managing interest rate risk: gap and earnings sensitivity

1

Managing Interest Rate Risk: GAP and Earnings Sensitivity

7

2

Managing Interest Rate Risk

Interest Rate Risk The potential loss from unexpected

changes in interest rates which can significantly alter a bank’s profitability and market value of equity

3


Interest Rate Risk When a bank’s 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 stockholder’s equity

4


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

5


Interest Rate Risk Asset and Liability Management

Committee (ALCO) The bank’s ALCO primary responsibility

is interest rate risk management. The ALCO coordinates the bank’s

strategies to achieve the optimal risk/reward trade-off

6

Measuring Interest Rate Risk with GAP Three general factors potentially cause

a bank’s 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

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 bank’s initial spread is 4%. What is the bank’s risk?

8

Measuring Interest Rate Risk with GAP Traditional Static Gap Analysis

Static GAP Analysis

GAPt = RSAt - RSLt

RSAt

Rate Sensitive Assets Those assets that will mature or reprice in

a given time period (t) RSLt

Rate Sensitive Liabilities Those liabilities that will mature or reprice

in a given time period (t)

9

Measuring Interest Rate Risk with GAP Traditional Static Gap Analysis

Steps in GAP Analysis1. 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

10

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

11

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

12


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

13


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 0–90 days.

14


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 loan’s effective rate sensitivity depends on how frequently the prime rate actually changes

15

Measuring Interest Rate Risk with GAP Factors Affecting Net Interest Income

Rate, Composition (Mix) and Volume Effects

All affect net interest income

16


Changes in the Level of Interest Rates The sign of GAP (positive or negative)

indicates the nature of the bank’s 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

17


Changes in the Level of Interest Rates The sign of GAP (positive or negative)

indicates the nature of the bank’s 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 bank’s net interest margin

18

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

19


20


Changes in the Level of Interest Rates GAP analysis assumes a parallel shift

in the yield curve

21


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:

∆NIIEXP = GAP x ∆iEXP

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

22


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 bank’s 1-year GAP?

23



RSA1 YR = $0

RSL1 YR = $10,000

GAP1 YR = $0 - $10,000 = -$10,000

The bank’s one year funding GAP is -$10,000 If interest rates rise (fall) by 1% in 1 year, the

bank’s net interest margin and net interest income will fall (rise)

∆NIIEXP = GAP x ∆iEXP = -$10,000 x 1% = -$100

24



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 bank’s initial spread is 1.05%. What is the bank’s 6-month GAP?

25



RSA6 MO = $30,000

RSL6 MO = $0

GAP6 MO = $30,000 – $0 = $30,000 The bank’s 6-month funding GAP is $30,000 If interest rates rise (fall) by 1% in 6

months, the bank’s net interest margin and net interest income will rise (fall)

∆NIIEXP = GAP x ∆iEXP = $30,000 x 1% = $300

26


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)

27


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

28


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

30


Example 3.0

Assets Yield Liabilities CostRate sensitive 500$ 8.0% 600$ 4.0%Fixed rate 350$ 11.0% 220$ 6.0%Non earning 150$ 100$

920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

31


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

32


Example 3.0 Earning Assets

$500 + $350 = $850 Net Interest Margin

$41.3/$850 = 4.86% Funding GAP

$500 - $600 = -$100

33


Example 3.1 What if all rates increase by 1%?


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

34


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.

Interest Income 83.50$ Interest Expense 43.20$ Net Interest Income 40.30$ Net Interest Margin 4.74%Funding GAP (100)$ ∆NIIEXP (1.00)$

35


Example 3.2 What if all rates fall by 1%?


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

36


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.

Interest Income 73.50$ Interest Expense 31.20$ Net Interest Income 42.30$ Net Interest Margin 4.98%Funding GAP (100)$ ∆NIIEXP 1.00$

37


Example 3.3 What if rates rise but the spread falls by

1%?


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

38



1%?

Both NII and NIM fall with a decrease in the spread. Why the larger change?

Note: ∆NIIEXP ≠ GAP x ∆iEXP Why?

Interest Income 81.00$ Interest Expense 46.20$ Net Interest Income 34.80$ Net Interest Margin 4.09%Funding GAP (100)$

39


Example 3.4 What if rates fall but the spread falls by

1%?


