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**Managing Interest Rate Risk: GAP and Earnings Sensitivity**

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**Managing 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

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**Managing 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

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**Managing 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

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**Managing 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

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**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

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**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?

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**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)

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**Measuring Interest Rate Risk with GAP**

Traditional Static Gap Analysis Steps in GAP Analysis Develop an interest rate forecast Select a series of “time buckets” or time 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

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**Measuring Interest Rate Risk with GAP**

What Determines Rate Sensitivity The initial issue is to determine what features make an asset or liability rate sensitive

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**Measuring Interest Rate Risk with GAP**

Expected Repricing versus Actual Repricing In general, an asset or liability is normally classified as rate sensitive within a time interval if: It matures It represents an interim or partial principal payment The interest rate applied to the outstanding principal balance changes contractually during the interval The interest rate applied to the outstanding principal balance changes when some base rate or index changes and management expects the base rate/index to change during the time interval

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**Measuring Interest Rate Risk with GAP**

What Determines Rate Sensitivity Maturity If any asset or liability matures within a time interval, the principal amount will be repriced The question is what principal amount is expected to reprice Interim or Partial Principal Payment Any principal payment on a loan is rate sensitive if management expects to receive it within the time interval Any interest received or paid is not included in the GAP calculation

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**Measuring Interest Rate Risk with GAP**

What Determines Rate Sensitivity Contractual Change in Rate Some assets and deposit liabilities earn or pay rates that vary contractually with some index These instruments are repriced whenever the index changes If management knows that the index will contractually change within 90 days, the underlying asset or liability is rate sensitive within 0–90 days.

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**Measuring Interest Rate Risk with GAP**

What Determines Rate Sensitivity Change in Base Rate or Index Some loans and deposits carry interest rates tied to indexes where the bank has no control or definite knowledge of when the index will change. For example, prime rate loans typically state that the bank can contractually change prime daily The loan is rate sensitive in the sense that its yield can change at any time However, the loan’s effective rate sensitivity depends on how frequently the prime rate actually changes

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Rate, Composition (Mix) and Volume Effects All affect net interest income

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Level of Interest Rates The sign of GAP (positive or negative) indicates the nature of the 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

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Level of Interest Rates The sign of GAP (positive or negative) indicates the nature of the 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

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Level of Interest Rates If a bank has a zero GAP, RSAs equal RSLs and equal interest rate changes do not alter net interest income because changes in interest income equal changes in interest expense It is virtually impossible for a bank to have a zero GAP given the complexity and size of bank balance sheets

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Level of Interest Rates GAP analysis assumes a parallel shift in the yield curve

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Level of Interest Rates If there is a parallel shift in the yield curve then changes in Net Interest Income are directly proportional to the size of the GAP: ∆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

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Level of Interest Rates Example 1 Recall the bank that makes a $25,000 five-year car loan to a customer at fixed rate of 8.5%. The bank initially funds the car loan with a one-year $25,000 CD at a cost of 4.5%. What is the bank’s 1-year GAP?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Level of Interest Rates Example 1 RSA1 YR = $0 RSL1 YR = $10,000 GAP1 YR = $0 - $25,000 = -$25,000 The bank’s one year funding GAP is -$25,000 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

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Level of Interest Rates Example 2 Assume a bank accepts an 18-month $30,000 CD deposit at a cost of 3.75% and invests the funds in a $30,000 6-month T-Bill at rate of 4.80%. The bank’s initial spread is 1.05%. What is the bank’s 6-month GAP?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Level of Interest Rates Example 2 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

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in the Relationship Between Asset Yields and Liability Costs Net interest income may differ from that expected if the spread between earning asset yields and the interest cost of interest-bearing liabilities changes The spread may change because of a nonparallel shift in the yield curve or because of a change in the difference between different interest rates (basis risk)

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in Volume Net interest income varies directly with changes in the volume of earning assets and interest-bearing liabilities, regardless of the level of interest rates For example, if a bank doubles in size but the portfolio composition and interest rates remain unchanged, net interest income will double because the bank earns the same interest spread on twice the volume of earning assets such that NIM is unchanged

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Changes in Portfolio Composition Any variation in portfolio mix potentially alters net interest income There is no fixed relationship between changes in portfolio mix and net interest income The impact varies with the relationships between interest rates on rate-sensitive and fixed-rate instruments and with the magnitude of funds shifts

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.0

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.0 Interest Income ($500 x 8%) + ($350 x 11%) = $78.50 Interest Expense ($600 x 4%) + ($220 x 6%) = $37.20 Net Interest Income $ $37.20 = $41.30

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.0 Earning Assets $500 + $350 = $850 Net Interest Margin $41.3/$850 = 4.86% Funding GAP $500 - $600 = -$100

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.1 What if all rates increase by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.1 What if all rates increase by 1%? With a negative GAP, interest income increases by less than the increase in interest expense. Thus, both NII and NIM fall.

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.2 What if all rates fall by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.2 What if all rates fall by 1%? With a negative GAP, interest income decreases by less than the decrease in interest expense. Thus, both NII and NIM increase.

