Managing Interest Rate Risk: GAP and Earnings Sensitivity
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Slide 2
Managing Interest Rate Risk Interest Rate Risk The potential
loss from unexpected changes in interest rates which can
significantly alter a banks profitability and market value of
equity 2
Slide 3
Managing Interest Rate Risk Interest Rate Risk When a banks
assets and liabilities do not reprice at the same time, the result
is a change in net interest income The change in the value of
assets and the change in the value of liabilities will also differ,
causing a change in the value of stockholders equity 3
Slide 4
Managing Interest Rate Risk Interest Rate Risk Banks typically
focus on either: Net interest income or The market value of
stockholders' equity GAP Analysis A static measure of risk that is
commonly associated with net interest income (margin) targeting
Earnings Sensitivity Analysis Earnings sensitivity analysis extends
GAP analysis by focusing on changes in bank earnings due to changes
in interest rates and balance sheet composition 4
Slide 5
Managing Interest Rate Risk Interest Rate Risk Asset and
Liability Management Committee (ALCO) The banks ALCO primary
responsibility is interest rate risk management. The ALCO
coordinates the banks strategies to achieve the optimal risk/reward
trade-off 5
Slide 6
Measuring Interest Rate Risk with GAP Three general factors
potentially cause a banks net interest income to change. Rate
Effects Unexpected changes in interest rates Composition (Mix)
Effects Changes in the mix, or composition, of assets and/or
liabilities Volume Effects Changes in the volume of earning assets
and interest-bearing liabilities 6
Slide 7
Measuring Interest Rate Risk with GAP Consider a bank that
makes a $25,000 five-year car loan to a customer at fixed rate of
8.5%. The bank initially funds the car loan with a one-year $25,000
CD at a cost of 4.5%. The banks initial spread is 4%. What is the
banks risk? 7
Slide 8
Measuring Interest Rate Risk with GAP Traditional Static Gap
Analysis Static GAP Analysis GAP t = RSA t - RSL t RSA t Rate
Sensitive Assets Those assets that will mature or reprice in a
given time period (t) RSL t Rate Sensitive Liabilities Those
liabilities that will mature or reprice in a given time period (t)
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Measuring Interest Rate Risk with GAP Traditional Static Gap
Analysis Steps in GAP Analysis 1. Develop an interest rate forecast
2. Select a series of time buckets or time intervals for
determining when assets and liabilities will reprice 3. Group
assets and liabilities into these buckets 4. Calculate the GAP for
each bucket 5. Forecast the change in net interest income given an
assumed change in interest rates 9
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Measuring Interest Rate Risk with GAP What Determines Rate
Sensitivity The initial issue is to determine what features make an
asset or liability rate sensitive 10
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Measuring Interest Rate Risk with GAP Expected Repricing versus
Actual Repricing In general, an asset or liability is normally
classified as rate sensitive within a time interval if: It matures
It represents an interim or partial principal payment The interest
rate applied to the outstanding principal balance changes
contractually during the interval The interest rate applied to the
outstanding principal balance changes when some base rate or index
changes and management expects the base rate/index to change during
the time interval 11
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Measuring Interest Rate Risk with GAP What Determines Rate
Sensitivity Maturity If any asset or liability matures within a
time interval, the principal amount will be repriced The question
is what principal amount is expected to reprice Interim or Partial
Principal Payment Any principal payment on a loan is rate sensitive
if management expects to receive it within the time interval Any
interest received or paid is not included in the GAP calculation
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Measuring Interest Rate Risk with GAP What Determines Rate
Sensitivity Contractual Change in Rate Some assets and deposit
liabilities earn or pay rates that vary contractually with some
index These instruments are repriced whenever the index changes If
management knows that the index will contractually change within 90
days, the underlying asset or liability is rate sensitive within
090 days. 13
Slide 14
Measuring Interest Rate Risk with GAP What Determines Rate
Sensitivity Change in Base Rate or Index Some loans and deposits
carry interest rates tied to indexes where the bank has no control
or definite knowledge of when the index will change. For example,
prime rate loans typically state that the bank can contractually
change prime daily The loan is rate sensitive in the sense that its
yield can change at any time However, the loans effective rate
sensitivity depends on how frequently the prime rate actually
changes 14
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Rate, Composition (Mix) and Volume Effects All
affect net interest income 15
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Level of Interest Rates The sign of
GAP (positive or negative) indicates the nature of the banks
interest rate risk A negative (positive) GAP, indicates that the
bank has more (less) RSLs than RSAs. When interest rates rise
(fall) during the time interval, the bank pays higher (lower) rates
on all repriceable liabilities and earns higher (lower) yields on
all repriceable assets 16
Slide 17
Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Level of Interest Rates The sign of
GAP (positive or negative) indicates the nature of the banks
interest rate risk If all rates rise (fall) by equal amounts at the
same time, both interest income and interest expense rise (fall),
but interest expense rises (falls) more because more liabilities
are repriced Net interest income thus declines (increases), as does
the banks net interest margin 17
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Level of Interest Rates If a bank
has a zero GAP, RSAs equal RSLs and equal interest rate changes do
not alter net interest income because changes in interest income
equal changes in interest expense It is virtually impossible for a
bank to have a zero GAP given the complexity and size of bank
balance sheets 18
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income 19
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Level of Interest Rates GAP analysis
assumes a parallel shift in the yield curve 20
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Level of Interest Rates If there is
a parallel shift in the yield curve then changes in Net Interest
Income are directly proportional to the size of the GAP: NII EXP =
GAP x i EXP It is rare, however, when the yield curve shifts
parallel. If rates do not change by the same amount and at the same
time, then net interest income may change by more or less 21
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Level of Interest Rates Example 1
Recall the bank that makes a $25,000 five- year car loan to a
customer at fixed rate of 8.5%. The bank initially funds the car
loan with a one-year $25,000 CD at a cost of 4.5%. What is the
banks 1-year GAP? 22
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Level of Interest Rates Example 1
RSA 1 YR = $0 RSL 1 YR = $10,000 GAP 1 YR = $0 - $25,000 = -$25,000
The banks one year funding GAP is - $25,000 If interest rates rise
(fall) by 1% in 1 year, the banks net interest margin and net
interest income will fall (rise) NII EXP = GAP x i EXP = -$10,000 x
1% = - $100 23
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Level of Interest Rates Example 2
Assume a bank accepts an 18-month $30,000 CD deposit at a cost of
3.75% and invests the funds in a $30,000 6-month T- Bill at rate of
4.80%. The banks initial spread is 1.05%. What is the banks 6-
month GAP? 24
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Level of Interest Rates Example 2
RSA 6 MO = $30,000 RSL 6 MO = $0 GAP 6 MO = $30,000 $0 = $30,000
The banks 6-month funding GAP is $30,000 If interest rates rise
(fall) by 1% in 6 months, the banks net interest margin and net
interest income will rise (fall) NII EXP = GAP x i EXP = $30,000 x
1% = $300 25
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in the Relationship Between Asset Yields
and Liability Costs Net interest income may differ from that
expected if the spread between earning asset yields and the
interest cost of interest-bearing liabilities changes The spread
may change because of a nonparallel shift in the yield curve or
because of a change in the difference between different interest
rates (basis risk) 26
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in Volume Net interest income varies
directly with changes in the volume of earning assets and
interest-bearing liabilities, regardless of the level of interest
rates For example, if a bank doubles in size but the portfolio
composition and interest rates remain unchanged, net interest
income will double because the bank earns the same interest spread
on twice the volume of earning assets such that NIM is unchanged
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Changes in Portfolio Composition Any variation in
portfolio mix potentially alters net interest income There is no
fixed relationship between changes in portfolio mix and net
interest income The impact varies with the relationships between
interest rates on rate-sensitive and fixed-rate instruments and
with the magnitude of funds shifts 28
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.0 30
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.0 Interest Income ($500 x 8%) + ($350 x
11%) = $78.50 Interest Expense ($600 x 4%) + ($220 x 6%) = $37.20
Net Interest Income $78.50 - $37.20 = $41.30 31
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.0 Earning Assets $500 + $350 = $850 Net
Interest Margin $41.3/$850 = 4.86% Funding GAP $500 - $600 = -$100
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.1 What if all rates increase by 1%?