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

40


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: ∆NIIEXP ≠ GAP x ∆iEXP


41


Example 3.5 What if rates rise and the spread rises

by 1%?


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

42


Example 3.5 What if rates rise and the spread rises by

1%?

Both NII and NIM increase with an increase in the spread.



43


Example 3.6 What if rates fall and the spread rises

by 1%? Assets Yield Liabilities Cost

Rate sensitive 500$ 7.0% 600$ 2.0%Fixed rate 350$ 11.0% 220$ 6.0%Non earning 150$ 100$

920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

44


Example 3.6 What if rates fall and the spread rises by

1%?




45


Example 3.7 What if the bank proportionately

doubles in size?

Assets Yield Liabilities CostRate sensitive 1,000$ 8.0% 1,200$ 4.0%Fixed rate 700$ 11.0% 440$ 6.0%Non earning 300$ 200$

1,840$ Equity

160$ Total 2,000$ 2,000$

Balance Sheet

46


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 bank’s risk?


47


Example 4.0


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

48


Example 4.0

Bank has a positive GAP

Interest Income 75.50$ Interest Expense 40.20$ Net Interest Income 35.30$ Net Interest Margin 4.15%Funding GAP 150$

49


Example 4.1 What if rates increase by 1%?


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

50



With a positive GAP, interest income increases by more than the increase in interest expense. Thus, both NII and NIM rise.

Interest Income 81.50$ Interest Expense 44.70$ Net Interest Income 36.80$ Net Interest Margin 4.33%Funding GAP 150$ ∆NIIEXP 1.50$

51


Example 4.2 What if rates decrease by 1%?


920$ Equity

80$

Total 1,000$ 1,000$

Balance Sheet

52


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.

Interest Income 69.50$ Interest Expense 35.70$ Net Interest Income 33.80$ Net Interest Margin 3.98%Funding GAP 150$ ∆NIIEXP (1.50)$

53



1%?Assets Yield Liabilities Cost


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

54



1%?

Both NII and NIM fall with a decrease in the spread. Why the larger change?

Note: ∆NIIEXP ≠ GAP x ∆iEXP Why?


55


Example 4.4 What if rates fall and the spread falls by



920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

56



1%?

Both NII and NIM fall with a decrease in the spread.



57



by 1%?


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

58


Example 4.5 What if rates rise and the spread rises by

1%?




59


Example 4.6 What if rates fall and the spread rises

by 1%?


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

60


Example 4.6 What if rates fall and the spread rises by

1%?




61


Example 4.7 What if the bank proportionately

doubles in size?

Assets Yield Liabilities CostRate sensitive 1,200$ 8.0% 900$ 4.0%Fixed rate 500$ 11.0% 740$ 6.0%Non earning 300$ 200$

1,840$ Equity

160$

Total 2,000$ 2,000$

Balance Sheet

62


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 bank’s risk?


63


Example 5.0


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

64


Example 5.0

Bank has zero GAP

Interest Income 75.50$ Interest Expense 37.20$ Net Interest Income 38.30$ Net Interest Margin 4.51%Funding GAP -$

65




920$ Equity

80$

Total 1,000$ 1,000$

Balance Sheet

66



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!


67





920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

68


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: ∆NIIEXP ≠ GAP x ∆iEXP

Interest Income 66.50$ Interest Expense 34.20$

Net Interest Income 32.30$ Net Interest Margin 3.80%Funding GAP -$

69



by 1%?


920$ Equity

80$ Total 1,000$ 1,000$

Balance Sheet

70


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: ∆NIIEXP ≠ GAP x ∆iEXP


71


Summary of Base Cases

If a Negative GAP gives the largest NII and NIM, why not plan for a Negative GAP?

Positive Zero NegativeNII $35.30 $38.20 $41.30NIM 4.15% 4.51% 4.86%

GAP

72

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

74

Measuring Interest Rate Risk with GAP Rate Sensitivity Reports

Many managers monitor their bank’s risk position and potential changes in net interest income using rate sensitivity reports

These report classify a bank’s assets and liabilities as rate sensitive in selected time buckets through one year

75


Periodic GAP The Gap for each time bucket and

measures the timing of potential income effects from interest rate changes

76


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 bank’s net interest sensitivity throughout the time interval

78

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

79

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 bank’s

assets and liabilities

80

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

81

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 bank’s 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

82

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

83


Steps to Earnings Sensitivity Analysis1. 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

84


Steps to Earnings Sensitivity Analysis4. 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

85


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

86


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

87


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

88


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

89


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 bank’s benchmark interest rate

93


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

94


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.

