Managing Interest Rate Risk: GAP and Earnings Sensitivity

Managing Interest Rate Risk: GAP and Earnings Sensitivity
Bank Management, 6th edition. Timothy W. Koch and S. Scott MacDonald Copyright © 2006 by South-Western, a division of Thomson Learning Managing Interest Rate Risk: GAP and Earnings Sensitivity Chapter 5

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.

Interest Rate Risk: GAP & Earnings Sensitivity
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

Interest Rate Risk Banks typically focus on either: GAP Analysis
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

Asset and Liability Management Committee (ALCO)
The ALCO’s primary responsibility is interest rate risk management. The ALCO coordinates the bank’s strategies to achieve the optimal risk/reward trade-off.

Two Types of Interest Rate Risk
Spread Risk (reinvestment rate risk) Changes in interest rates will change the bank’s cost of funds as well as the return on their invested assets. They may change by different amounts. Price Risk Changes in interest rates may change the market values of the bank’s assets and liabilities by different amounts.

Interest Rate Risk: Spread (Reinvestment Rate) Risk
If interest rates change, the bank will have to reinvest the cash flows from assets or refinance rolled-over liabilities at a different interest rate in the future. An increase in rates, ceteris paribus, increases a bank’s interest income but also increases the bank’s interest expense. Static GAP Analysis considers the impact of changing rates on the bank’s net interest income.

Interest Rate Risk: Price Risk
If interest rates change, the market values of assets and liabilities also change. The longer is duration, the larger is the change in value for a given change in interest rates. Duration GAP considers the impact of changing rates on the market value of equity.

Measuring Interest Rate Risk with GAP
Example: A bank makes a $10,000 four-year car loan to a customer at fixed rate of 8.5%. The bank initially funds the car loan with a one-year $10,000 CD at a cost of 4.5%. The bank’s initial spread is 4%. What is the bank’s risk?

Traditional 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)

Traditional Static GAP Analysis What is the bank’s 1-year GAP with the auto loan? RSA1yr = $0 RSL1yr = $10,000 GAP1yr = $0 - $10,000 = -$10,000 The bank’s one year funding GAP is -10,000 If interest rates rise in 1 year, the bank’s margin will fall. The opposite is also true that if rates fall, the margin will rise.

Traditional Static GAP Analysis Funding GAP Focuses on managing net interest income in the short-run Assumes a ‘parallel shift in the yield curve,’ or that all rates change at the same time, in the same direction and by the same amount. Does this ever happen?

Traditional Static GAP Analysis Steps in GAP Analysis
Develop an interest rate forecast Select a series of “time buckets” or intervals for determining when assets and liabilities will reprice Group assets and liabilities into these “buckets ” Calculate the GAP for each “bucket ” Forecast the change in net interest income given an assumed change in interest rates

What Determines Rate Sensitivity (Ignoring Embedded Options)?
An asset or liability is considered rate sensitivity if during the time interval: It matures It represents and interim, or partial, principal payment It can be repriced The interest rate applied to the outstanding principal changes contractually during the interval The outstanding principal can be repriced when some base rate of index changes and management expects the base rate / index to change during the interval

What are RSAs and RSLs? Considering a 0-90 day “time bucket,” RSAs and RSLs include: Maturing instruments or principal payments If an asset or liability matures within 90 days, the principal amount will be repriced Any full or partial principal payments within 90 days will be repriced Floating and variable rate instruments If the index will contractually change within 90 days, the asset or liability is rate sensitive The rate may change daily if their base rate changes. Issue: do you expect the base rate to change?

Factors Affecting Net Interest Income
Changes in the level of interest rates Changes in the composition of assets and liabilities Changes in the volume of earning assets and interest-bearing liabilities outstanding Changes in the relationship between the yields on earning assets and rates paid on interest-bearing liabilities

Factors Affecting Net Interest Income: An Example
Consider the following balance sheet:

Examine the impact of the following changes
A 1% increase in the level of all short-term rates? A 1% decrease in the spread between assets yields and interest costs such that the rate on RSAs increases to 8.5% and the rate on RSLs increase to 5.5%? Changes in the relationship between short-term asset yields and liability costs A proportionate doubling in size of the bank.

1% increase in short-term rates
With a negative GAP, more liabilities than assets reprice higher; hence NII and NIM fall

1% decrease in the spread
NII and NIM fall (rise) with a decrease (increase) in the spread. Why the larger change?

Changes in the Slope of the Yield Curve
If liabilities are short-term and assets are long-term, the spread will widen as the yield curve increases in slope narrow when the yield curve decreases in slope and/or inverts

Proportionate doubling in size
NII and GAP double, but NIM stays the same. What has happened to risk?