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.1 What if all rates increase by 1%? With
a negative GAP, interest income increases by less than the increase
in interest expense. Thus, both NII and NIM fall. 34
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.2 What if all rates fall by 1%? 35
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.2 What if all rates fall by 1%? With a
negative GAP, interest income decreases by less than the decrease
in interest expense. Thus, both NII and NIM increase. 36
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.3 What if rates rise but the spread falls
by 1%? 37
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.3 What if rates rise but the spread falls
by 1%? Both NII and NIM fall with a decrease in the spread. Why the
larger change? Note: NII EXP GAP x i EXP Why? 38
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.4 What if rates fall but the spread falls
by 1%? 39
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.4 What if rates fall and the spread falls
by 1%? Both NII and NIM fall with a decrease in the spread. Note:
NII EXP GAP x i EXP 40
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.5 What if rates rise and the spread rises
by 1%? 41
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.5 What if rates rise and the spread rises
by 1%? Both NII and NIM increase with an increase in the spread.
Note: NII EXP GAP x i EXP 42
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.6 What if rates fall and the spread rises
by 1%? 43
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.6 What if rates fall and the spread rises
by 1%? Both NII and NIM increase with an increase in the spread.
Note: NII EXP GAP x i EXP 44
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.7 What if the bank proportionately
doubles in size? 45
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 3.7 What if the bank proportionately
doubles in size? Both NII doubles but NIM stays the same. Why? What
has happened to the banks risk? 46
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.0 47
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.0 Bank has a positive GAP 48
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.1 What if rates increase by 1%? 49
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.1 What if rates increase by 1%? With a
positive GAP, interest income increases by more than the increase
in interest expense. Thus, both NII and NIM rise. 50
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.2 What if rates decrease by 1%? 51
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.2 What if rates decrease by 1%? With a
positive GAP, interest income decreases by more than the decrease
in interest expense. Thus, both NII and NIM fall. 52
Slide 53
Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.3 What if rates rise but the spread falls
by 1%? 53
Slide 54
Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.3 What if rates rise but the spread falls
by 1%? Both NII and NIM fall with a decrease in the spread. Why the
larger change? Note: NII EXP GAP x i EXP Why? 54
Slide 55
Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.4 What if rates fall and the spread falls
by 1%? 55
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.4 What if rates fall and the spread falls
by 1%? Both NII and NIM fall with a decrease in the spread. Note:
NII EXP GAP x i EXP 56
Slide 57
Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.5 What if rates rise and the spread rises
by 1%? 57
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.5 What if rates rise and the spread rises
by 1%? Both NII and NIM increase with an increase in the spread.
Note: NII EXP GAP x i EXP 58
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.6 What if rates fall and the spread rises
by 1%? 59
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.6 What if rates fall and the spread rises
by 1%? Both NII and NIM increase with an increase in the spread.
Note: NII EXP GAP x i EXP 60
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.7 What if the bank proportionately
doubles in size? 61
Slide 62
Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 4.7 What if the bank proportionately
doubles in size? Both NII doubles but NIM stays the same. Why? What
has happened to the banks risk? 62
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 5.0 63
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 5.0 Bank has zero GAP 64
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 5.1 What if rates increase by 1%? 65
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 5.1 What if rates increase by 1%? With a
zero GAP, interest income increases by the amount as the increase
in interest expense. Thus, there is no change in NII or NIM!
66
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 5.2 What if rates fall and the spread falls
by 1%? 67
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 5.2 What if rates fall and the spread falls
by 1%? Even with a zero GAP, interest income falls by more than the
decrease in interest expense. Thus, both NII and NIM fall with a
decrease in the spread. Note: NII EXP GAP x i EXP 68
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 5.3 What if rates rise and the spread rises
by 1%? 69
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Example 5.3 What if rates rise and the spread rises
by 1%? Even with a zero GAP, interest income rises by more than the
increase in interest expense. Thus, both NII and NIM increase with
an increase in the spread. Note: NII EXP GAP x i EXP 70
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Measuring Interest Rate Risk with GAP Factors Affecting Net
Interest Income Summary of Base Cases If a Negative GAP gives the
largest NII and NIM, why not plan for a Negative GAP? 71
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Measuring Interest Rate Risk with GAP Rate, Volume, and Mix
Analysis Many financial institutions publish a summary in their
annual report of how net interest income has changed over time They
separate changes attributable to shifts in asset and liability
composition and volume from changes associated with movements in
interest rates 72
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Measuring Interest Rate Risk with GAP Rate Sensitivity Reports
Many managers monitor their banks risk position and potential
changes in net interest income using rate sensitivity reports These
report classify a banks assets and liabilities as rate sensitive in
selected time buckets through one year 74
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Measuring Interest Rate Risk with GAP Rate Sensitivity Reports
Periodic GAP The Gap for each time bucket and measures the timing
of potential income effects from interest rate changes 75
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Measuring Interest Rate Risk with GAP Rate Sensitivity Reports
Cumulative GAP The sum of periodic GAP's and measures aggregate
interest rate risk over the entire period Cumulative GAP is
important since it directly measures a banks net interest
sensitivity throughout the time interval 76
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Measuring Interest Rate Risk with GAP Strengths and Weaknesses
of Static GAP Analysis Strengths Easy to understand Works well with
small changes in interest rates 78
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Measuring Interest Rate Risk with GAP Strengths and Weaknesses
of Static GAP Analysis Weaknesses Ex-post measurement errors
Ignores the time value of money Ignores the cumulative impact of
interest rate changes Typically considers demand deposits to be
non-rate sensitive Ignores embedded options in the banks assets and
liabilities 79
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Measuring Interest Rate Risk with GAP GAP Ratio GAP Ratio =
RSAs/RSLs A GAP ratio greater than 1 indicates a positive GAP A GAP
ratio less than 1 indicates a negative GAP 80
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Measuring Interest Rate Risk with GAP GAP Divided by Earning
Assets as a Measure of Risk An alternative risk measure that
relates the absolute value of a banks GAP to earning assets The
greater this ratio, the greater the interest rate risk Banks may
specify a target GAP-to-earning- asset ratio in their ALCO policy
statements A target allows management to position the bank to be
either asset sensitive or liability sensitive, depending on the
outlook for interest rates 81
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Earnings Sensitivity Analysis Allows management to incorporate
the impact of different spreads between asset yields and liability
interest costs when rates change by different amounts 82
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Earnings Sensitivity Analysis Steps to Earnings Sensitivity
Analysis 1. Forecast interest rates. 2. Forecast balance sheet size
and composition given the assumed interest rate environment 3.
Forecast when embedded options in assets and liabilities will be
exercised such that prepayments change, securities are called or
put, deposits are withdrawn early, or rate caps and rate floors are
exceeded under the assumed interest rate environment 83
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Earnings Sensitivity Analysis Steps to Earnings Sensitivity
Analysis 4. Identify when specific assets and liabilities will
reprice given the rate environment 5. Estimate net interest income
and net income under the assumed rate environment 6. Repeat the
process to compare forecasts of net interest income and net income
across different interest rate environments versus the base case
The choice of base case is important because all estimated changes
in earnings are compared with the base case estimate 84
Slide 85
Earnings Sensitivity Analysis The key benefits of conducting
earnings sensitivity analysis are that managers can estimate the
impact of rate changes on earnings while allowing for the
following: Interest rates to follow any future path Different rates
to change by different amounts at different times Expected changes
in balance sheet mix and volume Embedded options to be exercised at
different times and in different interest rate environments
Effective GAPs to change when interest rates change Thus, a bank
does not have a single static GAP, but instead will experience
amounts of RSAs and RSLs that change when interest rates change
85
Slide 86
Earnings Sensitivity Analysis Exercise of Embedded Options in
Assets and Liabilities The most common embedded options at banks
include the following: Refinancing of loans Prepayment (even
partial) of principal on loans Bonds being called Early withdrawal
of deposits Caps on loan or deposit rates Floors on loan or deposit
rates Call or put options on FHLB advances Exercise of loan
commitments by borrowers 86
Slide 87
Earnings Sensitivity Analysis Exercise of Embedded Options in
Assets and Liabilities The implications of embedded options Does
the bank or the customer determine when the option is exercised?