95


Explanation of Sensitivity Results FSB’s 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

96

Income Statement GAP

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

97


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

98


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

100

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

101

Managing the GAP and Earnings Sensitivity Risk How to Adjust the Effective GAP or

Earnings Sensitivity Profile

102

Managing Interest Rate Risk: Economic Value of Equity

8

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

104

Managing Interest Rate Risk:Economic Value of Equity 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

105

Managing Interest Rate Risk:Economic Value of Equity GAP and Earnings Sensitivity versus

Duration GAP and EVE Sensitivity

106

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 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

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

109

Measuring Interest Rate Risk with Duration GAP Duration GAP Analysis

Compares the price sensitivity of a bank’s 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

110

Measuring Interest Rate Risk with Duration GAP Duration, Modified Duration, and

Effective Duration Macaulay’s 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

n

*)1(

Cashflow

Dt

tt

P

ti

111


Effective Duration Macaulay’s Duration (D)

Macaulay’s duration is a measure of price sensitivity where P refers to the price of the underlying security:

Δii)(1

D

P

ΔP

112


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)

113


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 bond’s price if interest rates fall by 25 basis points?

114


Effective Duration Example

Since the bond is a zero-coupon bond, Macaulay’s 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 bond’s price will change by approximately 9.524 × .0025 × $7,835.26 = $186.56

115


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

116

Measuring Interest Rate Risk with Duration GAP Duration, Modified Duration, and Effective Duration

Effective Duration

where: Pi- = Price if rates fall

Pi+ = Price if rates rise

P0 = Initial (current) price

i+ = Initial market rate plus the increase in the rate

i- = Initial market rate minus the decrease in the rate

)i (iP

P PDuration Effective

-0

i-i

-

-

117



Example Consider a 3-year, 9.4 percent semi-annual

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

118



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

119



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

120



Example

54.20.044) .050$10,000(

9,847.72$ $10,000Duration Effective

-

-

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

122


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

123


Weighted Average Duration of Bank Assets (DA):

where 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

n

iiiDawDA

124


Weighted Average Duration of Bank Liabilities (DL):

where 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

m

jjjDlzDL

125


Let MVA and MVL equal the market values of assets and liabilities, respectively

If ΔEVE = ΔMVA – ΔMVLand

Duration GAP = DGAP = DA – (MVL/MVA)DLthen

ΔEVE = -DGAP[Δy/(1+y)]MVAwhere y is the interest rate

126


To protect the economic value of equity against any change when rates change , the bank could set the duration gap to zero:

MVAy)(1

yDGAP- ΔEVE

127


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

128

Measuring Interest Rate Risk with Duration GAP A Duration Application for Banks

129


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

130


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)

131


132


Duration GAP Summary

133


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

MVA]y)(1

yDGAP[- ΔEVE

134


DGAP As a Measure of Risk In this case:

The actual decrease, as shown in Exhibit 8.3, was $12

91.12$000,1$]10.1

01.1.42[- ΔEVE

135


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

136


137


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

138


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

139


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

140


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

141


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

142


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

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

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

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

147


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

ΔMVE = -DGAP[Δy/(1+y)]MVA ΔMVE = -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

148


149


First Savings Bank The previous slide shows that FSB’s 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

150


First Savings Bank Effective “Duration” of Equity

Recall, duration measures the percentage change in market value for a given change in interest rates

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 = $8,200 / $82,563 = 9.9 years

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

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

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

154


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

155


Interest Rate Risk: An Example Consider the case where a bank has

two alternative for funding $1,000 for two years

0 1 2

$60 $60

Two-Year Security

0 1 2

$55 ?

One-Year Security & then another One-Year Security

156


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%

157


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

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.

