the
economic value stockholders’ equity
will change when interest rates
change.
Two Types of Interest Rate Risk
 Reinvestment Rate Risk
 Changes
in interest rates will change
the bank’s cost of funds as well as the
return on invested assets
 Price Risk
 Changes
in interest rates will change
the market values of the bank’s assets
and liabilities
Reinvestment Rate Risk
 If interest rates change, the bank will
have to reinvest the cash flows from
assets or refinance rolled-over
liabilities at a different interest rate in
the future
 An
increase in rates increases a bank’s
return on assets but also increases the
bank’s cost of funds
Price Risk
 If interest rates change, the value of
assets and liabilities also change.
 The
longer the duration, the larger the
change in value for a given change in
interest rates
 Duration GAP considers the impact of
changing rates on the market value of
equity
Reinvestment Rate Risk and Price Risk
 Reinvestment Rate Risk
 If
interest rates rise (fall), the yield from
the reinvestment of the cash flows
rises (falls) and the holding period
return (HPR) increases (decreases).
 Price risk
 If
interest rates rise (fall), the price falls
(rises). Thus, if you sell the security
prior to maturity, the HPR falls (rises).
Reinvestment Rate Risk and Price Risk
 Increases in interest rates will increase
the HPR from a higher reinvestment
rate but reduce the HPR from capital
losses if the security is sold prior to
maturity.
 Decreases in interest rates will
decrease the HPR from a lower
reinvestment rate but increase the
HPR from capital gains if the security
is sold prior to maturity.
Reinvestment Rate Risk and Price Risk
 An immunized security or portfolio is
one in which the gain from the higher
reinvestment rate is just offset by the
capital loss.
 For an individual security,
immunization occurs when an
investor’s holding period equals the
duration of the security.
Steps in Duration GAP Analysis
 Forecast interest rates.
 Estimate the market values of bank assets,
liabilities and stockholders’ equity.
 Estimate the weighted average duration of
assets and the weighted average duration of
liabilities.

Incorporate the effects of both on- and offbalance sheet items. These estimates are
used to calculate duration gap.
 Forecasts changes in the market value of
stockholders’ equity across different
interest rate environments.
Weighted Average Duration of Bank Assets
 Weighted Average Duration of Bank
Assets (DA)
n
DA   w iDai
 Where
i
wi = Market value of asset i divided by
the market value of all bank assets
 Dai = Macaulay’s duration of asset i
 n = number of different bank assets

Weighted Average Duration of Bank Liabilities
 Weighted Average Duration of Bank
Liabilities (DL)
m
DL   z jDlj
 Where
j
zj = Market value of liability j divided by
the market value of all bank liabilities
 Dlj= Macaulay’s duration of liability j
 m = number of different bank liabilities

Duration GAP and Economic Value of Equity
 Let MVA and MVL equal the market values of
assets and liabilities, respectively.
 If: ΔEVE  ΔMVA  ΔMVL
and
Duration GAP
DGAP  DA - (MVL/MVA)D L
 Then:
 y 
ΔEVE  - DGAP 
MVA

 (1  y) 

where y = the general level of interest
rates
Duration GAP and Economic Value of Equity
 To protect the economic value of
equity against any change when rates
change , the bank could set the
duration gap to zero:
 y 
ΔEVE  - DGAP 
MVA

 (1  y) 
Hypothetical Bank Balance Sheet
1
Assets
Cash
Earning assets
3-yr Commercial loan
6-yr Treasury bond
84 1
Total Earning Assets
Non-cash earning(1
assets
.12)1
Total assets D 
Liabilities
Interest bearing liabs.
1-yr Time deposit
3-yr Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity
Par
$1,000 % Coup
Years
Mat.
$100
$
$ 700 12.00%
3
$ 200
8.00%
6
84

2
84

3
$ 900 2 
$ (1-.12)
(1.12)3
$ 1,000
700
$ 620
$ 300
$ 920
$ $ 920
$
80
$ 1,000
YTM
Market
Value
5.00%
7.00%
1
3

