Managing Interest Rate Risk: GAP and Earnings Sensitivity

Managing Interest Rate Risk: GAP and Earnings Sensitivity

Managing Interest Rate Risk (I): GAP and Earnings Sensitivity Interest Rate Risk Interest Rate Risk The potential loss from unexpected changes in interest rates which can significantly alter a banks profitability and market value of equity. When a banks assets and liabilities do not reprice at the same time, the result is a change in net interest income. The change in the value of assets and the change in the value of liabilities will also differ, causing a change in the value of stockholders equity Banks typically focus on either: Net interest income or The market value of stockholders' equity The ALCO coordinates the banks strategies to achieve the optimal risk/reward trade-off. 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 Two Types of Interest Rate Risk Spread Risk (reinvestment/refinancing risk) Changes in interest rates will change the banks cost of funds as well as the return on their invested assets. They may change by different amounts. Static GAP Analysis considers the impact of changing rates on the banks net interest income. Price Risk Changes in interest rates may change the market values of the banks assets and liabilities by different amounts. Duration GAP considers the impact of changing rates on the market value of equity. 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: An Example Consider the following balance sheet: Expected Balance Sheet for Hypothetical Bank Assets Yield Liabilities Cost Rate sensitive $ 500 8.0% $ 600 4.0% Fixed rate $ 350 11.0% $ 220 6.0% Non earning $ 150 $ 100 $ 920 Equity

$ 80 Total $ 1,000 $ 1,000 NII = (0.08 x 500 + 0.11 x 350) - (0.04 x 600 + 0.06 x 220) NII = 78.5 - 37.2 = 41.3 NIM = 41.3 / 850 = 4.86% GAP = 500 - 600 = -100 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 shortterm asset yields and liability costs A proportionate doubling in size of the bank? 1% increase in short-term rates Expected Balance Sheet for Hypothetical Bank Assets Yield Liabilities Cost Rate sensitive $ 500 9.0% $ 600 5.0% Fixed rate $ 350 11.0% $ 220 6.0% Non earning $ 150 $ 100 $

920 Equity $ 80 Total $ 1,000 $ 1,000 NII = (0.09 x 500 + 0.11 x 350) - (0.05 x 600 + 0.06 x 220) NII = 83.5 - 43.2 = 40.3 NIM = 40.3 / 850 = 4.74% With a negative GAP, more GAP = 500 - 600 = -100 liabilities than assets reprice higher; hence NII and NIM fall 1% decrease in the spread Expected Balance Assets Rate sensitive $ 500 Fixed rate $ 350 Non earning $ 150 Total $ 1,000 Sheet for Hypothetical Bank Yield Liabilities Cost 8.5% $ 600 5.5% 11.0% $ 220

6.0% $ 100 $ 920 Equity $ 80 $ 1,000 NII = (0.085 x 500 + 0.11 x 350) - (0.055 x 600 + 0.06 x 220) NII = 81 - 46.2 = 34.8 NII and NIM fall (rise) with a NIM = 34.8 / 850 = 4.09% decrease (increase) in the GAP = 500 - 600 = -100 spread. Why the larger change? Proportionate doubling in size Expected Balance Assets Rate sensitive $ 1,000 Fixed rate $ 700 Non earning $ 300 Total $ 2,000 Sheet for Hypothetical Bank Yield Liabilities Cost 8.0% $ 1,200 4.0% 11.0%

$ 440 6.0% $ 200 $ 1,840 Equity $ 160 $ 2,000 NII = (0.08 x 1000 + 0.11 x 700) - (0.04 x 1200 + 0.06 x 440) NII = 157 - 74.4 = 82.6 NIM = 82.6 / 1700 = 4.86% NII and GAP double, but GAP = 1000 - 1200 = -200 stays the same. NIM What has happened to risk? RSAs increase to $540 while fixed-rate assets decrease to $310 and RSLs decrease to $560 while fixed-rate liabilities increase to $260 Expected Balance Sheet for Hypothetical Bank Assets Yield Liabilities Cost Rate sensitive $ 540 8.0% $ 560 4.0% Fixed rate $ 310 11.0% $ 260 6.0% Non earning $ 150 $ 100