Changes in the Volume of Earning Assets and Interest-Bearing Liabilities
Net interest income varies directly with changes in the volume of earning assets and interest-bearing liabilities, regardless of the level of interest rates

RSAs increase to $540 while fixed-rate assets decrease to $310 and RSLs decrease to $560 while fixed-rate liabilities increase to $260 Although the bank’s GAP (and hence risk) is lower, NII is also lower.

Changes in Portfolio Composition and Risk
To reduce risk, a bank with a negative GAP would try to increase RSAs (variable rate loans or shorter maturities on loans and investments) and decrease RSLs (issue relatively more longer-term CDs and fewer fed funds purchased) Changes in portfolio composition also raise or lower interest income and expense based on the type of change

Changes in Net Interest Income are directly proportional to the size of the GAP
If there is a parallel shift in the yield curve: 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. We can figure out how much. How?

Summary of GAP and the Change in NII

Rate, Volume, and Mix Analysis
Banks often publish a summary of how net interest income has changed over time. They separate changes over time to: shifts in assets and liability composition and volume changes associated with movements in interest rates. The purpose is to assess what factors influence shifts in net interest income over time.

Measuring Interest Rate Risk: Synovus

Interest Rate-Sensitivity Reports Classifies a bank’s assets and liabilities into time intervals according to the minimum number of days until each instrument is expected to be repriced. GAP values are reported a periodic and cumulative basis for each time interval. Periodic GAP Is the Gap for each time bucket and measures the timing of potential income effects from interest rate changes Cumulative GAP It is 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.

Advantages and Disadvantages of Static GAP Analysis
Easy to understand Works well with small changes in interest rates Disadvantages 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

Measuring Interest Rate Risk with the 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

What is the ‘Optimal GAP’
There is no general optimal value for a bank's GAP in all environments. Generally, the farther a bank's GAP is from zero, the greater is the bank's risk. A bank must evaluate its overall risk and return profile and objectives to determine its optimal GAP

GAP and Variability in Earnings
Neither the GAP nor GAP ratio provide direct information on the potential variability in earnings when rates change. Consider two banks, both with $500 million in total assets. Bank A: $3 mil in RSAs and $2 mil in RSLs. GAP = $1 mil and GAP ratio = 1.5 mil Bank B: $300 mil in RSAs and $200 mil RSLs. GAP equals $100 mill and 1.5 GAP ratio. Clearly, the second bank assumes greater interest rate risk because its net interest income will change more when interest rates change.

Link Between GAP and Net Interest Margin
Many banks will specify a target GAP to earning asset ratio in the ALCO policy statements

Establishing a Target GAP: An Example
Consider a bank with $50 million in earning assets that expects to generate a 5% NIM. The bank will risk changes in NIM equal to plus or minus 20% during the year Hence, NIM should fall between 4% and 6%.

Establishing a Target GAP: An Example (continued)
If management expects interest rates to vary up to 4 percent during the upcoming year, the bank’s ratio of its 1-year cumulative GAP (absolute value) to earning assets should not exceed 25 percent. Target GAP/Earning assets = (.20)(0.05) / 0.04 = 0.25 Management’s willingness to allow only a 20 percent variation in NIM sets limits on the GAP, which would be allowed to vary from $12.5 million to $12.5 million, based on $50 million in earning assets.

Speculating on the GAP Many bank managers attempt to adjust the interest rate risk exposure of a bank in anticipation of changes in interest rates. This is speculative because it assumes that management can forecast rates better than the market.

Can a Bank Effectively Speculate on the GAP?
Difficult to vary the GAP and win as this requires consistently accurate interest rate forecasts A bank has limited flexibility in adjusting its GAP; e.g., loan and deposit terms There is no adjustment for the timing of cash flows or dynamics of the changing GAP position

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.

Steps to Earnings Sensitivity Analysis
Forecast future interest rates Identify changes in the composition of assets and liabilities in different rate environments Forecast when embedded options will be exercised Identify when specific assets and liabilities will reprice given the rate environment Estimate net interest income and net income Repeat the process to compare forecasts of net interest income and net income across different interest rate environments.

Earnings Sensitivity Analysis and the Exercise of Embedded Options
Many bank assets and liabilities contain different types of options, both explicit and implicit: Option to refinance a loan Call option on a federal agency bond the bank owns Depositors have the option to withdraw funds prior to maturity Cap (maximum) rate on a floating-rate loan

Earnings Sensitivity Analysis Recognizes that 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.