How and by what amount is the bank being compensated for selling
the option, or how much must it pay to buy the option? When will
the option be exercised? This is often determined by the economic
and interest rate environment Static GAP analysis ignores these
embedded options 87
Slide 88
Earnings Sensitivity Analysis Different Interest Rates Change
by Different Amounts at Different Times It is well recognized that
banks are quick to increase base loan rates but are slow to lower
base loan rates when rates fall 88
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Earnings Sensitivity Analysis Earnings Sensitivity: An Example
Consider the rate sensitivity report for First Savings Bank (FSB)
as of year-end 2008 that is presented on the next slide The report
is based on the most likely interest rate scenario FSB is a $1
billion bank that bases its analysis on forecasts of the federal
funds rate and ties other rates to this overnight rate As such, the
federal funds rate serves as the banks benchmark interest rate
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Earnings Sensitivity Analysis Explanation of Sensitivity
Results This example demonstrates the importance of understanding
the impact of exercising embedded options and the lags between the
pricing of assets and liabilities. The framework uses the federal
funds rate as the benchmark rate such that rate shocks indicate how
much the funds rate changes Summary results are known as Earnings-
at-Risk Simulation or Net Interest Income Simulation 93
Slide 94
Earnings Sensitivity Analysis Explanation of Sensitivity
Results Earnings-at-Risk The potential variation in net interest
income across different interest rate environments, given different
assumptions about balance sheet composition, when embedded options
will be exercised, and the timing of repricings. 94
Slide 95
Earnings Sensitivity Analysis Explanation of Sensitivity
Results FSBs earnings sensitivity results reflect the impacts of
rate changes on a bank with this profile There are two basic causes
or drivers behind the estimated earnings changes First, other
market rates change by different amounts and at different times
relative to the federal funds rate Second, embedded options
potentially alter cash flows when the options go in the money
95
Slide 96
Income Statement GAP An interest rate risk model which modifies
the standard GAP model to incorporate the different speeds and
amounts of repricing of specific assets and liabilities given an
interest rate change 96
Slide 97
Income Statement GAP Beta GAP The adjusted GAP figure in a
basic earnings sensitivity analysis derived from multiplying the
amount of rate- sensitive assets by the associated beta factors and
summing across all rate- sensitive assets, and subtracting the
amount of rate-sensitive liabilities multiplied by the associated
beta factors summed across all rate- sensitive liabilities 97
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Income Statement GAP Balance Sheet GAP The effective amount of
assets that reprice by the full assumed rate change minus the
effective amount of liabilities that reprice by the full assumed
rate change. Earnings Change Ratio (ECR) A ratio calculated for
each asset or liability that estimates how the yield on assets or
rate paid on liabilities is assumed to change relative to a 1
percent change in the base rate 98
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Managing the GAP and Earnings Sensitivity Risk Steps to reduce
risk Calculate periodic GAPs over short time intervals Match fund
repriceable assets with similar repriceable liabilities so that
periodic GAPs approach zero Match fund long-term assets with non-
interest-bearing liabilities Use off-balance sheet transactions to
hedge 100
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Managing the GAP and Earnings Sensitivity Risk How to Adjust
the Effective GAP or Earnings Sensitivity Profile 101
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Managing Interest Rate Risk: Economic Value of Equity 102
Slide 103
Managing Interest Rate Risk: Economic Value of Equity Economic
Value of Equity (EVE) Analysis Focuses on changes in stockholders
equity given potential changes in interest rates 103
Slide 104
Managing Interest Rate Risk: Economic Value of Equity Duration
GAP Analysis Compares the price sensitivity of a banks total assets
with the price sensitivity of its total liabilities to assess the
impact of potential changes in interest rates on stockholders
equity 104
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Managing Interest Rate Risk: Economic Value of Equity GAP and
Earnings Sensitivity versus Duration GAP and EVE Sensitivity
105
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Managing Interest Rate Risk: Economic Value of Equity Recall
from Chapter 6 Duration is a measure of the effective maturity of a
security Duration incorporates the timing and size of a securitys
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 106
Slide 107
Managing Interest Rate Risk: Economic Value of Equity Market
Value Accounting Issues EVE sensitivity analysis is linked with the
debate concerning whether market value accounting is appropriate
for financial institutions Recently many large commercial and
investment banks reported large write-downs of mortgage-related
assets, which depleted their capital Some managers argued that the
write-downs far exceeded the true decline in value of the assets
and because banks did not need to sell the assets they should not
be forced to recognize the paper losses 107
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108
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Measuring Interest Rate Risk with Duration GAP Duration GAP
Analysis Compares the price sensitivity of a banks total assets
with the price sensitivity of its total liabilities to assess
whether the market value of assets or liabilities changes more when
rates change 109
Slide 110
Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Macaulays Duration (D)
where P* is the initial price, i is the market interest rate, and t
is equal to the time until the cash payment is made 110
Slide 111
Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Macaulays Duration (D)
Macaulays duration is a measure of price sensitivity where P refers
to the price of the underlying security: 111
Slide 112
Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Modified Duration
Indicates how much the price of a security will change in
percentage terms for a given change in interest rates Modified
Duration = D/(1+i) 112
Slide 113
Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Example Assume that a
ten-year zero coupon bond has a par value of $10,000, current price
of $7,835.26, and a market rate of interest of 5%. What is the
expected change in the bonds price if interest rates fall by 25
basis points? 113
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Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Example Since the bond is
a zero-coupon bond, Macaulays Duration equals the time to maturity,
10 years. With a market rate of interest, the Modified Duration is
10/(1.05) = 9.524 years. If rates change by 0.25% (.0025), the
bonds price will change by approximately 9.524 .0025 $7,835.26 =
$186.56 114
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Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Effective Duration Used
to estimate a securitys price sensitivity when the security
contains embedded options Compares a securitys estimated price in a
falling and rising rate environment 115
Slide 116
Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Effective Duration where:
P i- = Price if rates fall P i+ = Price if rates rise P 0 = Initial
(current) price i + = Initial market rate plus the increase in the
rate i - = Initial market rate minus the decrease in the rate
116
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Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Effective Duration
Example Consider a 3-year, 9.4 percent semi-annual coupon bond
selling for $10,000 par to yield 9.4 percent to maturity Macaulays
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 117
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Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Effective Duration
Example Assume 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 118
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Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration 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 119
Slide 120
Measuring Interest Rate Risk with Duration GAP Duration,
Modified Duration, and Effective Duration Effective Duration
Example 120
Slide 121
Measuring Interest Rate Risk with Duration GAP Duration GAP