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.3 What if rates rise but the spread falls by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.3 What if rates rise but the spread falls by 1%? Both NII and NIM fall with a decrease in the spread. Why the larger change? Note: ∆NIIEXP ≠ GAP x ∆iEXP Why?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.4 What if rates fall but the spread falls by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.4 What if rates fall and the spread falls by 1%? Both NII and NIM fall with a decrease in the spread. Note: ∆NIIEXP ≠ GAP x ∆iEXP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.5 What if rates rise and the spread rises by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.5 What if rates rise and the spread rises by 1%? Both NII and NIM increase with an increase in the spread. Note: ∆NIIEXP ≠ GAP x ∆iEXP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.6 What if rates fall and the spread rises by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.6 What if rates fall and the spread rises by 1%? Both NII and NIM increase with an increase in the spread. Note: ∆NIIEXP ≠ GAP x ∆iEXP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.7 What if the bank proportionately doubles in size?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 3.7 What if the bank proportionately doubles in size? Both NII doubles but NIM stays the same. Why? What has happened to the bank’s risk?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.0

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.0 Bank has a positive GAP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.1 What if rates increase by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.1 What if rates increase by 1%? With a positive GAP, interest income increases by more than the increase in interest expense. Thus, both NII and NIM rise.

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.2 What if rates decrease by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.2 What if rates decrease by 1%? With a positive GAP, interest income decreases by more than the decrease in interest expense. Thus, both NII and NIM fall.

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.3 What if rates rise but the spread falls by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.3 What if rates rise but the spread falls by 1%? Both NII and NIM fall with a decrease in the spread. Why the larger change? Note: ∆NIIEXP ≠ GAP x ∆iEXP Why?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.4 What if rates fall and the spread falls by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.4 What if rates fall and the spread falls by 1%? Both NII and NIM fall with a decrease in the spread. Note: ∆NIIEXP ≠ GAP x ∆iEXP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.5 What if rates rise and the spread rises by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.5 What if rates rise and the spread rises by 1%? Both NII and NIM increase with an increase in the spread. Note: ∆NIIEXP ≠ GAP x ∆iEXP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.6 What if rates fall and the spread rises by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.6 What if rates fall and the spread rises by 1%? Both NII and NIM increase with an increase in the spread. Note: ∆NIIEXP ≠ GAP x ∆iEXP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.7 What if the bank proportionately doubles in size?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 4.7 What if the bank proportionately doubles in size? Both NII doubles but NIM stays the same. Why? What has happened to the bank’s risk?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 5.0

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 5.0 Bank has zero GAP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 5.1 What if rates increase by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 5.1 What if rates increase by 1%? With a zero GAP, interest income increases by the amount as the increase in interest expense. Thus, there is no change in NII or NIM!

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 5.2 What if rates fall and the spread falls by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 5.2 What if rates fall and the spread falls by 1%? Even with a zero GAP, interest income falls by more than the decrease in interest expense. Thus, both NII and NIM fall with a decrease in the spread. Note: ∆NIIEXP ≠ GAP x ∆iEXP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 5.3 What if rates rise and the spread rises by 1%?

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Example 5.3 What if rates rise and the spread rises by 1%? Even with a zero GAP, interest income rises by more than the increase in interest expense. Thus, both NII and NIM increase with an increase in the spread. Note: ∆NIIEXP ≠ GAP x ∆iEXP

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**Measuring Interest Rate Risk with GAP**

Factors Affecting Net Interest Income Summary of Base Cases If a Negative GAP gives the largest NII and NIM, why not plan for a Negative GAP?

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**Measuring Interest Rate Risk with GAP**

Rate, Volume, and Mix Analysis Many financial institutions publish a summary in their annual report of how net interest income has changed over time They separate changes attributable to shifts in asset and liability composition and volume from changes associated with movements in interest rates

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**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

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**Measuring Interest Rate Risk with GAP**

Rate Sensitivity Reports Periodic GAP The Gap for each time bucket and measures the timing of potential income effects from interest rate changes

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**Measuring Interest Rate Risk with GAP**

Rate Sensitivity Reports Cumulative GAP The sum of periodic GAP's and measures aggregate interest rate risk over the entire period Cumulative GAP is important since it directly measures a bank’s net interest sensitivity throughout the time interval

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**Measuring Interest Rate Risk with GAP**

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

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**Measuring Interest Rate Risk with GAP**

Strengths and Weaknesses of Static GAP Analysis Weaknesses Ex-post measurement errors Ignores the time value of money Ignores the cumulative impact of interest rate changes Typically considers demand deposits to be non-rate sensitive Ignores embedded options in the bank’s assets and liabilities

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**Measuring Interest Rate Risk with GAP**

GAP Ratio GAP Ratio = RSAs/RSLs A GAP ratio greater than 1 indicates a positive GAP A GAP ratio less than 1 indicates a negative GAP

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**Measuring Interest Rate Risk with GAP**

GAP Divided by Earning Assets as a Measure of Risk An alternative risk measure that relates the absolute value of a 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

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**Earnings Sensitivity Analysis**

Allows management to incorporate the impact of different spreads between asset yields and liability interest costs when rates change by different amounts

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**Earnings Sensitivity Analysis**

Steps to Earnings Sensitivity Analysis Forecast interest rates. Forecast balance sheet size and composition given the assumed interest rate environment 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

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**Earnings Sensitivity Analysis**