Recall the our example from before:
GAP1Yr = $0 - $10,000 = -$10,000 What if rates increased? 1 year GAP Position Change in Rates Base -3 -2 -1 GAP1yr +1 +2 +3 -1,000 -2,000 -8,000 -10,000 Re-finance the auto loans All CD’s will mature

What about the 3 Month GAP Position?
Base GAP3m = $10,000 - $10,000 = 0 3 Month GAP Position Change in Rates Base -3 -2 -1 GAP3m +1 +2 +3 +8,000 +6,000 +2,000 -1,000 -3,000 -6,000 Re-finance auto loans, and less likely to “pull” CD’s People will “pull” the CD’s for higher returns

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

Earnings Sensitivity Analysis (Base Case) Example
Assets

Earnings Sensitivity Analysis (Base Case) Example
Liabilities and GAP Measures

Interest Rate Forecasts
d u n s o r c a t v . I m p l i w R T ( h ) % 4 5 2 3 7 1 9 M k L y Interest Rate Forecasts M o s t L i k e l y F r c a n d R m p D . 2005 P 6 5 4 3 2 1 2006 7 9 2007

Earnings Sensitivity Analysis Results
For the bank: The embedded options can potentially alter the bank’s cash flows Interest rates change by different amounts at different times Summary results are known as Earnings-at-Risk or Net Interest Income Simulation

Earnings Sensitivity Analysis
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. Demonstrates the potential volatility in earnings across these environments The greater is the potential variation in earnings (earnings at risk), the greater is the amount of risk assumed by a bank , or The greater is the maximum loss, the greater is risk

Income Statement GAP Income Statement GAP
Forecasts the change in net interest income given a 1% rise or fall in the bank’s benchmark rate over the next year. It converts contractual GAP data to figures evidencing the impact of a 1% rate movement. Income statement GAP is also know in the industry as Beta GAP analysis

Income Statement GAP Adjusts the Balance Sheet GAP to Incorporate the Earnings Change Ratio
This ratio indicates how the yield on each asset and rate paid on each liability is assumed to change relative to a 1 percent move in the benchmark rate.

Income Statement GAP

Managing the GAP and Earnings Sensitivity Risk
Steps to reduce risk Calculate periodic GAPs over short time intervals. Fund repriceable assets with matching repriceable liabilities so that periodic GAPs approach zero. Fund long-term assets with matching noninterest-bearing liabilities. Use off-balance sheet transactions to hedge.

Adjust the Effective Rate Sensitivity of a Bank’s Assets and Liabilities
Objective Approaches Reduce asset sensitivity Buy longer-term securities. Lengthen the maturities of loans. Move from floating-rate loans to term loans. Increase asset sensitivity Buy short-term securities. Shorten loan maturities. Make more loans on a floating-rate basis. Reduce liability sensitivity Pay premiums to attract longer-term deposit instruments. Issue long-term subordinated debt. Increase liability sensitivity Pay premiums to attract short-term deposit instruments. Borrow more via non-core purchased liabilities.

Managing Interest Rate Risk: Duration GAP and Economic Value of Equity
Bank Management, 6th edition. Timothy W. Koch and S. Scott MacDonald Copyright © 2006 by South-Western, a division of Thomson Learning Managing Interest Rate Risk: Duration GAP and Economic Value of Equity Chapter 6

Measuring Interest Rate Risk with Duration GAP
Economic Value of Equity Analysis Focuses on changes in stockholders’ equity given potential changes in interest rates Duration GAP Analysis Compares the price sensitivity of a bank’s total assets with the price sensitivity of its total liabilities to assess the impact of potential changes in interest rates on stockholders’ equity.

Recall from Chapter 4 Duration is a measure of the effective maturity of a security. Duration incorporates the timing and size of a security’s cash flows. Duration measures how price sensitive a security is to changes in interest rates. The greater (shorter) the duration, the greater (lesser) the price sensitivity.

Duration and Price Volatility
Duration as an Elasticity Measure Duration versus Maturity Consider the cash flows for these two securities over the following time line

Duration versus Maturity
The maturity of both is 20 years Maturity does not account for the differences in timing of the cash flows What is the effective maturity of both? The effective maturity of the first security is: (1,000/1,000) x 20 = 20 years The effective maturity of the second security is: [(900/1,000) x 1]+[(100/1,000) x 20] = 2.9 years Duration is similar, however, it uses a weighted average of the present values of the cash flows

Duration is an approximate measure of the price elasticity of demand

The longer the duration, the larger the change in price for a given change in interest rates.