Model Focuses on 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 and focuses on price sensitivity 121
Slide 122
Measuring Interest Rate Risk with Duration GAP Duration GAP
Model 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 off-balance sheet items. These
estimates are used to calculate duration gap Forecasts changes in
the market value of stockholders equity across different interest
rate environments 122
Slide 123
Measuring Interest Rate Risk with Duration GAP Duration GAP
Model Weighted Average Duration of Bank Assets (DA): where w i =
Market value of asset i divided by the market value of all bank
assets Da i = Macaulays duration of asset i n = number of different
bank assets 123
Slide 124
Measuring Interest Rate Risk with Duration GAP Duration GAP
Model Weighted Average Duration of Bank Liabilities (DL): where z j
= Market value of liability j divided by the market value of all
bank liabilities Dl j = Macaulays duration of liability j m =
number of different bank liabilities 124
Slide 125
Measuring Interest Rate Risk with Duration GAP Duration GAP
Model Let MVA and MVL equal the market values of assets and
liabilities, respectively If EVE = MVA MVL and Duration GAP = DGAP
= DA (MVL/MVA)DL then EVE = -DGAP[y/(1+y)]MVA where y is the
interest rate 125
Slide 126
Measuring Interest Rate Risk with Duration GAP Duration GAP
Model To protect the economic value of equity against any change
when rates change, the bank could set the duration gap to zero:
126
Slide 127
Measuring Interest Rate Risk with Duration GAP Duration GAP
Model DGAP as a Measure of Risk The sign and size of DGAP provide
information about whether rising or falling rates are beneficial or
harmful and how much risk the bank is taking If DGAP is positive,
an increase in rates will lower EVE, while a decrease in rates will
increase EVE If DGAP is negative, an increase in rates will
increase EVE, while a decrease in rates will lower EVE The closer
DGAP is to zero, the smaller is the potential change in EVE for any
change in rates 127
Slide 128
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks 128
Slide 129
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks Implications of DGAP The value of DGAP at
1.42 years indicates that the bank has a substantial mismatch in
average durations of assets and liabilities Since the DGAP is
positive, the market value of assets will change more than the
market value of liabilities if all rates change by comparable
amounts In this example, an increase in rates will cause a decrease
in EVE, while a decrease in rates will cause an increase in EVE
129
Slide 130
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks Implications of DGAP > 0 A positive DGAP
indicates that assets are more price sensitive than liabilities
When interest rates rise (fall), assets will fall proportionately
more (less) in value than liabilities and EVE will fall (rise)
accordingly. Implications of DGAP < 0 A negative DGAP indicates
that liabilities are more price sensitive than assets When interest
rates rise (fall), assets will fall proportionately less (more) in
value that liabilities and the EVE will rise (fall) 130
Slide 131
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks 131
Slide 132
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks Duration GAP Summary 132
Slide 133
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks DGAP As a Measure of Risk DGAP measures can
be used to approximate the expected change in economic value of
equity for a given change in interest rates 133
Slide 134
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks DGAP As a Measure of Risk In this case: The
actual decrease, as shown in Exhibit 8.3, was $12 134
Slide 135
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks 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 or a combination of both 135
Slide 136
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks 136
Slide 137
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks An Immunized Portfolio With a 1% increase in
rates, the EVE did not change with the immunized portfolio versus
$12.0 when the portfolio was not immunized 137
Slide 138
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks An Immunized Portfolio If DGAP > 0, reduce
interest rate risk by: shortening asset durations Buy short-term
securities and sell long- term securities Make floating-rate loans
and sell fixed-rate loans lengthening liability durations Issue
longer-term CDs Borrow via longer-term FHLB advances Obtain more
core transactions accounts from stable sources 138
Slide 139
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks An Immunized Portfolio If DGAP < 0, reduce
interest rate risk by: lengthening asset durations Sell short-term
securities and buy long-term securities Sell floating-rate loans
and make fixed-rate loans Buy securities without call options
shortening liability durations Issue shorter-term CDs Borrow via
shorter-term FHLB advances Use short-term purchased liability
funding from federal funds and repurchase agreements 139
Slide 140
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks Banks may choose to target variables other
than the market value of equity in managing interest rate risk Many
banks are interested in stabilizing the book value of net interest
income This can be done for a one-year time horizon, with the
appropriate duration gap measure 140
Slide 141
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks DGAP* = MVRSA(1 DRSA) MVRSL(1 DRSL) where
MVRSA = cumulative market value of rate- sensitive assets (RSAs)
MVRSL = cumulative market value of rate- sensitive liabilities
(RSLs) DRSA = composite duration of RSAs for the given time horizon
DRSL = composite duration of RSLs for the given time horizon
141
Slide 142
Measuring Interest Rate Risk with Duration GAP A Duration
Application for Banks DGAP* > 0 Net interest income will
decrease (increase) when interest rates decrease (increase) DGAP*
< 0 Net interest income will decrease (increase) when interest
rates increase (decrease) DGAP* = 0 Interest rate risk eliminated A
major point is that duration analysis can be used to stabilize a
number of different variables reflecting bank performance 142
Slide 143
Economic Value of Equity Sensitivity Analysis Involves the
comparison of changes in the Economic Value of Equity (EVE) across
different interest rate environments An important component of EVE
sensitivity analysis is allowing different rates to change by
different amounts and incorporating projections of when embedded
customer options will be exercised and what their values will be
143
Slide 144
Economic Value of Equity Sensitivity Analysis Estimating the
timing of cash flows and subsequent durations of assets and
liabilities is complicated by: Prepayments that exceed (fall short
of) those expected A bond being A deposit that is withdrawn early
or a deposit that is not withdrawn as expected 144
Slide 145
Economic Value of Equity Sensitivity Analysis EVE Sensitivity
Analysis: An Example First Savings Bank Average duration of assets
equals 2.6 years Market value of assets equals $1,001,963,000
Average duration of liabilities equals 2 years Market value of
liabilities equals $919,400,000 145
Slide 146
146
Slide 147
Economic Value of Equity Sensitivity Analysis EVE Sensitivity
Analysis: An Example First Savings Bank Duration Gap 2.6
($919,400,000/$1,001,963,000) 2.0 = 0.765 years Example: A 1%
increase in rates would reduce EVE by $7.2 million MVE =
-DGAP[y/(1+y)]MVA MVE = -0.765 (0.01/1.0693) $1,001,963,000 =
-$7,168,257 Recall that the average rate on assets is 6.93% The
estimate of -$7,168,257 ignores the impact of interest rates on
embedded options and the effective duration of assets and
liabilities 147
Slide 148
Economic Value of Equity Sensitivity Analysis EVE Sensitivity
Analysis: An Example 148
Slide 149
Economic Value of Equity Sensitivity Analysis EVE Sensitivity
Analysis: An Example First Savings Bank The previous slide shows
that FSBs EVE will fall by $8.2 million if rates are rise by 1%
This differs from the estimate of -$7,168,257 because this
sensitivity analysis takes into account the embedded options on
loans and deposits For example, with an increase in interest rates,
depositors may withdraw a CD before maturity to reinvest the funds
at a higher interest rate 149
Slide 150
Economic Value of Equity Sensitivity Analysis EVE Sensitivity
Analysis: An Example First Savings Bank Effective Duration of
Equity Recall, duration measures the percentage change in market
value for a given change in interest rates A banks duration of
equity measures the percentage change in EVE that will occur with a
1 percent change in rates: Effective duration of equity = $8,200 /
$82,563 = 9.9 years 150
Slide 151
Earnings Sensitivity Analysis versus EVE Sensitivity Analysis