Steps to Earnings Sensitivity Analysis Identify when specific assets and liabilities will reprice given the rate environment Estimate net interest income and net income under the assumed rate environment 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

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**Earnings Sensitivity Analysis**

The key benefits of conducting earnings sensitivity analysis are that managers can estimate the impact of rate changes on earnings while allowing for the following: Interest rates to follow any future path Different rates to change by different amounts at different times Expected changes in balance sheet mix and volume Embedded options to be exercised at different times and in different interest rate environments Effective GAPs to change when interest rates change Thus, a bank does not have a single static GAP, but instead will experience amounts of RSAs and RSLs that change when interest rates change

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**Earnings Sensitivity Analysis**

Exercise of Embedded Options in Assets and Liabilities The most common embedded options at banks include the following: Refinancing of loans Prepayment (even partial) of principal on loans Bonds being called Early withdrawal of deposits Caps on loan or deposit rates Floors on loan or deposit rates Call or put options on FHLB advances Exercise of loan commitments by borrowers

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**Earnings Sensitivity Analysis**

Exercise of Embedded Options in Assets and Liabilities The implications of embedded options Does the bank or the customer determine when the option is exercised? How and by what amount is the bank being compensated for selling the option, or how much must it pay to buy the option? When will the option be exercised? This is often determined by the economic and interest rate environment Static GAP analysis ignores these embedded options

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**Earnings Sensitivity Analysis**

Different Interest Rates Change by Different Amounts at Different Times It is well recognized that banks are quick to increase base loan rates but are slow to lower base loan rates when rates fall

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**Earnings Sensitivity Analysis**

Earnings Sensitivity: An Example Consider the rate sensitivity report for First Savings Bank (FSB) as of year-end 2008 that is presented on the next slide The report is based on the most likely interest rate scenario FSB is a $1 billion bank that bases its analysis on forecasts of the federal funds rate and ties other rates to this overnight rate As such, the federal funds rate serves as the bank’s benchmark interest rate

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**Earnings Sensitivity Analysis**

Explanation of Sensitivity Results This example demonstrates the importance of understanding the impact of exercising embedded options and the lags between the pricing of assets and liabilities. The framework uses the federal funds rate as the benchmark rate such that rate shocks indicate how much the funds rate changes Summary results are known as Earnings-at-Risk Simulation or Net Interest Income Simulation

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**Earnings Sensitivity Analysis**

Explanation of Sensitivity Results Earnings-at-Risk The potential variation in net interest income across different interest rate environments, given different assumptions about balance sheet composition, when embedded options will be exercised, and the timing of repricings.

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**Earnings Sensitivity Analysis**

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

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**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

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**Income Statement GAP Beta GAP**

The adjusted GAP figure in a basic earnings sensitivity analysis derived from multiplying the amount of rate-sensitive assets by the associated beta factors and summing across all rate-sensitive assets, and subtracting the amount of rate-sensitive liabilities multiplied by the associated beta factors summed across all rate-sensitive liabilities

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**Income Statement GAP Balance Sheet GAP Earnings Change Ratio (ECR)**

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

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**Managing the GAP and Earnings Sensitivity Risk**

Steps to reduce risk Calculate periodic GAPs over short time intervals Match fund repriceable assets with similar repriceable liabilities so that periodic GAPs approach zero Match fund long-term assets with non-interest-bearing liabilities Use off-balance sheet transactions to hedge

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**Managing the GAP and Earnings Sensitivity Risk**

How to Adjust the Effective GAP or Earnings Sensitivity Profile

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**Managing Interest Rate Risk: Economic Value of Equity**

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**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

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**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

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**Managing Interest Rate Risk: Economic Value of Equity**

GAP and Earnings Sensitivity versus Duration GAP and EVE Sensitivity

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**Managing Interest Rate Risk: Economic Value of Equity**

Recall from Chapter 6 Duration is a measure of the effective maturity of a security Duration incorporates the timing and size of a 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

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**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

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**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

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**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

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**Measuring Interest Rate Risk with Duration GAP**

Duration, Modified Duration, and 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:

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**Measuring Interest Rate Risk with Duration GAP**

Duration, Modified Duration, and Effective Duration Modified Duration Indicates how much the price of a security will change in percentage terms for a given change in interest rates Modified Duration = D/(1+i)

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**Measuring Interest Rate Risk with Duration GAP**

Duration, Modified Duration, and Effective Duration Example Assume that a ten-year zero coupon bond has a par value of $10,000, current price of $7,835.26, and a market rate of interest of 5%. What is the expected change in the bond’s price if interest rates fall by 25 basis points?