$ 920 Equity $ 80 Total $ 1,000 $ 1,000 NII = (0.08 x 540 + 0.11 x 310) - (0.04 x 560 + 0.06 x 260) NII = 77.3 - 38 = 39.3 Although the banks GAP NIM = 39.3 / 850 = 4.62% (and hence risk) is lower, GAP = 540 - 560 = -20 NII is also lower. Changes in Net Interest Income are directly proportional to the size of the GAP If there is a parallel shift in the yield curve: NIINIIexp GAP 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. Summary of GAP and the Change in NII GAP Summary Change in Interest Income Increase >

Decrease > Positive Positive Change in Interest Income Increase Decrease Negative Negative Increase Decrease Increase Decrease < < Increase Decrease Decrease Increase Zero Zero Increase Decrease Increase Decrease = =

Increase Decrease None None GAP Change in Interest Expense Increase Decrease Change in Net Interest Income Increase Decrease 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 earned on: Taxable loans, net Tax-exempt loans, net Taxable investment securities Tax-exempt investment securities Interest earning deposits with banks Federal funds sold and securities purchased under resale agreements Mortgage loans held for sale Total interest income Interest paid on: Interest bearing demand deposits Money market accounts Savings deposits Time deposits Federal funds purchased and securities sold under repurchase agreements Other borrowed funds Total interest expense Net interest income 2008 Compared to 2007 2007 Compared to 2006 Change Due to * Change Due to * Volume Yield/Rate Net Change Volume Yield/Rate Net Change $ 149,423 (117,147) 32,276 161,222 36,390 197,612 1,373 (586) 787 1,108 (450) 658 (5,313) (916) (6,229)

4,507 2,570 7,077 2,548 74 2,622 2,026 (206) 1,820 223 (176) 47 28 48 76 406 (1,745) (1,339) 7,801 156,461 (1,680) (122,176) 6,121 34,285 6,074 21,380 (369) 32,015 (12,517) (36,244) (3,307) (22,545) (6,165)

21,318 74,253 82,208 1,447 1,410 2,857 (113) 170,225 549 40,311 436 210,536 (6,443) (14,864) (3,676) 9,470 1,537 4,654 (660) 38,824 5,433 13,888 (67) 32,812 6,970 18,542 (727) 71,636 (29,744)

(35,909) 23,148 15,870 39,018 (4,272) (108,629) (13,547) 17,046 (34,376) 68,661 21,960 89,463 80,762 3,361 71,297 (30,986) 25,321 160,760 49,776 Interest Rate-Sensitivity Reports Classifies a banks 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 banks net interest sensitivity throughout the time interval. Measuring Interest Rate Risk with GAP 1-7 Days Assets U.S. Treas & ag MM Inv Municipals FF & Repo's Comm loans Install loans Cash Other assets Total Assets 5.0 1.0 0.3 6.3 Liabilities and Equity MMDA Super NOW 2.2 CD's < 100,000 0.9 CD's > 100,000 1.9 FF purchased NOW Savings DD Other liabilities Equity Total Liab & Eq. 5.0

Periodic GAP Cumulative GAP 1.3 1.3 8-30 Days 31-90 Days 0.7 3.6 1.2 0.7 1.2 1.8 1.0 0.3 3.7 2.2 7.6 2.9 1.6 4.7 1.3 4.6 1.9 15.5 8.2

10.0 10.0 13.8 0.5 15.0 5.0 12.3 2.0 4.0 5.1 12.9 91-180 181-365 Over Not Rate Days Days 1 year Sensitive 6.9 7.9 9.0 1.8 1.2 9.6 35.0 9.0 5.7 14.7 9.5 3.0

11.5 5.0 42.5 13.8 9.0 5.7 100.0 13.5 1.0 7.0 21.5 17.3 2.2 19.6 27.9 9.6 1.9 13.5 1.0 7.0 100.0 2.9 1.9 11.0 30.3 24.4 3.0 4.8 4.0 5.3