Strengths and Weaknesses: DGAP and EVE-Sensitivity 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 151
Slide 152
Earnings Sensitivity Analysis versus EVE Sensitivity Analysis
Strengths and Weaknesses: DGAP and EVE- Sensitivity 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 152
Slide 153
A Critique of Strategies for Managing Earnings and EVE
Sensitivity GAP and DGAP Management Strategies 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 changing GAP and DGAP 153
Slide 154
A Critique of Strategies for Managing Earnings and EVE
Sensitivity Interest Rate Risk: An Example Consider the case where
a bank has two alternatives for funding $1,000 for two years A
2-year security yielding 6 percent Two consecutive 1-year
securities, with the current 1-year yield equal to 5.5 percent It
is not known today what a 1-year security will yield in one year
154
Slide 155
A Critique of Strategies for Managing Earnings and EVE
Sensitivity Interest Rate Risk: An Example Consider the case where
a bank has two alternative for funding $1,000 for two years
155
Slide 156
A Critique of Strategies for Managing Earnings and EVE
Sensitivity Interest Rate Risk: An Example Consider the case where
a bank has two alternative for funding $1,000 for two years 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 of : 6% + 6% = 5.5% + x so x must = 6.5% 156
Slide 157
A Critique of Strategies for Managing Earnings and EVE
Sensitivity Interest Rate Risk: An Example Consider the case where
a bank has two alternative for investing $1,000 for two years 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% By choosing one
or the other, the depositor and the bank place a bet that the
actual rate in one year will differ from the forward rate of 6.5
percent 157
Slide 158
Yield Curve Strategies 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 rates to
fall and the yield curve to return to its normal shape. 158
Slide 159
Yield Curve Strategies 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 Follow strategies to become more
liability sensitive and/or lengthen the duration of assets versus
the duration of liabilities 159
Slide 160
160
Slide 161
Using Derivatives to Manage Interest Rate Risk 161
Slide 162
Using Derivatives to Manage Interest Rate Risk Derivative Any
instrument or contract that derives its value from another
underlying asset, instrument, or contract 162
Slide 163
Using Derivatives to Manage Interest Rate Risk Derivatives Used
to Manage Interest Rate Risk Financial Futures Contracts Forward
Rate Agreements Interest Rate Swaps Options on Interest Rates
Interest Rate Caps Interest Rate Floors 163
Slide 164
Characteristics of Financial Futures Financial Futures
Contracts A commitment, between a buyer and a seller, on the
quantity of a standardized financial asset or index Futures Markets
The organized exchanges where futures contracts are traded Interest
Rate Futures When the underlying asset is an interest-bearing
security 164
Slide 165
Characteristics of Financial Futures Buyers A buyer of a
futures contract is said to be long futures Agrees to pay the
underlying futures price or take delivery of the underlying asset
Buyers gain when futures prices rise and lose when futures prices
fall 165
Slide 166
Characteristics of Financial Futures Sellers A seller of a
futures contract is said to be short futures Agrees to receive the
underlying futures price or to deliver the underlying asset Sellers
gain when futures prices fall and lose when futures prices rise
166
Slide 167
Characteristics of Financial Futures Cash or Spot Market Market
for any asset where the buyer tenders payment and takes possession
of the asset when the price is set Forward Contract Contract for
any asset where the buyer and seller agree on the assets price but
defer the actual exchange until a specified future date 167
Slide 168
Characteristics of Financial Futures Forward versus Futures
Contracts Futures Contracts Traded on formal exchanges Examples:
Chicago Board of Trade and the Chicago Mercantile Exchange Involve
standardized instruments Positions require a daily marking to
market Positions require a deposit equivalent to a performance bond
168
Slide 169
Characteristics of Financial Futures Forward versus Futures
Contracts Forward contracts Terms are negotiated between parties Do
not necessarily involve standardized assets Require no cash
exchange until expiration No marking to market 169
Slide 170
Characteristics of Financial Futures A Brief Example Assume you
want to invest $1 million in 10-year T-bonds in six months and
believe that rates will fall You would like to lock in the 4.5% 10-
year yield prevailing today If such a contract existed, you would
buy a futures contract on 10-year T-bonds with an expiration date
just after the six-month period Assume that such a contract is
priced at a 4.45% rate 170
Slide 171
Characteristics of Financial Futures A Brief Example If 10-year
Treasury rates actually fall sharply during the six months, the
futures rate will similarly fall such that the futures price rises
An increase in the futures price generates a profit on the futures
trade You will eventually sell the futures contract to exit the
trade 171
Slide 172
Characteristics of Financial Futures A Brief Example You will
eventually sell the futures contract to exit the trade Your
effective yield will be determined by the prevailing 10-year
Treasury rate and the gain (or loss) on the futures trade In this
example, the decline in 10-year rates will be offset by profits on
the long futures position 172
Slide 173
Characteristics of Financial Futures A Brief Example The
10-year Treasury rate falls by 0.80%, which represents an
opportunity loss However, buying a futures contract generates a
0.77% profit The effective yield on the investment equals the
prevailing 3.70% rate at the time of investment plus the 0.77%
futures profit, or 4.47% 173
Slide 174
Characteristics of Financial Futures A Brief Example 174
Slide 175
Characteristics of Financial Futures Types of Future Traders
Commission Brokers Execute trades for other parties Locals Trade
for their own account Locals are speculators 175
Slide 176
Characteristics of Financial Futures Types of Future Traders
Speculator Takes a position with the objective of making a profit
Tries to guess the direction that prices will move and time trades
to sell (buy) at higher (lower) prices than the purchase price
176
Slide 177
Characteristics of Financial Futures Types of Future Traders
Scalper A speculator who tries to time price movements over very
short time intervals and takes positions that remain outstanding
for only minutes 177
Slide 178
Characteristics of Financial Futures Types of Future Traders
Day Trader Similar to a scalper but tries to profit from short-term
price movements during the trading day; normally offsets the
initial position before the market closes such that no position
remains outstanding overnight 178
Slide 179
Characteristics of Financial Futures Types of Future Traders
Position Trader A speculator who holds a position for a longer
period in anticipation of a more significant, longer-term market
moves 179
Slide 180
Characteristics of Financial Futures Types of Future Traders
Hedger Has an existing or anticipated position in the cash market
and trades futures contracts to reduce the risk associated with
uncertain changes in the value of the cash position Takes a
position in the futures market whose value varies in the opposite
direction as the value of the cash position when rates change Risk
is reduced because gains or losses on the futures position at least
partially offset gains or losses on the cash position 180
Slide 181
Characteristics of Financial Futures Types of Future Traders
Hedger versus Speculator The essential difference between a
speculator and hedger is the objective of the trader A speculator
wants to profit on trades A hedger wants to reduce risk associated
with a known or anticipated cash position 181
Slide 182
Characteristics of Financial Futures Types of Future Traders
Spreader versus Arbitrageur Both are speculators that take
relatively low-risk positions Futures Spreader May simultaneously
buy a futures contract and sell a related futures contract trying
to profit on anticipated movements in the price difference The
position is generally low risk because the prices of both contracts
typically move in the same direction 182
Slide 183
Characteristics of Financial Futures Types of Future Traders
Arbitrageur Tries to profit by identifying the same asset that is
being traded at two different prices in different markets at the
same time Buys the asset at the lower price and simultaneously
sells it at the higher price Arbitrage transactions are thus low
risk and serve to bring prices back in line in the sense that the
same asset should trade at the same price in all markets 183