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**Measuring Interest Rate Risk with Duration GAP**

Duration, Modified Duration, and Effective Duration Example Since the bond is a zero-coupon bond, Macaulay’s Duration equals the time to maturity, 10 years. With a market rate of interest, the Modified Duration is 10/(1.05) = years. If rates change by 0.25% (.0025), the bond’s price will change by approximately × × $7, = $186.56

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**Measuring Interest Rate Risk with Duration GAP**

Duration, Modified Duration, and 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

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**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

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**Measuring Interest Rate Risk with Duration GAP**

Duration, Modified Duration, and Effective Duration Effective Duration Example Consider a 3-year, 9.4 percent semi-annual coupon bond selling for $10,000 par to yield 9.4 percent to maturity 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

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**Measuring Interest Rate Risk with Duration GAP**

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

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**Measuring Interest Rate Risk with Duration GAP**

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

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**Measuring Interest Rate Risk with Duration GAP**

Duration, Modified Duration, and Effective Duration Effective Duration Example

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**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

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**Measuring Interest Rate Risk with Duration GAP**

Duration GAP Model Steps in Duration GAP Analysis Forecast interest rates Estimate the market values of bank assets, liabilities and stockholders’ equity Estimate the weighted average duration of assets and the weighted average duration of liabilities Incorporate the effects of both on- and off-balance sheet items. These estimates are used to calculate duration gap Forecasts changes in the market value of stockholders’ equity across different interest rate environments

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**Measuring Interest Rate Risk with Duration GAP**

Duration GAP Model 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

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**Measuring Interest Rate Risk with Duration GAP**

Duration GAP Model 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

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**Measuring Interest Rate Risk with Duration GAP**

Duration GAP Model Let MVA and MVL equal the market values of assets and liabilities, respectively If ΔEVE = ΔMVA – ΔMVL and Duration GAP = DGAP = DA – (MVL/MVA)DL then ΔEVE = -DGAP[Δy/(1+y)]MVA where y is the interest rate

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**Measuring Interest Rate Risk with Duration GAP**

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

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**Measuring Interest Rate Risk with Duration GAP**

Duration GAP Model DGAP as a Measure of Risk The sign and size of DGAP provide information about whether rising or falling rates are beneficial or harmful and how much risk the bank is taking If DGAP is positive, an increase in rates will lower EVE, while a decrease in rates will increase EVE If DGAP is negative, an increase in rates will increase EVE, while a decrease in rates will lower EVE The closer DGAP is to zero, the smaller is the potential change in EVE for any change in rates

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**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks

129
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks Implications of DGAP The value of DGAP at 1.42 years indicates that the bank has a substantial mismatch in average durations of assets and liabilities Since the DGAP is positive, the market value of assets will change more than the market value of liabilities if all rates change by comparable amounts In this example, an increase in rates will cause a decrease in EVE, while a decrease in rates will cause an increase in EVE

130
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks Implications of DGAP > 0 A positive DGAP indicates that assets are more price sensitive than liabilities When interest rates rise (fall), assets will fall proportionately more (less) in value than liabilities and EVE will fall (rise) accordingly. Implications of DGAP < 0 A negative DGAP indicates that liabilities are more price sensitive than assets When interest rates rise (fall), assets will fall proportionately less (more) in value that liabilities and the EVE will rise (fall)

131
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks

132
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks Duration GAP Summary

133
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks DGAP As a Measure of Risk DGAP measures can be used to approximate the expected change in economic value of equity for a given change in interest rates

134
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks DGAP As a Measure of Risk In this case: The actual decrease, as shown in Exhibit 8.3, was $12

135
**Measuring Interest Rate Risk with Duration GAP**

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

136
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks

137
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks An Immunized Portfolio With a 1% increase in rates, the EVE did not change with the immunized portfolio versus $12.0 when the portfolio was not immunized

138
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks An Immunized Portfolio If DGAP > 0, reduce interest rate risk by: shortening asset durations Buy short-term securities and sell long-term securities Make floating-rate loans and sell fixed-rate loans lengthening liability durations Issue longer-term CDs Borrow via longer-term FHLB advances Obtain more core transactions accounts from stable sources

139
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks An Immunized Portfolio If DGAP < 0, reduce interest rate risk by: lengthening asset durations Sell short-term securities and buy long-term securities Sell floating-rate loans and make fixed-rate loans Buy securities without call options shortening liability durations Issue shorter-term CDs Borrow via shorter-term FHLB advances Use short-term purchased liability funding from federal funds and repurchase agreements

140
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks Banks may choose to target variables other than the market value of equity in managing interest rate risk Many banks are interested in stabilizing the book value of net interest income This can be done for a one-year time horizon, with the appropriate duration gap measure

141
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks DGAP* = MVRSA(1 − DRSA) − MVRSL(1 − DRSL) where MVRSA = cumulative market value of rate-sensitive assets (RSAs) MVRSL = cumulative market value of rate-sensitive liabilities (RSLs) DRSA = composite duration of RSAs for the given time horizon DRSL = composite duration of RSLs for the given time horizon

142
**Measuring Interest Rate Risk with Duration GAP**

A Duration Application for Banks DGAP* > 0 Net interest income will decrease (increase) when interest rates decrease (increase) DGAP* < 0 Net interest income will decrease (increase) when interest rates increase (decrease) DGAP* = 0 Interest rate risk eliminated A major point is that duration analysis can be used to stabilize a number of different variables reflecting bank performance

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
**Economic Value of Equity Sensitivity Analysis**

EVE Sensitivity Analysis: An Example First Savings Bank Duration Gap 2.6 – ($919,400,000/$1,001,963,000) × 2.0 = years Example: A 1% increase in rates would reduce EVE by $7.2 million ΔMVE = -DGAP[Δy/(1+y)]MVA ΔMVE = (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
**Economic Value of Equity Sensitivity Analysis**