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

161

Using Derivatives to Manage Interest Rate Risk

9

162

Using Derivatives to Manage Interest Rate Risk Derivative

Any instrument or contract that derives its value from another underlying asset, instrument, or contract

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

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

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

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

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 asset’s price but defer the actual exchange until a specified future date

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

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

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

171


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

172


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

173


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%

174


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

176


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

177


Scalper A speculator who tries to time price

movements over very short time intervals and takes positions that remain outstanding for only minutes

178


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

179


Position Trader A speculator who holds a position for a

longer period in anticipation of a more significant, longer-term market moves

180


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

181


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

182


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

183


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

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 asset’s value

185


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

186


Marking-to-Market The daily settlement process where at

the end of every trading day, a trader’s 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

187


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

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

189


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)

190


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)

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

193


Deposit Futures SETTLEMENT

The previous day’s closing price VOLUME

The previous day’s volume of contracts traded during the day

OPEN INTEREST The total number of futures contracts

outstanding at the end of the day.

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

195

Characteristics of Financial Futures Expectations Embedded in Future

Rates

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

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

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

199


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

200


If the futures rate increases to 3.08% the next day, the trader’s 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

201


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

202


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

203

Characteristics of Financial Futures

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

205


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

206


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

208


Steps in Hedging1. 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

209


Steps in Hedging5. 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

210


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

211


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 today’s 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.

212


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

213


A Long Hedge: Reduce Risk Associated With A Decrease In Interest Rates The time line of the bank’s hedging

activities:

214


215


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

216


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

217


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

218


A Long Hedge: Reduce Risk Associated With A Decrease In Interest Rates The time line of the bank’s hedging

activities:

219


220


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

221


Change in the Basis Effective Return

= Initial Cash Rate – Change in Basis

= Initial Cash Rate – (B2 – B1)

where :

B1 is the basis when the hedge is opened

B2 is the basis when the hedge is closed

222


Change in the Basis Effective Return: Long Hedge


= 2.68% - (0.10% - 0.34%) = 2.92%

Effective Return: Short Hedge


= 3.00% - (0.14% - -0.17%) = 2.69%

223


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

224


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

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

226


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 firm’s total risk because these hedges ignore all other portfolio components

227


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%

228


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

229


Creating a Synthetic Liability with a Short Hedge

231


The Mechanics of Applying a Microhedge1. Determine the bank’s interest rate

position

2. Forecast the dollar flows or value expected in cash market transactions

3. Choose the appropriate futures contract

232


The Mechanics of Applying a Microhedge4. 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

bMfF

Mc ANF

contract futureson movement rate Expected

instrumentcash on movement rate Expected b

233


The Mechanics of Applying a Microhedge5. Determine the Appropriate Time

Frame for the Hedge

6. Monitor Hedge Performance

234

Macrohedging Applications

Macrohedging Focuses on reducing interest rate risk

associated with a bank’s entire portfolio rather than with individual transactions

235


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 bank’s higher net interest income will be offset by losses on the futures position

If rates fall, the bank’s lower net interest income will be offset by gains on the futures position

236


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 bank’s lower net interest income will be offset by gains on the futures position

If rates fall, the bank’s higher net interest income will be offset by losses on the futures position

237


Hedging: Duration GAP and EVE Sensitivity To eliminate interest rate risk, a bank

could structure its portfolio so that its duration gap equals zero

MVA]y)(1

yDGAP[- ΔEVE

238


Hedging: Duration GAP and EVE Sensitivity Futures can be used to adjust the

bank’s 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

0i1

DF(MVF)

i1

DL(MVRSL)

i1

DA(MVRSA)

fla

239


Hedging: Duration GAP and EVE Sensitivity Example:

With a positive duration gap, the EVE will decline if interest rates rise

240



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

241



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

0 (1.049)

0.25(MVF)

(1.06)

1.59($920)

(1.10)

2.88($900)

242


Accounting Requirements and Tax Implications Regulators generally limit a bank’s 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 bank’s risk exposure, and the bank must designate the contract as a hedge

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

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

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

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

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%

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%

249


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

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

251


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

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

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

254


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

255


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

256


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

257


Plan Vanilla Example

259


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)

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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%

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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 bank’s interest rate risk exposure

None requires much of an initial cash commitment to take a position

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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 traded out more than three to four years, while interest rate swaps often extend 10 to 30 years

The market for FRAs is not that liquid and most contracts are short term

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Basic Interest Rate Swaps as a Risk Management Tool The Risk with Swaps

Counterparty risk is extremely important to swap participants

Credit risk exists because the counterparty to a swap contract may default

This is not as great for a single contract since the swap parties exchange only net interest payments