Slide 184
Characteristics of Financial Futures The Mechanics of Futures
Trading Initial Margin A cash deposit (or U.S. government
securities) with the exchange simply for initiating a transaction
Initial margins are relatively low, often involving less than 5% of
the underlying assets value 184
Slide 185
Characteristics of Financial Futures The Mechanics of Futures
Trading Maintenance Margin The minimum deposit required at the end
of each day Unlike margin accounts for stocks, futures margin
deposits represent a guarantee that a trader will be able to make
any mandatory payment obligations 185
Slide 186
Characteristics of Financial Futures The Mechanics of Futures
Trading Marking-to-Market The daily settlement process where at the
end of every trading day, a traders margin account is: Credited
with any gains Debited with any losses Variation Margin The daily
change in the value of margin account due to marking-to-market
186
Slide 187
Characteristics of Financial Futures The Mechanics of Futures
Trading Expiration Date Every futures contract has a formal
expiration date On the expiration date, trading stops and
participants settle their final positions Less than 1% of financial
futures contracts experience physical delivery at expiration
because most traders offset their futures positions in advance
187
Slide 188
Characteristics of Financial Futures An Example: 90-Day
Eurodollar Time Deposit Futures The underlying asset is a
Eurodollar time deposit with a 3-month maturity Eurodollar rates
are quoted on an interest-bearing basis, assuming a 360- day year
Each Eurodollar futures contract represents $1 million of initial
face value of Eurodollar deposits maturing three months after
contract expiration 188
Slide 189
Characteristics of Financial Futures An Example: 90-Day
Eurodollar Time Deposit Futures Contracts trade according to an
index: 100 Futures Price = Futures Rate An index of 94.50 indicates
a futures rate of 5.5% Each basis point change in the futures rate
equals a $25 change in value of the contract (0.001 x $1 million x
90/360) 189
Slide 190
Characteristics of Financial Futures An Example: 90-Day
Eurodollar Time Deposit Futures Over forty separate contracts are
traded at any point in time, as contracts expire in March, June,
September and December each year Buyers make a profit when futures
rates fall (prices rise) Sellers make a profit when futures rates
rise (prices fall) 190
Slide 191
191
Slide 192
Characteristics of Financial Futures An Example: 90-Day
Eurodollar Time Deposit Futures OPEN The index price at the open of
trading HIGH The high price during the day LOW The low price during
the day LAST The last price quoted during the day PT CHGE The
basis-point change between the last price quoted and the closing
price the previous day 192
Slide 193
Characteristics of Financial Futures An Example: 90-Day
Eurodollar Time Deposit Futures SETTLEMENT The previous days
closing price VOLUME The previous days volume of contracts traded
during the day OPEN INTEREST The total number of futures contracts
outstanding at the end of the day. 193
Slide 194
Characteristics of Financial Futures Expectations Embedded in
Future Rates According to the unbiased expectations theory, an
upward sloping yield curve indicates a consensus forecast that
short-term interest rates are expected to rise A flat yield curve
suggests that rates will remain relatively constant 194
Slide 195
Characteristics of Financial Futures Expectations Embedded in
Future Rates 195
Slide 196
Characteristics of Financial Futures Expectations Embedded in
Future Rates The previous slide presents two yield curves at the
close of business on June 5, 2008 There was a sharp decrease in
rates from one year prior. The yield curve in June 2008 was
relatively steep The difference between the one-month and 30- year
Treasury rates was 289 basis points The yield curve in June 2007
was relatively flat 196
Slide 197
Characteristics of Financial Futures Expectations Embedded in
Future Rates One interpretation of futures rates is that they
provide information about consensus expectations of future cash
rates When futures rates continually rise as the expiration dates
of the futures contracts extend into the future, it signals an
expected increase in subsequent cash market rates 197
Slide 198
Characteristics of Financial Futures Daily Marking-To-Market
Consider a trader trading on June 6, 2008 who buys one December
2008 three- month Eurodollar futures contract at $96.98 posting
$1,100 in cash as initial margin Maintenance margin is set at $700
per contract The futures contract expires approximately six months
after the initial purchase, during which time the futures price and
rate fluctuate daily 198
Slide 199
Characteristics of Financial Futures Daily Marking-To-Market
Suppose that on June 13 the futures rate falls fro 3.02% to 2.92%
The trader could withdraw $250 (10 basis points $25) from the
margin account, representing the increase in value of the position
199
Slide 200
Characteristics of Financial Futures Daily Marking-To-Market If
the futures rate increases to 3.08% the next day, the traders long
position decreases in value The 16 basis-point increase represents
a $400 drop in margin such that the ending account balance would
equal $950 200
Slide 201
Characteristics of Financial Futures Daily Marking-To-Market If
the futures rate increases further to 3.23%, the trader must make a
variation margin payment sufficient to bring the account up to $700
In this case, the account balance would have fallen to $575 and the
margin contribution would equal $125 The exchange member may close
the account if the trader does not meet the variation margin
requirement 201
Slide 202
Characteristics of Financial Futures Daily Marking-To-Market
The Basis Basis = Cash Price Futures Price or Basis = Futures Rate
Cash Rate It may be positive or negative, depending on whether
futures rates are above or below spot rates May swing widely in
value far in advance of contract expiration 202
Slide 203
Characteristics of Financial Futures 203
Slide 204
Speculation versus Hedging Speculators Take On Risk To Earn
Speculative Profits Speculation is extremely risky Example You
believe interest rates will fall, so you buy Eurodollar futures If
rates fall, the price of the underlying Eurodollar rises, and thus
the futures contract value rises earning you a profit If rates
rise, the price of the Eurodollar futures contract falls in value,
resulting in a loss 204
Slide 205
Speculation versus Hedging Hedgers Take Positions to Avoid or
Reduce Risk A hedger already has a position in the cash market and
uses futures to adjust the risk of being in the cash market The
focus is on reducing or avoiding risk 205
Slide 206
Speculation versus Hedging Hedgers Take Positions to Avoid or
Reduce Risk Example A bank anticipates needing to borrow $1,000,000
in 60 days. The bank is concerned that rates will rise in the next
60 days A possible strategy would be to short Eurodollar futures.
If interest rates rise (fall), the short futures position will
increase (decrease) in value. This will (partially) offset the
increase (decrease) in borrowing costs 206
Slide 207
207
Slide 208
Speculation versus Hedging Steps in Hedging 1. Identify the
cash market risk exposure to reduce 2. Given the cash market risk,
determine whether a long or short futures position is needed 3.
Select the best futures contract 4. Determine the appropriate
number of futures contracts to trade 208
Slide 209
Speculation versus Hedging Steps in Hedging 5. Buy or sell the
appropriate futures contracts 6. Determine when to get out of the
hedge position, either by reversing the trades, letting contracts
expire, or making or taking delivery 7. Verify that futures trading
meets regulatory requirements and the banks internal risk policies
209
Slide 210
Speculation versus Hedging A Long Hedge: Reduce Risk Associated
With A Decrease In Interest Rates A long hedge (buy futures) is
appropriate for a participant who wants to reduce spot market risk
associated with a decline in interest rates If spot rates decline,
futures rates will typically also decline so that the value of the
futures position will likely increase. Any loss in the cash market
is at least partially offset by a gain in futures 210
Slide 211
Speculation versus Hedging A Long Hedge: Reduce Risk Associated
With A Decrease In Interest Rates On June 6, 2008, your bank
expects to receive a $1 million payment on November 28, 2008, and
anticipates investing the funds in three-month Eurodollar time
deposits The cash market risk exposure is that the bank would like
to invest the funds at todays rates, but will not have access to
the funds for over five months In June 2008, the market expected
Eurodollar rates to increase as evidenced by rising futures rates.