EVE Sensitivity Analysis: An Example

149
**Economic Value of Equity Sensitivity Analysis**

EVE Sensitivity Analysis: An Example 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
**Economic Value of Equity Sensitivity Analysis**

EVE Sensitivity Analysis: An Example First Savings Bank Effective “Duration” of Equity Recall, duration measures the percentage change in market value for a given change in interest rates A 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
**A Critique of Strategies for Managing Earnings and EVE Sensitivity**

Interest Rate Risk: An Example Consider the case where a bank has two alternatives for funding $1,000 for two years A 2-year security yielding 6 percent Two consecutive 1-year securities, with the current 1-year yield equal to 5.5 percent It is not known today what a 1-year security will yield in one year

155
**A Critique of Strategies for Managing Earnings and EVE Sensitivity**

Interest Rate Risk: An Example Consider the case where a bank has two alternative for funding $1,000 for two years

156
**A Critique of Strategies for Managing Earnings and EVE Sensitivity**

Interest Rate Risk: An Example Consider the case where a bank has two alternative for funding $1,000 for two years For the two consecutive 1-year securities to generate the same $120 in interest, ignoring compounding, the 1-year security must yield 6.5% one year from the present This break-even rate is a 1-year forward rate of : 6% + 6% = 5.5% + x so x must = 6.5%

157
**A Critique of Strategies for Managing Earnings and EVE Sensitivity**

Interest Rate Risk: An Example Consider the case where a bank has two alternative for investing $1,000 for two years By investing in the 1-year security, a depositor is betting that the 1-year interest rate in one year will be greater than 6.5% By issuing the 2-year security, the bank is betting that the 1-year interest rate in one year will be greater than 6.5% By choosing one or the other, the depositor and the bank “place a bet” that the actual rate in one year will differ from the forward rate of 6.5 percent

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**

162
**Using Derivatives to Manage Interest Rate Risk**

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
**Characteristics of Financial Futures**

A Brief Example If 10-year Treasury rates actually fall sharply during the six months, the futures rate will similarly fall such that the futures price rises An increase in the futures price generates a profit on the futures trade You will eventually sell the futures contract to exit the trade

172
**Characteristics of Financial Futures**

A Brief Example You will eventually sell the futures contract to exit the trade Your effective yield will be determined by the prevailing 10-year Treasury rate and the gain (or loss) on the futures trade In this example, the decline in 10-year rates will be offset by profits on the long futures position

173
**Characteristics of Financial Futures**

A Brief Example The 10-year Treasury rate falls by 0.80%, which represents an opportunity loss However, buying a futures contract generates a 0.77% profit The effective yield on the investment equals the prevailing 3.70% rate at the time of investment plus the 0.77% futures profit, or 4.47%

174
**Characteristics of Financial Futures**

A Brief Example

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
**Characteristics of Financial Futures**

Types of Future Traders Speculator Takes a position with the objective of making a profit Tries to guess the direction that prices will move and time trades to sell (buy) at higher (lower) prices than the purchase price

177
**Characteristics of Financial Futures**

Types of Future Traders Scalper A speculator who tries to time price movements over very short time intervals and takes positions that remain outstanding for only minutes

178
**Characteristics of Financial Futures**

Types of Future Traders Day Trader Similar to a scalper but tries to profit from short-term price movements during the trading day; normally offsets the initial position before the market closes such that no position remains outstanding overnight

179
**Characteristics of Financial Futures**

Types of Future Traders Position Trader A speculator who holds a position for a longer period in anticipation of a more significant, longer-term market moves

180
**Characteristics of Financial Futures**

Types of Future Traders Hedger Has an existing or anticipated position in the cash market and trades futures contracts to reduce the risk associated with uncertain changes in the value of the cash position Takes a position in the futures market whose value varies in the opposite direction as the value of the cash position when rates change Risk is reduced because gains or losses on the futures position at least partially offset gains or losses on the cash position

181
**Characteristics of Financial Futures**

Types of Future Traders Hedger versus Speculator The essential difference between a speculator and hedger is the objective of the trader A speculator wants to profit on trades A hedger wants to reduce risk associated with a known or anticipated cash position

182
**Characteristics of Financial Futures**

Types of Future Traders Spreader versus Arbitrageur Both are speculators that take relatively low-risk positions Futures Spreader May simultaneously buy a futures contract and sell a related futures contract trying to profit on anticipated movements in the price difference The position is generally low risk because the prices of both contracts typically move in the same direction

183
**Characteristics of Financial Futures**

Types of Future Traders Arbitrageur Tries to profit by identifying the same asset that is being traded at two different prices in different markets at the same time Buys the asset at the lower price and simultaneously sells it at the higher price Arbitrage transactions are thus low risk and serve to bring prices back in line in the sense that the same asset should trade at the same price in all markets

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
**Characteristics of Financial Futures**

The Mechanics of Futures Trading Maintenance Margin The minimum deposit required at the end of each day Unlike margin accounts for stocks, futures margin deposits represent a guarantee that a trader will be able to make any mandatory payment obligations

186
**Characteristics of Financial Futures**

The Mechanics of Futures Trading Marking-to-Market The daily settlement process where at the end of every trading day, a 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
**Characteristics of Financial Futures**