-20.3 -15.0 -14.4 -29.4 6.0 -23.4 30.2 6.8 Total Advantages and Disadvantages of Static GAP Analysis Advantages 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 nonrate sensitive Ignores embedded options in the banks assets and liabilities Link Between GAP and Net Interest Margin Many banks will specify a target GAP to earning asset ratio in the ALCO policy statements Target Gap

(Allowable % Change in NIM)(Expected NIM) Earning assets Expected % change in interest rates 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%. If management expects interest rates to vary up to 4 percent during the upcoming year, the banks 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 Managements 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. 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 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. Earnings Sensitivity Analysis (Base Case) Example Assets Total 3 Months >3-6 >6-12 or Less Months Months >1-3 Years >3-5 Years >5-10 Years >10-20 Years >20 Years Loans Prime Based Equity Credit Lines Fixed Rate >1 yr Var Rate Mtg I Yr 30-Yr Fix Mortgage

Consumer Credit Card Investments Eurodollars CMOs FixRate US Treasury Fed Funds Sold Cash & Due From Banks Loan Loss Reserve Non-earning Assets Total Assets 100,000 25,000 170,000 55,000 250,000 100,000 25,000 100,000 25,000 18,000 13,750 5,127 6,000 3,000 80,000 35,000 75,000 25,000 80,000 2,871 15,000 -15,000 60,000 1,000,000

18,000 13,750 5,129 6,000 3,000 36,000 27,500 9,329 12,000 6,000 96,000 2,000 32,792 48,000 13,000 28,916 116,789 28,000 2,872 5,000 5,224 5,000 13,790 25,000 5,284 40,000 51,918 4,959 25,000

278,748 53,751 101,053 228,582 104,200 121,748 51,918 15,000 -15,000 60,000 60,000 Earnings Sensitivity Analysis (Base Case) Example Liabilities and GAP Measures Total 3 Months >3-6 >6-12 or Less Months Months >1-3 Years >3-5 Years >5-10 Years >10-20 Years >20 Years Deposits MMDAs Retail CDs Savings NOW DDA Personal

Comm'l DDA 240,000 400,000 35,000 40,000 55,000 60,000 240,000 60,000 25,000 50,000 25,000 60,000 90,000 160,000 30,000 35,000 40,000 55,000 36,000 24,000 Borrowings TT&L L-T notes FR Fed Funds Purch NIR Liabilities Capital Tot Liab & Equity Swaps- Pay Fixed GAP CUMULATIVE GAP 30,000

65,000 1,000,000 50,000 0 349,000 60,000 90,000 160,000 50,000 -20,252 -6,249 11,053 -20,252 -26,501 -15,448 30,000 50,000 0 30,000 65,000 261,000 -25,000 -25,000 43,582 28,134 49,200 71,748 51,918 -201,000 77,334 149,082 201,000 0 Interest Rate Forecasts Fed Funds Forecast vs. Implied Forward Rates 4.50 Market Implied Rates 4.25

4.00 Most LikelyForecast 3.75 3.50 3.25 3.00 1 3 5 7 9 11 13 15 17 19 21 23 Time (month) Most LikelyForecast and Rate Ramps Dec. 2005 6 5 4 3 2 0 11 1 3 5 7 9 11 1 3 5 7 9 12 2006 2007 .5 Sensitivity of Earnings: Year One Change in NII ($MM) 2 (.5) (1.0) (1.5) ALCO Guideline Board Limit (2.0) (2.5) (3.0)

(3.5) - 300 1.0 .5 Change in NII ($MM) Earnings sensitivity over one and two years versus most likely rate scenario 1.0 -200 -100 ML +100 +200 Ramped Change in Rates from Most Likely (Basis Point) +300 Sensitivity of Earnings: Year Two 2 (.5) (1.0) (1.5) ALCO Guideline Board Limit (2.0) (2.5) (3.0) - 300 -200 -100 ML +100

+200 Ramped Change in Rates from Most Likely (Basis Points) +300 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 Banks 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.

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