Dur.
100
12.00% $ 700
8.00% $ 200
700
3
11.11% $ 900
(1.12)3 $ 10.00% $ 1,000
2.69
4.99
5.00% $ 620
7.00% $ 300
5.65% $ 920
$ 5.65% $ 920
$
80
$ 1,000
1.00
2.81
2.88
1.59
Calculating DGAP
 DA

($700/$1000)*2.69 + ($200/$1000)*4.99 = 2.88
 DL

($620/$920)*1.00 + ($300/$920)*2.81 = 1.59
 DGAP

2.88 - (920/1000)*1.59 = 1.42 years

What does this tell us?
 The average duration of assets is greater than the
average duration of liabilities; thus asset values
change by more than liability values.
1 percent increase in all rates.
1
Par
$1,000 % Coup
Years
Mat.
YTM
Market
Value
Assets
Cash
$ 100
$
Earning assets
3-yr Commercial loan
$ 700 12.00%
3
13.00% $
6-yr Treasury bond
$ 200
8.00%
6
9.00% $
Total Earning Assets
$ 900
12.13% $
3
84
700 $
Non-cash earning assets
$
PV 

t
t

1
Total assets
$ 1,000
10.88%3 $
1.13
1.13

Liabilities
Interest bearing liabs.
1-yr Time deposit
3-yr Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity
$ 620
$ 300
$ 920
$ $ 920
$
80
$ 1,000
5.00%
7.00%
1
3
6.00% $
8.00% $
6.64% $
$
6.64% $
$
$
Dur.
100
683
191
875
975
2.69
4.97
614
292
906
906
68
975
1.00
2.81
2.86
1.58
Calculating DGAP
 DA

($683/$974)*2.68 + ($191/$974)*4.97 = 2.86
 DA

($614/$906)*1.00 + ($292/$906)*2.80 = 1.58
 DGAP

2.86 - ($906/$974) * 1.58 = 1.36 years

What does 1.36 mean?
 The average duration of assets is greater than the
average duration of liabilities, thus asset values
change by more than liability values.
Change in the Market Value of Equity
y
ΔEVE  - DGAP[
]MVA
(1  y)
 In this case:
.01
ΔEVE  - 1.42[
]$1,000  $12.91
1.10
Positive and Negative Duration GAPs
 Positive DGAP

Indicates that assets are more price sensitive
than liabilities, on average.

Thus, when interest rates rise (fall), assets will
fall proportionately more (less) in value than
liabilities and EVE will fall (rise) accordingly.
 Negative DGAP

Indicates that weighted liabilities are more
price sensitive than weighted assets.