The Mechanics of Futures Trading Expiration Date Every futures contract has a formal expiration date On the expiration date, trading stops and participants settle their final positions Less than 1% of financial futures contracts experience physical delivery at expiration because most traders offset their futures positions in advance

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
**Characteristics of Financial Futures**

An Example: 90-Day Eurodollar Time Deposit Futures Contracts trade according to an index: 100 – Futures Price = Futures Rate An index of 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
**Characteristics of Financial Futures**

An Example: 90-Day Eurodollar Time Deposit Futures Over forty separate contracts are traded at any point in time, as contracts expire in March, June, September and December each year Buyers make a profit when futures rates fall (prices rise) Sellers make a profit when futures rates rise (prices fall)

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
**Characteristics of Financial Futures**

An Example: 90-Day Eurodollar Time 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
**Characteristics of Financial Futures**

Daily Marking-To-Market Suppose that on June 13 the futures rate falls fro 3.02% to 2.92% The trader could withdraw $250 (10 basis points × $25) from the margin account, representing the increase in value of the position

200
**Characteristics of Financial Futures**

Daily Marking-To-Market 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
**Characteristics of Financial Futures**

Daily Marking-To-Market If the futures rate increases further to 3.23%, the trader must make a variation margin payment sufficient to bring the account up to $700 In this case, the account balance would have fallen to $575 and the margin contribution would equal $125 The exchange member may close the account if the trader does not meet the variation margin requirement

202
**Characteristics of Financial Futures**

Daily Marking-To-Market The Basis Basis = Cash Price – Futures Price or Basis = Futures Rate – Cash Rate It may be positive or negative, depending on whether futures rates are above or below spot rates May swing widely in value far in advance of contract expiration

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
**Speculation versus Hedging**

Hedgers Take Positions to Avoid or Reduce Risk A hedger already has a position in the cash market and uses futures to adjust the risk of being in the cash market The focus is on reducing or avoiding risk

206
**Speculation versus Hedging**

Hedgers Take Positions to Avoid or Reduce Risk Example A bank anticipates needing to borrow $1,000,000 in 60 days. The bank is concerned that rates will rise in the next 60 days A possible strategy would be to short Eurodollar futures. If interest rates rise (fall), the short futures position will increase (decrease) in value. This will (partially) offset the increase (decrease) in borrowing costs

208
**Speculation versus Hedging**

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

209
**Speculation versus Hedging**

Steps in Hedging 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

210
**Speculation versus Hedging**

A Long Hedge: Reduce Risk Associated With A Decrease In Interest Rates A long hedge (buy futures) is appropriate for a participant who wants to reduce spot market risk associated with a decline in interest rates If spot rates decline, futures rates will typically also decline so that the value of the futures position will likely increase. Any loss in the cash market is at least partially offset by a gain in futures

211
**Speculation versus Hedging**

A Long Hedge: Reduce Risk Associated With A Decrease In Interest Rates On June 6, 2008, your bank expects to receive a $1 million payment on November 28, 2008, and anticipates investing the funds in three-month Eurodollar time deposits The cash market risk exposure is that the bank would like to invest the funds at 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
**Speculation versus Hedging**

A Long Hedge: Reduce Risk Associated With A Decrease In Interest Rates In order to hedge, the bank should buy futures contracts The best futures contract will generally be the first contract that expires after the known cash transaction date. This contract is best because its futures price will generally show the highest correlation with the cash price In this example, the December 2008 Eurodollar futures contract is the first to expire after November 2008

213
**Speculation versus Hedging**

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

214
**Speculation versus Hedging**

215
**Speculation versus Hedging**

A Short Hedge: Reduce Risk Associated With A Increase In Interest Rates A short hedge (sell futures) is appropriate for a participant who wants to reduce spot market risk associated with an increase in interest rates If spot rates increase, futures rates will typically also increase so that the value of the futures position will likely decrease. Any loss in the cash market is at least partially offset by a gain in the futures market

216
**Speculation versus Hedging**

A Short Hedge: Reduce Risk Associated With A Increase In Interest Rates On June 6, 2008, your bank expects to sell a six-month $1 million Eurodollar deposit on August 17, 2008 The cash market risk exposure is that interest rates may rise and the value of the Eurodollar deposit will fall by August 2008 In order to hedge, the bank should sell futures contracts

217
**Speculation versus Hedging**

A Long Hedge: Reduce Risk Associated With A Decrease In Interest Rates In order to hedge, the bank should sell futures contracts In this example, the September 2008 Eurodollar futures contract is the first to expire after September 17, 2008

218
**Speculation versus Hedging**

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

219
**Speculation versus Hedging**

220
**Speculation versus Hedging**

Change in the Basis Long and short hedges work well if the futures rate moves in line with the spot rate The actual risk assumed by a trader in both hedges is that the basis might change between the time the hedge is initiated and closed

221
**Speculation versus Hedging**

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
**Speculation versus Hedging**

Change in the Basis Effective Return: Long Hedge = Initial Cash Rate – (B2 – B1) = 2.68% - (0.10% %) = 2.92% Effective Return: Short Hedge = 3.00% - (0.14% %) = 2.69%

223
**Speculation versus Hedging**

Basis Risk and Cross Hedging Cross Hedge Where a trader uses a futures contract based on one security that differs from the security being hedged in the cash market