The notional principal amount never changes hands, such that a party will not lose that amount

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Interest Rate Caps and Floors

Buying an Interest Rate Cap Interest Rate Cap

An agreement between two counterparties that limits the buyer’s interest rate exposure to a maximum rate

Buying a cap is the same as purchasing a call option on an interest rate

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Buying an Interest Rate Floor Interest Rate Floor

An agreement between two counterparties that limits the buyer’s interest rate exposure to a minimum rate

Buying a floor is the same as purchasing a put option on an interest rate

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Interest Rate Collar and Reverse Collar Interest Rate Collar

The simultaneous purchase of an interest rate cap and sale of an interest rate floor on the same index for the same maturity and notional principal amount

A collar creates a band within which the buyer’s effective interest rate fluctuates

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Interest Rate Collar and Reverse Collar Zero Cost Collar

A collar where the buyer pays no net premium

The premium paid for the cap equals the premium received for the floor

Reverse Collar Buying an interest rate floor and

simultaneously selling an interest rate cap Used to protect a bank against falling interest

rates

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Interest Rate Collar and Reverse Collar The size of the premiums for caps and

floors is determined by: The relationship between the strike rate

an the current index This indicates how much the index must

move before the cap or floor is in-the-money The shape of yield curve and the

volatility of interest rates With an upward sloping yield curve, caps

will be more expensive than floors

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Protecting Against Falling Interest Rates Assume that a bank is asset sensitive

The bank holds loans priced at prime plus 1% and funds the loans with a three-year fixed-rate deposit at 3.75% percent

Management believes that interest rates will fall over the next three years

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Protecting Against Falling Interest Rates It is considering three alternative

approaches to reduce risk associated with falling rates:

1. Entering into a basic interest rate swap to pay three-month LIBOR and receive a fixed rate

2. Buying an interest rate floor

3. Buying a reverse collar Note that, initially, the bank holds assets

priced based on prime and deposits priced based on a fixed rate of 3.75%

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Protecting Against Falling Interest Rates Strategy: Use a Basic Interest Rate

Swap: Pay Floating and Receive Fixed As shown on the next slide, the use of

the swap effectively fixes the spread near the current level, except for basis risk

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Protecting Against Falling Interest Rates Strategy: Buy a Floor on the Floating

Rate As shown on the next slide, the use of

the floor protects against loss from falling rates while retaining the benefits from rising rates

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Protecting Against Falling Interest Rates Strategy: Buy a Reverse Collar: Sell a Cap

and Buy a Floor on the Floating Rate As shown on the next slide, the use of the

reverse collar differs from a pure floor by eliminating some of the potential benefits in a rising-rate environment

The bank actually receives a net premium up front and while this is attractive up front, if rates increase sufficiently, the bank does not benefit

The net result is that the bank’s spread will vary within a band

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Protecting Against Rising Interest Rates Assume that a bank is liability sensitive

That bank has made three-year fixed-rate term loans at 7% funded with three-month Eurodollar deposits for which it pays the prevailing LIBOR minus 0.25%

Management believes is concerned that interest rates will rise over the next three years

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Protecting Against Rising Interest Rates

It is considering three alternative approaches to reduce risk associated with rising rates:

1. Entering into a basic interest rate swap to pay a fixed rate and receive the three-month LIBOR

2. Buying an interest rate cap

3. Buying a collar

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Protecting Against Rising Interest Rates Strategy: Use a Basic Interest Rate

Swap: Pay Fixed and Receive Floating As shown on the next slide, the use of

the swap effectively fixes the spread near the current level, except for basis risk

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Protecting Against Rising Interest Rates Strategy: Buy a Cap on the Floating

Rate As shown on the next slide, the use of

the cap protects against loss from rising rates while retaining the benefits from falling rates

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Protecting Against Rising Interest Rates Strategy: Buy a Collar: Buy a Cap and

Sell a Floor on the Floating Rate As shown on the next slide, the use of

the collar differs from a pure cap by eliminating some of the potential benefits in a falling-rate environment

The net result is that the collar effectively creates a band within which the bank’s margin will fluctuate

managing interest rate risk: gap and earnings sensitivity

Documents

rate forecastselect

fixed rate

rate risk management

rate effectsunexpected

liability rate sensitive

banks risk

banks assets

value of assets