Thus, when interest rates rise (fall), assets will
fall proportionately less (more) in value that
liabilities and the EVE will rise (fall).
DGAP Summary
DGAP Summary
Positive
Positive
Change in
Interest
Rates
Increase
Decrease
Decrease > Decrease → Decrease
Increase > Increase → Increase
Negative
Negative
Increase
Decrease
Decrease < Decrease → Increase
Increase < Increase → Decrease
Zero
Zero
Increase
Decrease
Decrease = Decrease →
Increase = Increase →
DGAP
Assets
Liabilities
Equity
None
None
An Immunized Portfolio
 To immunize the EVE from rate
changes in the example, the bank
would need to:
 decrease
the asset duration by 1.42
years or
 increase the duration of liabilities by
1.54 years
 DA / ( MVA/MVL)
= 1.42 / ($920 / $1,000)
= 1.54 years
Immunized Portfolio
1
Par
Years
$1,000 % Coup Mat.
Assets
Cash
$ 100
Earning assets
3-yr Commercial loan
$ 700
6-yr Treasury bond
$ 200
Total Earning Assets $ 900
Non-cash earning assets$ Total assets
$ 1,000
Liabilities
Interest bearing liabs.
1-yr Time deposit
$ 340
3-yr Certificate of deposit$ 300
6-yr Zero-coupon CD* $ 444
Tot. Int Bearing Liabs. $ 1,084
Tot. non-int. bearing
$ Total liabilities
$ 1,084
Total equity
$ 80
YTM
Market
Value
$
12.00%
8.00%
5.00%
7.00%
0.00%
3
6
1
3
6
100
12.00% $ 700
8.00% $ 200
11.11% $ 900
$ 10.00% $ 1,000
5.00%
7.00%
8.00%
6.57%
$
$
$
$
$
6.57% $
$
DGAP = 2.88 – 0.92 (3.11) ≈ 0
Dur.
340
300
280
920
920
80
2.69
4.99
2.88
1.00
2.81
6.00
3.11
Immunized Portfolio with a 1% increase in rates
1
Par
$1,000
Assets
Cash
$ 100.0
Earning assets
3-yr Commercial loan
$ 700.0
6-yr Treasury bond
$ 200.0
Total Earning Assets $ 900.0
Non-cash earning assets$
Total assets
$ 1,000.0
Liabilities
Interest bearing liabs.
1-yr Time deposit
$ 340.0
3-yr Certificate of deposit$ 300.0
6-yr Zero-coupon CD* $ 444.3
Tot. Int Bearing Liabs. $ 1,084.3
Tot. non-int. bearing
$
Total liabilities
$ 1,084.3
Total equity
$ 80.0
Years
% Coup Mat.
YTM
Market
Value
Dur.
$ 100.0
12.00%
8.00%
5.00%
7.00%
0.00%
3
6
1
3
6
13.00% $ 683.5
9.00% $ 191.0
12.13% $ 874.5
$ 10.88% $ 974.5
6.00%
8.00%
9.00%
7.54%
$ 336.8
$ 292.3
$ 264.9
$ 894.0
$ 7.54% $ 894.0
$ 80.5
2.69
4.97
2.86
1.00
2.81
6.00
3.07
Immunized Portfolio with a 1% increase in rates
 EVE changed by only $0.5 with the
immunized portfolio versus $25.0
when the portfolio was not immunized.
Stabilizing the Book Value of Net Interest Income
 This can be done for a 1-year time horizon,
with the appropriate duration gap measure

DGAP* MVRSA(1- DRSA) - MVRSL(1- DRSL)
where:



MVRSA = cumulative market value of RSAs
MVRSL = cumulative market value of RSLs
DRSA = composite duration of RSAs for the
given time horizon
 Equal to the sum of the products of each asset’s
duration with the relative share of its total asset
market value

DRSL = composite duration of RSLs for the
given time horizon
 Equal to the sum of the products of each liability’s
duration with the relative share of its total liability
market value.
Stabilizing the Book Value of Net Interest Income
 If DGAP* is positive, the bank’s net interest
income will decrease when interest rates
decrease, and increase when rates increase.

If DGAP* is negative, the relationship is
reversed.
 Only when DGAP* equals zero is interest
rate risk eliminated.