Measuring Duration Duration is a weighted average of the time until the expected cash flows from a security will be received, relative to the security’s price Macaulay’s Duration

Measuring Duration Example
What is the duration of a bond with a $1,000 face value, 10% annual coupon payments, 3 years to maturity and a 12% YTM? The bond’s price is $

What is the duration of a bond with a $1,000 face value, 10% coupon, 3 years to maturity but the YTM is 5%?The bond’s price is $1,

What is the duration of a bond with a $1,000 face value, 10% coupon, 3 years to maturity but the YTM is 20%?The bond’s price is $

What is the duration of a zero coupon bond with a $1,000 face value, 3 years to maturity but the YTM is 12%? By definition, the duration of a zero coupon bond is equal to its maturity

Duration and Modified Duration
The greater the duration, the greater the price sensitivity Modified Duration gives an estimate of price volatility:

Effective Duration Effective Duration
Used to estimate a security’s price sensitivity when the security contains embedded options. Compares a security’s estimated price in a falling and rising rate environment.

Effective Duration Where: Pi- = Price if rates fall
Pi+ = Price if rates rise P0 = Initial (current) price i+ = Initial market rate plus the increase in rate i- = Initial market rate minus the decrease in rate

Effective Duration Example
Consider a 3-year, 9.4 percent 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.

Assume, instead, that the bond is callable at par in the near-term . If rates fall, the price will not rise much above the par value since it will likely be called If rates rise, the bond is unlikely to be called and the price will fall

If rates rise 30 basis points to 5% semiannually, the price will fall to $9, If rates fall 30 basis points to 4.4% semiannually, the price will remain at par

Duration GAP Duration GAP Model
Focuses on either managing the market value of stockholders’ equity The bank can protect EITHER the market value of equity or net interest income, but not both Duration GAP analysis emphasizes the impact on equity

Duration GAP Duration GAP Analysis
Compares the duration of a bank’s assets with the duration of the bank’s liabilities and examines how the economic value stockholders’ equity will change when interest rates change.

Two Types of Interest Rate Risk
Reinvestment Rate Risk Changes in interest rates will change the bank’s cost of funds as well as the return on invested assets Price Risk Changes in interest rates will change the market values of the bank’s assets and liabilities

Reinvestment Rate Risk
If interest rates change, the bank will have to reinvest the cash flows from assets or refinance rolled-over liabilities at a different interest rate in the future An increase in rates increases a bank’s return on assets but also increases the bank’s cost of funds

Price Risk If interest rates change, the value of assets and liabilities also change. The longer the duration, the larger the change in value for a given change in interest rates Duration GAP considers the impact of changing rates on the market value of equity

Reinvestment Rate Risk and Price Risk
If interest rates rise (fall), the yield from the reinvestment of the cash flows rises (falls) and the holding period return (HPR) increases (decreases). Price risk If interest rates rise (fall), the price falls (rises). Thus, if you sell the security prior to maturity, the HPR falls (rises).

Increases in interest rates will increase the HPR from a higher reinvestment rate but reduce the HPR from capital losses if the security is sold prior to maturity. Decreases in interest rates will decrease the HPR from a lower reinvestment rate but increase the HPR from capital gains if the security is sold prior to maturity.

An immunized security or portfolio is one in which the gain from the higher reinvestment rate is just offset by the capital loss. For an individual security, immunization occurs when an investor’s holding period equals the duration of the security.

Steps in Duration GAP Analysis
Forecast interest rates. Estimate the market values of bank assets, liabilities and stockholders’ equity. Estimate the weighted average duration of assets and the weighted average duration of liabilities. Incorporate the effects of both on- and 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.

Weighted Average Duration of Bank Assets
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

Weighted Average Duration of Bank Liabilities
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

Duration GAP and Economic Value of Equity
Let MVA and MVL equal the market values of assets and liabilities, respectively. If: and Duration GAP Then: where y = the general level of interest rates

Duration GAP and Economic Value of Equity
To protect the economic value of equity against any change when rates change , the bank could set the duration gap to zero:

Hypothetical Bank Balance Sheet

Calculating DGAP DA DL DGAP
($700/$1000)* ($200/$1000)*4.99 = 2.88 DL ($620/$920)* ($300/$920)*2.81 = 1.59 DGAP (920/1000)*1.59 = 1.42 years What does this tell us? The average duration of assets is greater than the average duration of liabilities; thus asset values change by more than liability values.

1 percent increase in all rates.