224
**Speculation versus Hedging**

Basis Risk and Cross Hedging Cross Hedge Example Using Eurodollar futures to hedge changes in the commercial paper rate Basis risk increases with a cross hedge because the futures and spot interest rates may not move closely together

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
**Microhedging Applications**

Banks are generally restricted in their use of financial futures for hedging purposes Banks must recognize futures on a micro basis by linking each futures transaction with a specific cash instrument or commitment Some feel that such micro linkages force microhedges that may potentially increase a firm’s total risk because these hedges ignore all other portfolio components

227
**Microhedging Applications**

Creating a Synthetic Liability with a Short Hedge Example Assume that on June 6, 2008, a bank agreed to finance a $1 million six-month loan Management wanted to match fund the loan by issuing a $1 million, six-month Eurodollar time deposit The six-month cash Eurodollar rate was 3% The three-month Eurodollar rate was 2.68% The three-month Eurodollar futures rate for September 2008 expiration equaled 2.83%

228
**Microhedging Applications**

Creating a Synthetic Liability with a Short Hedge Rather than issue a direct six-month Eurodollar liability at 3%, the bank created a synthetic six-month liability by shorting futures The objective was to use the futures market to borrow at a lower rate than the six-month cash Eurodollar rate A short futures position would reduce the risk of rising interest rates for the second cash Eurodollar borrowing

229
**Microhedging Applications**

Creating a Synthetic Liability with a Short Hedge

231
**Microhedging Applications**

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

232
**Microhedging Applications**

The Mechanics of Applying a Microhedge 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

233
**Microhedging Applications**

The Mechanics of Applying a Microhedge Determine the Appropriate Time Frame for the Hedge Monitor Hedge Performance

234
**Macrohedging Applications**

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

235
**Macrohedging Applications**

Hedging: GAP or Earnings Sensitivity If a bank loses when interest rates fall (the bank has a positive GAP), it should use a long hedge If rates rise, the 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
**Macrohedging Applications**

Hedging: GAP or Earnings Sensitivity If a bank loses when interest rates rise (the bank has a negative GAP), it should use a short hedge If rates rise, the 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
**Macrohedging Applications**

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

238
**Macrohedging Applications**

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

239
**Macrohedging Applications**

Hedging: Duration GAP and EVE Sensitivity Example: With a positive duration gap, the EVE will decline if interest rates rise

240
**Macrohedging Applications**

Hedging: Duration GAP and EVE Sensitivity Example: The bank needs to sell interest rate futures contracts in order to hedge its risk position The short position indicates that the bank will make a profit if futures rates increase

241
**Macrohedging Applications**

Hedging: Duration GAP and EVE Sensitivity Example: If the bank uses a Eurodollar futures contract currently trading at 4.9% with a duration of 0.25 years, the target market value of futures contracts (MVF) is: MVF = $4,096.82, so the bank should sell four Eurodollar futures contracts

242
**Macrohedging Applications**

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**

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
**Using Forward Rate Agreements to Manage Rate Risk**

Forward Rate Agreements: An Example Assume that in three months 3-month LIBOR equals 6% In this case, Metro Bank would receive from County Bank $2,463 The interest settlement amount is $2,500: Interest = ( )(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 = ( )(90/360) $1,000,000 = $5,000 Actual interest = $5,000 /[1 + (90/360).03] = $4,963

251
**Using Forward Rate Agreements to Manage Rate Risk**

Forward Rate Agreements: An Example County Bank would pay fixed-rate/receive floating-rate as a hedge if it was exposed to loss in a rising rate environment This is analogous to a short futures position Metro Bank would sell fixed-rate/receive floating-rate as a hedge if it was exposed to loss in a falling rate environment. This is analogous to a long futures position

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 Interest Rate Swaps as a Risk Management Tool**

Characteristics Basic (Plain Vanilla) Interest Rate Swap One party makes payments based on a fixed interest rate and receives floating rate payments The other party exchanges floating rate payments for fixed-rate payments When interest rates change, the party that benefits from a swap receives a net cash payment while the party that loses makes a net cash payment

255
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Basic (Plain Vanilla) Interest Rate Swap Conceptually, a basic interest rate swap is a package of FRAs As with FRAs, swap payments are netted and the notional principal never changes hands

256
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Plain Vanilla Example Using data for a 2-year swap based on 3-month LIBOR as the floating rate This swap involves eight quarterly payments. Party FIX agrees to pay a fixed rate Party FLT agrees to receive a fixed rate with cash flows calculated against a $10 million notional principal amount

257
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Plan Vanilla Example

259
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Plain Vanilla Example If the three-month LIBOR for the first pricing interval equals 3% The fixed payment for Party FIX is $83,770 and the floating rate receipt is $67,744 Party FIX will have to pay the difference of $16,026 The floating-rate payment for Party FLT is $67,744 and the fixed-rate receipt is$83,520 Party FLT will receive the difference of $15,776 The dealer will net $250 from the spread ($16,026 -$15,776)

260
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Plain Vanilla Example At the second and subsequent pricing intervals, only the applicable LIBOR is unknown As LIBOR changes, the amount that both Party FIX and Party FLT either pay or receive will change Party FIX will only receive cash at any pricing interval if three-month LIBOR exceeds 3.36% Party FLT will similarly receive cash as long as three-month LIBOR is less than 3.35%