Banks can use duration analysis to stabilize
a number of different variables reflecting
bank performance.
Economic Value of Equity Sensitivity Analysis
 Effectively involves the same steps as
earnings sensitivity analysis.
 In EVE analysis, however, the bank
focuses on:
 The
relative durations of assets and
liabilities
 How much the durations change in
different interest rate environments
 What happens to the economic value of
equity across different rate environments
Embedded Options
 Embedded options sharply influence the
estimated volatility in EVE
 Prepayments
that exceed (fall short of)
that expected will shorten (lengthen)
duration.
 A bond being called will shorten duration.
 A deposit that is withdrawn early will
shorten duration.
 A deposit that is not withdrawn as
expected will lengthen duration.
Assets
First Savings Bank Economic Value of Equity
Market Value/Duration Report as of 12/31/04
Most Likely Rate Scenario-Base Strategy
Book Value
Market Value Book Yield Duration*
$ 100,000
$
25,000
$ 170,000
$
55,000
$ 250,000
$ 100,000
$
25,000
$ 725,000
$ (15,000)
$ 710,000
$
$
$
$
$
$
$
$
$
$
102,000
25,500
170,850
54,725
245,000
100,500
25,000
723,575
11,250
712,325
9.00%
8.75%
7.50%
6.90%
7.60%
8.00%
14.00%
8.03%
0.00%
8.03%
1.1
0.5
6.0
1.9
1.0
2.6
8.0
2.5
Loans
Prime Based Ln
Equity Credit Lines
Fixed Rate > I yr
Var Rate Mtg 1 Yr
30-Year Mortgage
Consumer Ln
Credit Card
Total Loans
Loan Loss Reserve
Net Loans
Investments
Eurodollars
CMO Fix Rate
US Treasury
Total Investments
$
$
$
$
80,000 $
35,000 $
75,000 $
190,000 $
80,000
34,825
74,813
189,638
5.50%
6.25%
5.80%
5.76%
0.1
2.0
1.8
1.1
Fed Funds Sold
Cash & Due From
Non-int Rel Assets
Total Assets
$
$
$
$
25,000 $
15,000 $
60,000 $
100,000 $
25,000
15,000
60,000
100,000
5.25%
0.00%
0.00%
6.93%
6.5
8.0
2.6
First Savings Bank Economic Value of Equity
Liabilities
Market Value/Duration Report as of 12/31/04
Most Likely Rate Scenario-Base Strategy
Book Value
Market Value Book Yield Duration*
MMDA
Retail CDs
Savings
NOW
DDA Personal
Comm'l DDA
Total Deposits
TT&L
L-T Notes Fixed
Fed Funds Purch
NIR Liabilities
Total Liabilities
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
232,800
400,000
33,600
38,800
52,250
58,200
815,650
25,000
50,250
28,500
919,400
Equity
Total Liab & Equity
$
65,000 $
$ 1,000,000 $
82,563
1,001,963
Deposits
$
$
Off Balance Sheet
lnt Rate Swaps
Adjusted Equity
$
240,000
400,000
35,000
40,000
55,000
60,000
830,000
25,000
50,000
30,000
935,000
- $
1,250
65,000 $
83,813
2.25%
5.40%
4.00%
2.00%
5.00%
8.00%
5.25%
1.1
1.9
1.9
8.0
4.8
1.6
5.9
8.0
2.0
9.9
2.6
6.00%
Notional
2.8 50,000
7.9
Duration Gap for First Savings Bank EVE
 Market Value of Assets
 $1,001,963
 Duration of Assets
 2.6
years
 Market Value of Liabilities
 $919,400
 Duration of Liabilities
 2.0
years
Duration Gap for First Savings Bank EVE
 Duration Gap
2.6 – ($919,400/$1,001,963)*2.0
= 0.765 years
=
 Example:
A
1% increase in rates would reduce
EVE by $7.2 million
= 0.765 (0.01 / 1.0693) * $1,001,963

Recall that the average rate on assets
is 6.93%
Change in EVE (millions of dollars)
Sensitivity of EVE versus Most Likely (Zero Shock)
Interest Rate Scenario
20.0
10.0
13.6
8.8
8.2
2
(10.0)
ALCO Guideline
Board Limit
(20.0)
(8.2)
(20.4)
(30.0)
(36.6)
(40.0)
-300
-200
-100
0
+100
+200
+300
Shocks to Current Rates
Sensitivity of Economic Value of Equity measures the change in the economic value of
the corporation’s equity under various changes in interest rates. Rate changes are
instantaneous changes from current rates. The change in economic value of equity is
derived from the difference between changes in the market value of assets and changes
in the market value of liabilities.
Effective “Duration” of Equity
 By definition, duration measures the
percentage change in market value for
a given change in interest rates
 Thus,
a bank’s duration of equity
measures the percentage change in
EVE that will occur with a 1 percent
change in rates:

Effective duration of equity
9.9 yrs. = $8,200 / $82,563
Asset/Liability Sensitivity and DGAP
 Funding GAP and Duration GAP are NOT
directly comparable
 Funding
GAP examines various “time
buckets” while Duration GAP represents
the entire balance sheet.