Calculating DGAP DA DGAP ($683/$974)*2.68 + ($191/$974)*4.97 = 2.86
($614/$906)* ($292/$906)*2.80 = 1.58 DGAP ($906/$974) * 1.58 = 1.36 years What does 1.36 mean? The average duration of assets is greater than the average duration of liabilities, thus asset values change by more than liability values.

Change in the Market Value of Equity
In this case:

Positive and Negative Duration GAPs
Positive DGAP Indicates that assets are more price sensitive than liabilities, on average. Thus, when interest rates rise (fall), assets will fall proportionately more (less) in value than liabilities and EVE will fall (rise) accordingly. Negative DGAP Indicates that weighted liabilities are more price sensitive than weighted assets. Thus, when interest rates rise (fall), assets will fall proportionately less (more) in value that liabilities and the EVE will rise (fall).

DGAP Summary

An Immunized Portfolio
To immunize the EVE from rate changes in the example, the bank would need to: decrease the asset duration by 1.42 years or increase the duration of liabilities by 1.54 years DA / ( MVA/MVL) = 1.42 / ($920 / $1,000) = 1.54 years

Immunized Portfolio DGAP = 2.88 – 0.92 (3.11) ≈ 0

Immunized Portfolio with a 1% increase in rates

Immunized Portfolio with a 1% increase in rates
EVE changed by only $0.5 with the immunized portfolio versus $25.0 when the portfolio was not immunized.

Stabilizing the Book Value of Net Interest Income
This can be done for a 1-year time horizon, with the appropriate duration gap measure DGAP* MVRSA(1- DRSA) - MVRSL(1- DRSL) where: MVRSA = cumulative market value of RSAs MVRSL = cumulative market value of RSLs DRSA = composite duration of RSAs for the given time horizon Equal to the sum of the products of each asset’s duration with the relative share of its total asset market value DRSL = composite duration of RSLs for the given time horizon Equal to the sum of the products of each liability’s duration with the relative share of its total liability market value.

Stabilizing the Book Value of Net Interest Income
If DGAP* is positive, the bank’s net interest income will decrease when interest rates decrease, and increase when rates increase. If DGAP* is negative, the relationship is reversed. Only when DGAP* equals zero is interest rate risk eliminated. Banks can use duration analysis to stabilize a number of different variables reflecting bank performance.

Economic Value of Equity Sensitivity Analysis
Effectively involves the same steps as earnings sensitivity analysis. In EVE analysis, however, the bank focuses on: The relative durations of assets and liabilities How much the durations change in different interest rate environments What happens to the economic value of equity across different rate environments

Embedded Options Embedded options sharply influence the estimated volatility in EVE Prepayments that exceed (fall short of) that expected will shorten (lengthen) duration. A bond being called will shorten duration. A deposit that is withdrawn early will shorten duration. A deposit that is not withdrawn as expected will lengthen duration.

First Savings Bank Economic Value of Equity Market Value/Duration Report as of 12/31/04 Most Likely Rate Scenario-Base Strategy Assets

First Savings Bank Economic Value of Equity Market Value/Duration Report as of 12/31/04 Most Likely Rate Scenario-Base Strategy Liabilities

Duration Gap for First Savings Bank EVE
Market Value of Assets $1,001,963 Duration of Assets 2.6 years Market Value of Liabilities $919,400 Duration of Liabilities 2.0 years

Duration Gap for First Savings Bank EVE
= 2.6 – ($919,400/$1,001,963)*2.0 = years Example: A 1% increase in rates would reduce EVE by $7.2 million = (0.01 / ) * $1,001,963 Recall that the average rate on assets is 6.93%

Sensitivity of EVE versus Most Likely (Zero Shock) Interest Rate Scenario
Sensitivity of Economic Value of Equity measures the change in the economic value of the corporation’s equity under various changes in interest rates. Rate changes are instantaneous changes from current rates. The change in economic value of equity is derived from the difference between changes in the market value of assets and changes in the market value of liabilities.

Effective “Duration” of Equity
By definition, duration measures the percentage change in market value for a given change in interest rates Thus, a bank’s duration of equity measures the percentage change in EVE that will occur with a 1 percent change in rates: Effective duration of equity yrs. = $8,200 / $82,563

Asset/Liability Sensitivity and DGAP
Funding GAP and Duration GAP are NOT directly comparable Funding GAP examines various “time buckets” while Duration GAP represents the entire balance sheet. Generally, if a bank is liability (asset) sensitive in the sense that net interest income falls (rises) when rates rise and vice versa, it will likely have a positive (negative) DGAP suggesting that assets are more price sensitive than liabilities, on average.