261
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Convert a Floating-Rate Liability to a Fixed Rate Liability Consider a bank that makes a $1 million, three-year fixed-rate loan with quarterly interest at 8% It finances the loan by issuing a three-month Eurodollar deposit priced at three-month LIBOR

262
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Convert a Floating-Rate Liability to a Fixed Rate Liability By itself, this transaction exhibits considerable interest rate The bank is liability sensitive and loses (gains) if LIBOR rises (falls) The bank can use a basic swap to microhedge this transaction Using the data from Exhibit 9.8, the bank could agree to pay 3.72% and receive three-month LIBOR against $1 million for the three years By doing this, the bank locks in a borrowing cost of 3.72% because it will both receive and pay LIBOR every quarter

263
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Convert a Floating-Rate Liability to a Fixed Rate Liability The use of the swap enables the bank to reduce risk and lock in a spread of 4.28 percent (8.00 percent − 3.72 percent) on this transaction while effectively fixing the borrowing cost at 3.72 percent for three years

264
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Convert a Fixed-Rate Asset to a Floating-Rate Asset Consider a bank that has a customer who demands a fixed-rate loan The bank has a policy of making only floating-rate loans because it is liability sensitive and will lose if interest rates rise Ideally, the bank wants to price the loan based on prime Now assume that the bank makes the same $1 million, three-year fixed-rate loan as in the “Convert a Floating-Rate Liability to a Fixed Rate Liability” example

265
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Convert a Fixed-Rate Asset to a Floating-Rate Asset The bank could enter into a swap, agreeing to pay a 3.7% fixed rate and receive prime minus 2.40% with quarterly payments This effectively converts the fixed-rate loan into a variable rate loan that floats with the prime rate

266
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Create a Synthetic Hedge Some view basic interest rate swaps as synthetic securities As such, they enter into a swap contract that essentially replicates the net cash flows from a balance sheet transaction Suppose a bank buys a three-year Treasury yielding 2.73%, which it finances by issuing a three-month deposit As an alternative, the bank could enter into a three-month swap agreeing to pay three-month LIBOR and receive a fixed rate

267
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Macrohedge Banks can also use interest rate swaps to hedge their aggregate risk exposure measured by earnings and EVE sensitivity A bank that is liability sensitive or has a positive duration gap will take a basic swap position that potentially produces profits when rates increase With a basic swap, this means paying a fixed rate and receiving a floating rate Any profits can be used to offset losses from lost net interest income or declining

268
**Basic Interest Rate Swaps as a Risk Management Tool**

Characteristics Macrohedge In terms of GAP analysis, a liability-sensitive bank has more rate-sensitive liabilities than rate-sensitive assets To hedge, the bank needs the equivalent of more RSAs A swap that pays fixed and receives floating is comparable to increasing RSAs relative to RSLs because the receipt reprices with rate changes

269
**Basic Interest Rate Swaps as a Risk Management Tool**

Pricing Basic Swaps The floating rate is based on some predetermined money market rate or index The payment frequency is coincidentally set at every six months, three months, or one month, and is generally matched with the money market rate The fixed rate is set at a spread above the comparable maturity fixed rate security

270
**Basic Interest Rate Swaps as a Risk Management Tool**

Comparing Financial Futures, FRAs and Basic Swaps Similarities Each enables a party to enter an agreement, which provides for cash receipts or cash payments depending on how interest rates move Each allows managers to alter a bank’s interest rate risk exposure None requires much of an initial cash commitment to take a position

271
**Basic Interest Rate Swaps as a Risk Management Tool**

Comparing Financial Futures, FRAs and Basic Swaps Differences Financial futures are standardized contracts based on fixed principal amounts while with FRAs and interest rate swaps, parties negotiate the notional principal amount Financial futures require daily marking-to-market, which is not required with FRAs and swaps Many futures contracts cannot be 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

272
**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

273
**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

275
**Interest Rate Caps and Floors**

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

277
**Interest Rate Caps and Floors**

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

278
**Interest Rate Caps and Floors**

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

279
**Interest Rate Caps and Floors**

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

280
**Interest Rate Caps and Floors**

281
**Interest Rate Caps and Floors**

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

282
**Interest Rate Caps and Floors**

Protecting Against Falling Interest Rates It is considering three alternative approaches to reduce risk associated with falling rates: Entering into a basic interest rate swap to pay three-month LIBOR and receive a fixed rate Buying an interest rate floor 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%

283
**Interest Rate Caps and Floors**

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

285
**Interest Rate Caps and Floors**

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

287
**Interest Rate Caps and Floors**

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

289
**Interest Rate Caps and Floors**

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

290
**Interest Rate Caps and Floors**

Protecting Against Rising Interest Rates It is considering three alternative approaches to reduce risk associated with rising rates: Entering into a basic interest rate swap to pay a fixed rate and receive the three-month LIBOR Buying an interest rate cap Buying a collar

291
**Interest Rate Caps and Floors**

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

293
**Interest Rate Caps and Floors**

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

295
**Interest Rate Caps and Floors**

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

297
**Using Derivatives to Manage Interest Rate Risk**

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