211
Slide 212
Speculation versus Hedging A Long Hedge: Reduce Risk Associated
With A Decrease In Interest Rates In order to hedge, the bank
should buy futures contracts The best futures contract will
generally be the first contract that expires after the known cash
transaction date. This contract is best because its futures price
will generally show the highest correlation with the cash price In
this example, the December 2008 Eurodollar futures contract is the
first to expire after November 2008 212
Slide 213
Speculation versus Hedging A Long Hedge: Reduce Risk Associated
With A Decrease In Interest Rates The time line of the banks
hedging activities: 213
Slide 214
Speculation versus Hedging 214
Slide 215
Speculation versus Hedging A Short Hedge: Reduce Risk
Associated With A Increase In Interest Rates A short hedge (sell
futures) is appropriate for a participant who wants to reduce spot
market risk associated with an increase in interest rates If spot
rates increase, futures rates will typically also increase so that
the value of the futures position will likely decrease. Any loss in
the cash market is at least partially offset by a gain in the
futures market 215
Slide 216
Speculation versus Hedging A Short Hedge: Reduce Risk
Associated With A Increase In Interest Rates On June 6, 2008, your
bank expects to sell a six-month $1 million Eurodollar deposit on
August 17, 2008 The cash market risk exposure is that interest
rates may rise and the value of the Eurodollar deposit will fall by
August 2008 In order to hedge, the bank should sell futures
contracts 216
Slide 217
Speculation versus Hedging A Long Hedge: Reduce Risk Associated
With A Decrease In Interest Rates In order to hedge, the bank
should sell futures contracts In this example, the September 2008
Eurodollar futures contract is the first to expire after September
17, 2008 217
Slide 218
Speculation versus Hedging A Long Hedge: Reduce Risk Associated
With A Decrease In Interest Rates The time line of the banks
hedging activities: 218
Slide 219
Speculation versus Hedging 219
Slide 220
Speculation versus Hedging Change in the Basis Long and short
hedges work well if the futures rate moves in line with the spot
rate The actual risk assumed by a trader in both hedges is that the
basis might change between the time the hedge is initiated and
closed 220
Slide 221
Speculation versus Hedging Change in the Basis Effective Return
= Initial Cash Rate Change in Basis = Initial Cash Rate (B 2 B 1 )
where : B 1 is the basis when the hedge is opened B 2 is the basis
when the hedge is closed 221
Slide 222
Speculation versus Hedging Change in the Basis Effective
Return: Long Hedge = Initial Cash Rate (B 2 B 1 ) = 2.68% - (0.10%
- 0.34%) = 2.92% Effective Return: Short Hedge = Initial Cash Rate
(B 2 B 1 ) = 3.00% - (0.14% - -0.17%) = 2.69% 222
Slide 223
Speculation versus Hedging Basis Risk and Cross Hedging Cross
Hedge Where a trader uses a futures contract based on one security
that differs from the security being hedged in the cash market
223
Slide 224
Speculation versus Hedging Basis Risk and Cross Hedging Cross
Hedge Example Using Eurodollar futures to hedge changes in the
commercial paper rate Basis risk increases with a cross hedge
because the futures and spot interest rates may not move closely
together 224
Slide 225
Microhedging Applications Microhedge The hedging of a
transaction associated with a specific asset, liability or
commitment Macrohedge Taking futures positions to reduce aggregate
portfolio interest rate risk 225
Slide 226
Microhedging Applications Banks are generally restricted in
their use of financial futures for hedging purposes Banks must
recognize futures on a micro basis by linking each futures
transaction with a specific cash instrument or commitment Some feel
that such micro linkages force microhedges that may potentially
increase a firms total risk because these hedges ignore all other
portfolio components 226
Slide 227
Microhedging Applications Creating a Synthetic Liability with a
Short Hedge Example Assume that on June 6, 2008, a bank agreed to
finance a $1 million six-month loan Management wanted to match fund
the loan by issuing a $1 million, six-month Eurodollar time deposit
The six-month cash Eurodollar rate was 3% The three-month
Eurodollar rate was 2.68% The three-month Eurodollar futures rate
for September 2008 expiration equaled 2.83% 227
Slide 228
Microhedging Applications Creating a Synthetic Liability with a
Short Hedge Rather than issue a direct six-month Eurodollar
liability at 3%, the bank created a synthetic six-month liability
by shorting futures The objective was to use the futures market to
borrow at a lower rate than the six-month cash Eurodollar rate A
short futures position would reduce the risk of rising interest
rates for the second cash Eurodollar borrowing 228
Slide 229
Microhedging Applications Creating a Synthetic Liability with a
Short Hedge 229
Slide 230
230
Slide 231
Microhedging Applications The Mechanics of Applying a
Microhedge 1. Determine the banks interest rate position 2.
Forecast the dollar flows or value expected in cash market
transactions 3. Choose the appropriate futures contract 231
Slide 232
Microhedging Applications The Mechanics of Applying a
Microhedge 4. Determine the correct number of futures contracts
Where NF = number of futures contracts A = Dollar value of cash
flow to be hedged F = Face value of futures contract Mc = Maturity
or duration of anticipated cash asset or liability Mf = Maturity or
duration of futures contract 232
Slide 233
Microhedging Applications The Mechanics of Applying a
Microhedge 5. Determine the Appropriate Time Frame for the Hedge 6.
Monitor Hedge Performance 233
Slide 234
Macrohedging Applications Macrohedging Focuses on reducing
interest rate risk associated with a banks entire portfolio rather
than with individual transactions 234
Slide 235
Macrohedging Applications Hedging: GAP or Earnings Sensitivity
If a bank loses when interest rates fall (the bank has a positive
GAP), it should use a long hedge If rates rise, the banks higher
net interest income will be offset by losses on the futures
position If rates fall, the banks lower net interest income will be
offset by gains on the futures position 235
Slide 236
Macrohedging Applications Hedging: GAP or Earnings Sensitivity
If a bank loses when interest rates rise (the bank has a negative
GAP), it should use a short hedge If rates rise, the banks lower
net interest income will be offset by gains on the futures position
If rates fall, the banks higher net interest income will be offset
by losses on the futures position 236
Slide 237
Macrohedging Applications Hedging: Duration GAP and EVE
Sensitivity To eliminate interest rate risk, a bank could structure
its portfolio so that its duration gap equals zero 237
Slide 238
Macrohedging Applications Hedging: Duration GAP and EVE
Sensitivity Futures can be used to adjust the banks duration gap
The appropriate size of a futures position can be determined by
solving the following equation for the market value of futures
contracts (MVF), where DF is the duration of the futures contract
238
Slide 239
Macrohedging Applications Hedging: Duration GAP and EVE
Sensitivity Example: With a positive duration gap, the EVE will
decline if interest rates rise 239
Slide 240
Macrohedging Applications Hedging: Duration GAP and EVE
Sensitivity Example: The bank needs to sell interest rate futures
contracts in order to hedge its risk position The short position
indicates that the bank will make a profit if futures rates
increase 240
Slide 241
Macrohedging Applications Hedging: Duration GAP and EVE
Sensitivity Example: If the bank uses a Eurodollar futures contract
currently trading at 4.9% with a duration of 0.25 years, the target
market value of futures contracts (MVF) is: MVF = $4,096.82, so the
bank should sell four Eurodollar futures contracts 241
Slide 242
Macrohedging Applications Accounting Requirements and Tax
Implications Regulators generally limit a banks use of futures for
hedging purposes If a bank has a dealer operation, it can use
futures as part of its trading activities In such accounts, gains
and losses on these futures must be marked-to-market, thereby
affecting current income Microhedging To qualify as a hedge, a bank
must show that a cash transaction exposes it to interest rate risk,
a futures contract must lower the banks risk exposure, and the bank
must designate the contract as a hedge 242
Slide 243
Using Forward Rate Agreements to Manage Rate Risk Forward Rate
Agreements A forward contract based on interest rates based on a
notional principal amount at a specified future date Similar to
futures but differ in that they: Are negotiated between parties Do
not necessarily involve standardized assets Require no cash
exchange until expiration (i.e. there is no marking-to-market) No
exchange guarantees performance 243
Slide 244
Using Forward Rate Agreements to Manage Rate Risk Notional
Principal Serves as a reference figure in determining cash flows
for the two counterparties to a forward rate agreement agree
Notional refers to the condition that the principal does not change
hands, but is only used to calculate the value of interest payments
244
Slide 245
Using Forward Rate Agreements to Manage Rate Risk Buyer Agrees
to pay a fixed-rate coupon payment and receive a floating-rate
payment against the notional principal at some specified future
date 245
Slide 246
Using Forward Rate Agreements to Manage Rate Risk Seller Agrees
to pay a floating-rate payment and receive the fixed-rate payment