Strengths and Weaknesses: DGAP and EVE-Sensitivity Analysis
Duration analysis provides a comprehensive measure of interest rate risk Duration measures are additive This allows for the matching of total assets with total liabilities rather than the matching of individual accounts Duration analysis takes a longer term view than static gap analysis

Strengths and Weaknesses: DGAP and EVE-Sensitivity Analysis
It is difficult to compute duration accurately “Correct” duration analysis requires that each future cash flow be discounted by a distinct discount rate A bank must continuously monitor and adjust the duration of its portfolio It is difficult to estimate the duration on assets and liabilities that do not earn or pay interest Duration measures are highly subjective

Speculating on Duration GAP
It is difficult to actively vary GAP or DGAP and consistently win Interest rates forecasts are frequently wrong Even if rates change as predicted, banks have limited flexibility in vary GAP and DGAP and must often sacrifice yield to do so

Gap and DGAP Management Strategies Example
Cash flows from investing $1,000 either in a 2-year security yielding 6 percent or two consecutive 1-year securities, with the current 1-year yield equal to 5.5 percent.

It is not known today what a 1-year security will yield in one year. For the two consecutive 1-year securities to generate the same $120 in interest, ignoring compounding, the 1-year security must yield 6.5% one year from the present. This break-even rate is a 1-year forward rate, one year from the present: 6% + 6% = 5.5% + x so x must = 6.5%

By investing in the 1-year security, a depositor is betting that the 1-year interest rate in one year will be greater than 6.5% By issuing the 2-year security, the bank is betting that the 1-year interest rate in one year will be greater than 6.5%

Yield Curve Strategy When the U.S. economy hits its peak, the yield curve typically inverts, with short-term rates exceeding long-term rates. Only twice since WWII has a recession not followed an inverted yield curve As the economy contracts, the Federal Reserve typically increases the money supply, which causes the rates to fall and the yield curve to return to its “normal” shape.

Yield Curve Strategy To take advantage of this trend, when the yield curve inverts, banks could: Buy long-term non-callable securities Prices will rise as rates fall Make fixed-rate non-callable loans Borrowers are locked into higher rates Price deposits on a floating-rate basis Lengthen the duration of assets relative to the duration of liabilities

Interest Rates and the Business Cycle The general level of interest rates and the shape of the yield curve appear to follow the U.S. business cycle. T i m e I n t r s R a ( P c ) E x p o C L g - S h k u In expansionary stages rates rise until they reach a peak as the Federal Reserve tightens credit availability. In contractionary stages rates fall until they reach a trough when the U.S. economy falls into recession.

Using Derivatives to Manage Interest Rate Risk
Bank Management, 6th edition. Timothy W. Koch and S. Scott MacDonald Copyright © 2006 by South-Western, a division of Thomson Learning Using Derivatives to Manage Interest Rate Risk Chapter 7

Derivatives A derivative is any instrument or contract that derives its value from another underlying asset, instrument, or contract.

Managing 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

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

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 Note that prices and interest rates move inversely, so buyers gain when rates fall.

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 The same for sellers, so they gain when rates rise.

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

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

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

Types of Futures 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.

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.

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

Commission Brokers Execute trades for other parties Locals Trade for their own account Locals are speculators Scalper A speculator who tries to time price movements over very short time intervals and takes positions that remain outstanding for only minutes

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 Position Trader A speculator who holds a position for a longer period in anticipation of a more significant, longer-term market move.

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

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

Margin Requirements Initial Margin Maintenance 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 Maintenance Margin The minimum deposit required at the end of each day

Margin Requirements Unlike margin accounts for stocks, futures margin deposits represent a guarantee that a trader will be able to make any mandatory payment obligations Same effect as a performance bond

Margin Requirements Marking-to-Market Variation Margin
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

Expiration and Delivery
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

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.

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)

Contracts trade according to an index that equals 100% - the futures interest rate An index of indicates a futures rate of 5.5 percent 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)

Eurodollar Futures The first column indicates the settlement month and year Each row lists price and yield data for a distinct futures contract that expires sequentially every three months The next four columns report the opening price, high and low price, and closing settlement price. The next column, the change in settlement price from the previous day. The two columns under Yield convert the settlement price to a Eurodollar futures rate as: 100 - Settlement Price = Futures Rate

The Basis The basis is the cash price of an asset minus the corresponding futures price for the same asset at a point in time For financial futures, the basis can be calculated as the futures rate minus the spot 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