Generally, if a bank is liability (asset)
sensitive in the sense that net interest
income falls (rises) when rates rise and
vice versa, it will likely have a positive
(negative) DGAP suggesting that assets
are more price sensitive than liabilities, on
average.
Strengths and Weaknesses: DGAP and EVESensitivity Analysis
 Strengths
 Duration analysis provides a
comprehensive measure of interest rate
risk
 Duration measures are additive
 This allows for the matching of total
assets with total liabilities rather than the
matching of individual accounts
 Duration analysis takes a longer term
view than static gap analysis
Strengths and Weaknesses: DGAP and EVESensitivity Analysis
 Weaknesses
 It is difficult to compute duration
accurately
 “Correct” duration analysis requires that
each future cash flow be discounted by a
distinct discount rate
 A bank must continuously monitor and
adjust the duration of its portfolio
 It is difficult to estimate the duration on
assets and liabilities that do not earn or
pay interest
 Duration measures are highly subjective
Speculating on Duration GAP
 It is difficult to actively vary GAP or
DGAP and consistently win
 Interest
rates forecasts are frequently
wrong
 Even if rates change as predicted,
banks have limited flexibility in vary
GAP and DGAP and must often
sacrifice yield to do so
Gap and DGAP Management Strategies
Example
 Cash flows from investing $1,000 either
in a 2-year security yielding 6 percent or
two consecutive 1-year securities, with
the current 1-year yield equal to 5.5
percent.
0
1
2
Two-Year Security
$60
0
$60
1
2
One-Year Security & then
another One-Year Security
$55
?
Gap and DGAP Management Strategies
Example
 It is not known today what a 1-year
security will yield in one year.
 For the two consecutive 1-year
securities to generate the same $120
in interest, ignoring compounding, the
1-year security must yield 6.5% one
year from the present.
 This break-even rate is a 1-year
forward rate, one year from the
present:

6% + 6% = 5.5% + x
so x must = 6.5%
Gap and DGAP Management Strategies
Example
 By investing in the 1-year security, a
depositor is betting that the 1-year
interest rate in one year will be greater
than 6.5%
 By issuing the 2-year security, the
bank is betting that the 1-year interest
rate in one year will be greater than
6.5%
Yield Curve Strategy
 When the U.S. economy hits its peak,
the yield curve typically inverts, with
short-term rates exceeding long-term
rates.
 Only
twice since WWII has a recession
not followed an inverted yield curve
 As the economy contracts, the Federal
Reserve typically increases the money
supply, which causes the rates to fall
and the yield curve to return to its
“normal” shape.
Yield Curve Strategy
 To take advantage of this trend, when
the yield curve inverts, banks could:
 Buy

long-term non-callable securities
Prices will rise as rates fall
 Make

fixed-rate non-callable loans
Borrowers are locked into higher rates
 Price
deposits on a floating-rate basis
 Lengthen the duration of assets
relative to the duration of liabilities
Interest Rates and the Business Cycle
The general level of interest rates and the shape of the yield curve
appear to follow the U.S. business cycle.
Peak
In expansionary
Short-TermRates
stages rates rise until
they reach a peak as
the Federal Reserve
Long-TermRates
tightens credit
availability.
)t
n
e
c
r
e
P
(
s
e
t
a
Contraction
R
t Expansion
s
In contractionary
e
rstages rates fall until
e
tthey reach a trough
n
Iwhen the U.S.
Expansion
The inverted yield curve has predicted the last
five recessions
DATE WHEN 1-YEAR RATE
LENGTH OF TIME UNTIL
FIRST EXCEEDS 10-YEAR RATE START OF NEXT RECESSION
Trough
economy falls into
recession.
Time
Apr. ’68
Mar. ’73
Sept. ’78
Sept. ’80
Feb. ’89
Dec. ’00
20 months (Dec. ’69)
8 months (Nov. ’73)
16 months (Jan. ’80)
10 months (July ’81)
17 months (July ’90)
15 months (March ’01)
Bank Management, 6th edition.
Timothy W. Koch and S. Scott MacDonald
Copyright © 2006 by South-Western, a division of Thomson Learning
Managing Interest Rate Risk:
Duration GAP and Economic Value
of Equity
Chapter 6
Prof. Dr. Rainer Stachuletz edited and updated the PowerPoint slides for this edition.