against the same notional principal The buyer and seller will
receive or pay cash when the actual interest rate at settlement is
different than the exercise rate 246
Slide 247
Using Forward Rate Agreements to Manage Rate Risk Forward Rate
Agreements: An Example Suppose that Metro Bank (as the seller)
enters into a receive fixed-rate/pay floating-rating forward rate
agreement with County Bank (as the buyer) with a six-month maturity
based on a $1 million notional principal amount The floating rate
is the 3-month LIBOR and the fixed (exercise) rate is 5% 247
Slide 248
Using Forward Rate Agreements to Manage Rate Risk Forward Rate
Agreements: An Example Metro Bank would refer to this as a 3 vs. 6
FRA at 5% on a $1 million notional amount from County Bank The only
cash flow will be determined in six months at contract maturity by
comparing the prevailing 3-month LIBOR with 5% 248
Slide 249
Using Forward Rate Agreements to Manage Rate Risk Forward Rate
Agreements: An Example Assume that in three months 3-month LIBOR
equals 6% In this case, Metro Bank would receive from County Bank
$2,463 The interest settlement amount is $2,500: Interest = (.06
-.05)(90/360) $1,000,000 = $2,500 Because this represents interest
that would be paid three months later at maturity of the
instrument, the actual payment is discounted at the prevailing
3-month LIBOR Actual interest = $2,500/[1+(90/360).06]=$2,463
249
Slide 250
Using Forward Rate Agreements to Manage Rate Risk Forward Rate
Agreements: An Example If instead, LIBOR equals 3% in three months,
Metro Bank would pay County Bank: The interest settlement amount is
$5,000 Interest = (.05 -.03)(90/360) $1,000,000 = $5,000 Actual
interest = $5,000 /[1 + (90/360).03] = $4,963 250
Slide 251
Using Forward Rate Agreements to Manage Rate Risk Forward Rate
Agreements: An Example County Bank would pay fixed-rate/receive
floating-rate as a hedge if it was exposed to loss in a rising rate
environment This is analogous to a short futures position Metro
Bank would sell fixed-rate/receive floating-rate as a hedge if it
was exposed to loss in a falling rate environment. This is
analogous to a long futures position 251
Slide 252
Using Forward Rate Agreements to Manage Rate Risk Potential
Problems with FRAs There is no clearinghouse to guarantee, so you
might not be paid when the counterparty owes you cash It is
sometimes difficult to find a specific counterparty that wants to
take exactly the opposite position FRAs are not as liquid as many
alternatives 252
Slide 253
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Basic (Plain Vanilla) Interest Rate Swap An
agreement between two parties to exchange a series of cash flows
based on a specified notional principal amount Two parties facing
different types of interest rate risk can exchange interest
payments 253
Slide 254
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Basic (Plain Vanilla) Interest Rate Swap One party
makes payments based on a fixed interest rate and receives floating
rate payments The other party exchanges floating rate payments for
fixed-rate payments When interest rates change, the party that
benefits from a swap receives a net cash payment while the party
that loses makes a net cash payment 254
Slide 255
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Basic (Plain Vanilla) Interest Rate Swap
Conceptually, a basic interest rate swap is a package of FRAs As
with FRAs, swap payments are netted and the notional principal
never changes hands 255
Slide 256
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Plain Vanilla Example Using data for a 2-year swap
based on 3- month LIBOR as the floating rate This swap involves
eight quarterly payments. Party FIX agrees to pay a fixed rate
Party FLT agrees to receive a fixed rate with cash flows calculated
against a $10 million notional principal amount 256
Slide 257
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Plan Vanilla Example 257
Slide 258
258
Slide 259
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Plain Vanilla Example If the three-month LIBOR for
the first pricing interval equals 3% The fixed payment for Party
FIX is $83,770 and the floating rate receipt is $67,744 Party FIX
will have to pay the difference of $16,026 The floating-rate
payment for Party FLT is $67,744 and the fixed-rate receipt
is$83,520 Party FLT will receive the difference of $15,776 The
dealer will net $250 from the spread ($16,026 -$15,776) 259
Slide 260
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Plain Vanilla Example At the second and subsequent
pricing intervals, only the applicable LIBOR is unknown As LIBOR
changes, the amount that both Party FIX and Party FLT either pay or
receive will change Party FIX will only receive cash at any pricing
interval if three-month LIBOR exceeds 3.36% Party FLT will
similarly receive cash as long as three-month LIBOR is less than
3.35% 260
Slide 261
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Convert a Floating-Rate Liability to a Fixed Rate
Liability Consider a bank that makes a $1 million, three-year
fixed-rate loan with quarterly interest at 8% It finances the loan
by issuing a three- month Eurodollar deposit priced at three- month
LIBOR 261
Slide 262
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Convert a Floating-Rate Liability to a Fixed Rate
Liability By itself, this transaction exhibits considerable
interest rate The bank is liability sensitive and loses (gains) if
LIBOR rises (falls) The bank can use a basic swap to microhedge
this transaction Using the data from Exhibit 9.8, the bank could
agree to pay 3.72% and receive three-month LIBOR against $1 million
for the three years By doing this, the bank locks in a borrowing
cost of 3.72% because it will both receive and pay LIBOR every
quarter 262
Slide 263
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Convert a Floating-Rate Liability to a Fixed Rate
Liability The use of the swap enables the bank to reduce risk and
lock in a spread of 4.28 percent (8.00 percent 3.72 percent) on
this transaction while effectively fixing the borrowing cost at
3.72 percent for three years 263
Slide 264
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Convert a Fixed-Rate Asset to a Floating- Rate
Asset Consider a bank that has a customer who demands a fixed-rate
loan The bank has a policy of making only floating- rate loans
because it is liability sensitive and will lose if interest rates
rise Ideally, the bank wants to price the loan based on prime Now
assume that the bank makes the same $1 million, three-year
fixed-rate loan as in the Convert a Floating-Rate Liability to a
Fixed Rate Liability example 264
Slide 265
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Convert a Fixed-Rate Asset to a Floating- Rate
Asset The bank could enter into a swap, agreeing to pay a 3.7%
fixed rate and receive prime minus 2.40% with quarterly payments
This effectively converts the fixed-rate loan into a variable rate
loan that floats with the prime rate 265
Slide 266
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Create a Synthetic Hedge Some view basic interest
rate swaps as synthetic securities As such, they enter into a swap
contract that essentially replicates the net cash flows from a
balance sheet transaction Suppose a bank buys a three-year Treasury
yielding 2.73%, which it finances by issuing a three-month deposit
As an alternative, the bank could enter into a three-month swap
agreeing to pay three- month LIBOR and receive a fixed rate
266
Slide 267
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Macrohedge Banks can also use interest rate swaps
to hedge their aggregate risk exposure measured by earnings and EVE
sensitivity A bank that is liability sensitive or has a positive
duration gap will take a basic swap position that potentially
produces profits when rates increase With a basic swap, this means
paying a fixed rate and receiving a floating rate Any profits can
be used to offset losses from lost net interest income or declining
267
Slide 268
Basic Interest Rate Swaps as a Risk Management Tool
Characteristics Macrohedge In terms of GAP analysis, a liability-
sensitive bank has more rate-sensitive liabilities than
rate-sensitive assets To hedge, the bank needs the equivalent of
more RSAs A swap that pays fixed and receives floating is
comparable to increasing RSAs relative to RSLs because the receipt
reprices with rate changes 268
Slide 269
Basic Interest Rate Swaps as a Risk Management Tool Pricing
Basic Swaps The floating rate is based on some predetermined money
market rate or index The payment frequency is coincidentally set at
every six months, three months, or one month, and is generally
matched with the money market rate The fixed rate is set at a
spread above the comparable maturity fixed rate security 269
Slide 270
Basic Interest Rate Swaps as a Risk Management Tool Comparing
Financial Futures, FRAs and Basic Swaps Similarities Each enables a
party to enter an agreement, which provides for cash receipts or
cash payments depending on how interest rates move Each allows
managers to alter a banks interest rate risk exposure None requires
much of an initial cash commitment to take a position 270
Slide 271
Basic Interest Rate Swaps as a Risk Management Tool Comparing
Financial Futures, FRAs and Basic Swaps Differences Financial
futures are standardized contracts based on fixed principal amounts
while with FRAs and interest rate swaps, parties negotiate the
notional principal amount Financial futures require daily
marking-to-market, which is not required with FRAs and swaps Many
futures contracts cannot be