The Relationship Between Futures Rates and Cash Rates - One Possible Pattern on March 10
D e c e m b e r 2005 F u t u r e s R a t e ) t n e c r e P C a s h R a t e ( e t a R B a s i s F u t u r e s R a t e - C a s h R a t e March 10, August 23, Expiration December 20, 2005

Speculation versus Hedging
A speculator takes on additional risk to earn speculative profits Speculation is extremely risky 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

Example Speculating 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

Example Hedging 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

With financial futures, risk often cannot be eliminated, only reduced. Traders normally assume basis risk in that the basis might change adversely between the time the hedge is initiated and closed Perfect Hedge The gains (losses) from the futures position perfectly offset the losses (gains) on the spot position at each price

Profit Diagrams for the December 2005 Eurodollar Futures Contract: Mar 10, 2005

Steps in Hedging Identify the cash market risk exposure to reduce
Given the cash market risk, determine whether a long or short futures position is needed Select the best futures contract Determine the appropriate number of futures contracts to trade. Buy or sell the appropriate futures contracts Determine when to get out of the hedge position, either by reversing the trades, letting contracts expire, or making or taking delivery Verify that futures trading meets regulatory requirements and the banks internal risk policies

A Long Hedge 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

Long Hedge Example On March 10, 2005, your bank expects to receive a $1 million payment on November 8, 2005, and anticipates investing the funds in 3-month Eurodollar time deposits The cash market risk exposure is that the bank will not have access to the funds for eight months. In March 2005, the market expected Eurodollar rates to increase sharply as evidenced by rising futures rates.

Long Hedge Example In order to hedge, the bank should buy futures contracts The best futures contract will generally be the December 2005, 3-month Eurodollar futures contract, which is the first to expire after November 2005. The contract that expires immediately after the known cash transactions date is generally best because its futures price will show the highest correlation with the cash price.

Long Hedge Example The time line of the bank’s hedging activities would look something like this:

Long Hedge Example Date Cash Market Futures Market Basis 3/10/05
Bank anticipates investing $1 million Bank buys one December 2005 4.09% - 3.00% = 1.09% (Initial futures in Eurodollars in 8 months; current Eurodollar futures contract at position) cash rate 4.09%; price 95.91 11/8/05 Bank invests $1 million in 3 month Bank sells one December 2005 4.03% 3.93% 0.10% (Close futures Eurodollars at 3.93% 4.03%; price 95.97% Net effect Opportunity gain: Futures profit: Basis change: 0.10% 0.93%; 0.06%; 0.99% 93 basis points worth 6 basis points worth $25 each $2,325 $150 Cumulative e investment income: Interest at 3.93% $1,000,000(.0393)(90/360) = $9,825 Profit from futures trades $ 150 Total $9,975 Long Hedge Example

A Short Hedge 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

Short Hedge Example On March 10, 2005, your bank expects to sell a six-month $1 million Eurodollar deposit on August 15, 2005 The cash market risk exposure is that interest rates may rise and the value of the Eurodollar deposit will fall by August 2005 In order to hedge, the bank should sell futures contracts

Short Hedge Example The time line of the bank’s hedging activities would look something like this:

Short Hedge Example

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 In the long hedge position above, the spot rate increased by 0.93% while the futures rate fell by 0.06%. This caused the basis to fall by 0.99% (The basis fell from 1.09% to 0.10%, or by 0.99%)

Change in the Basis Effective Return from a Hedge Effective return
Total income from the combined cash and futures positions relative to the investment amount Effective return Initial Cash Rate - Change in Basis In the long hedge example: 3.00% - (-0.99%) = 3.99%

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 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

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

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 Many analysts feel that such micro linkages force microhedges that may potentially increase a firm’s total risk because these hedges ignore all other portfolio components

Creating a Synthetic Liability with a Short Hedge

The Mechanics of Applying a Microhedge
Determine the bank’s interest rate position Forecast the dollar flows or value expected in cash market transactions Choose the appropriate futures contract

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

Determine the Appropriate Time Frame for the Hedge Monitor Hedge Performance

Macrohedging Macrohedging
Focuses on reducing interest rate risk associated with a bank’s entire portfolio rather than with individual transactions

Macrohedging Hedging: GAP or Earnings Sensitivity
If GAP is positive, the bank is asset sensitive and its net interest income rises when interest rates rise and falls when interest rates fall If GAP is negative, the bank is liability sensitive and its net interest income falls when interest rates rise and rises when interest rates fall Positive GAP Use a long hedge Negative GAP Use a short hedge

Hedging: GAP or Earnings Sensitivity
Positive GAP 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

Hedging: GAP or Earnings Sensitivity
Negative GAP 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

Hedging: Duration GAP and EVE Sensitivity
To eliminate interest rate risk, a bank could structure its portfolio so that its duration gap equals zero

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

Example: A bank has a positive duration gap of 1.4 years, therefore, the market value of equity will decline if interest rates rise. 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

Example: Assume 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 = $4,024.36, so the bank should sell four Eurodollar futures contracts

Example: If all interest rates increased by 1%, the profit on the four futures contracts would total 4 x 100 x $25 = $10,000, which partially offset the $12,000 decrease in the economic value of equity associated with the increase in cash rates Recall from Exhibit 6.2, the unhedged bank had a reduction in EVE of $12,000

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

Using Forward Rate Agreements to Manage Interest Rate Risk
A forward contract based on interest rates based on a notional principal amount at a specified future date Buyer Agrees to pay a fixed-rate coupon payment (at the exercise rate) and receive a floating-rate payment Seller Agrees to make a floating-rate payment and receive a fixed-rate payment The buyer and seller will receive or pay cash when the actual interest rate at settlement is different than the exercise rate

Forward Rate Agreements (FRA)
Similar to futures but differ in that they: Are negotiated between parties Do not necessarily involve standardized assets Require no cash exchange until expiration There is no marking-to-market No exchange guarantees performance

Notional Principal The two counterparties to a forward rate agreement agree to a notional principal amount that serves as a reference figure in determining cash flows. Notional Refers to the condition that the principal does not change hands, but is only used to calculate the value of interest payments.

Notional Principal Buyer Seller
Agrees to pay a fixed-rate coupon payment and receive a floating-rate payment against the notional principal at some specified future date. Seller Agrees to pay a floating-rate payment and receive the fixed-rate payment against the same notional principal.

Example: Forward Rate Agreements
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 7%

Metro Bank would refer to this as a “3 vs. 6” FRA at 7 percent on a $1 million notional amount from County Bank The phrase “3 vs. 6” refers to a 3-month interest rate observed three months from the present, for a security with a maturity date six months from the present The only cash flow will be determined in six months at contract maturity by comparing the prevailing 3-month LIBOR with 7%

Assume that in three months 3-month LIBOR equals 8% In this case, Metro Bank would receive from County Bank $2,451. The interest settlement amount is $2,500: Interest = ( )(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).08]=$2,451

If instead, LIBOR equals 5% in three months, Metro Bank would pay County Bank: The interest settlement amount is $5,000 Interest = ( )(90/360) $1,000,000 = $5,000 Actual interest = $5,000 /[1 + (90/360).05] = $4,938

The FRA position is similar to a futures position 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

The FRA position is similar to a futures position Metro Bank would take its position as a hedge if it was exposed to loss in a falling (relative to forward rate) rate environment. This is analogous to a long futures position

Basic Interest Rate Swaps
Basic or 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

Basic or 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

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

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

Firms with a negative GAP can reduce risk by making a fixed-rate interest payment in exchange for a floating-rate interest receipt Firms with a positive GAP take the opposite position, by making floating-interest payments in exchange for a fixed-rate receipt

Basic interest rate swaps are used to: Adjust the rate sensitivity of an asset or liability For example, effectively converting a fixed-rate loan into a floating-rate loan Create a synthetic security For example, enter into a swap instead of investing in a security Macrohedge Use swaps to hedge the bank’s aggregate interest rate risk

Swap Dealers Handle most swap transactions Make a market in swap contracts Offer terms for both fixed-rate and floating rate payers and earn a spread for their services

Comparing Financial Futures, FRAs, and Basic Swaps There is some credit risk with swaps in that the counterparty may default on the exchange of the interest payments Only the interest payment exchange is at risk, not the principal

Interest Rate Caps and Floors
An agreement between two counterparties that limits the buyer’s interest rate exposure to a maximum limit Buying a interest rate cap is the same as purchasing a call option on an interest rate

Buying a Cap on 3-Month LIBOR at 4 percent

Interest Rate Floor An agreement between two counterparties that limits the buyer’s interest rate exposure to a minimum rate Buying an interest rate floor is the same as purchasing a put option on an interest rate

Buying a Floor on 3-Month LIBOR at 4 percent

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 It protects a bank from rising interest rates

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 It protects a bank from falling interest rates

Pricing Interest Rate Caps and Floors
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

Pricing Interest Rate Caps and Floors

Managing Interest Rate Risk: GAP and Earnings Sensitivity

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Managing Interest Rate Risk: GAP and Earnings Sensitivity

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