Managing Interest Rate Risk: Duration GAP And Economic .
Managing Interest Rate Risk(II):Duration GAP and Economic Valueof Equity
Measuring Interest Rate Risk with DurationGAP Economic Value of Equity Analysis Focuseson changes in stockholders’equity given potential changes ininterest rates Duration GAP Analysis Comparesthe price sensitivity of abank’s total assets with the pricesensitivity of its total liabilities toassess the impact of potential changesin interest rates on stockholders’equity.
Duration GAP Duration GAP Model Focuses on either managing the market value ofstockholders’ equity The bank can protect EITHER the market value ofequity or net interest income, but not both Duration GAP analysis emphasizes the impact onequityCompares the duration of a bank’s assets with theduration of the bank’s liabilities and examines how theeconomic value stockholders’ equity will change wheninterest rates change.
Steps in Duration GAP Analysis Forecast interest rates. Estimate the market values of bank assets,liabilities and stockholders’ equity. Estimate the weighted average duration ofassets and the weighted average duration ofliabilities. Incorporate the effects of both on- and offbalance sheet items. These estimates areused to calculate duration gap. Forecasts changes in the market value ofstockholders’ equity across differentinterest rate environments.
Weighted Average Duration of Bank Assets Weighted Average Duration of BankAssets (DA)nDA w iDai Whereiwi Market value of asset i divided bythe market value of all bank assets Dai Macaulay’s duration of asset i n number of different bank assets
Weighted Average Duration of Bank Liabilities Weighted Average Duration of BankLiabilities (DL)mDL z jDlj Wherejzj Market value of liability j divided bythe market value of all bank liabilities Dlj Macaulay’s duration of liability j m number of different bank liabilities
Duration GAP and Economic Value of Equity Let MVA and MVL equal the market values ofassets and liabilities, respectively.ΔEVE ΔMVA ΔMVL If:andDuration GAPDGAP DA - (MVL/MVA)D L Then: y ΔEVE - DGAP MVA (1 y) where y the general level of interestrates To protect the economic value of equityagainst any change when rates change , thebank could set the duration gap to zero:
Hypothetical Bank Balance Sheet1Par 1,000 % CoupYearsMat.AssetsCashEarning assets3-yr Commercial loan6-yr Treasury bond84 1Total Earning AssetsNon-cash earning assets(1.12)1Total assets D 700 12.00%3 2008.00%684 284 3 900 2 (1.12) (1.12)3 1,000LiabilitiesInterest bearing liabs.1-yr Time deposit3-yr Certificate of depositTot. Int Bearing Liabs.Tot. non-int. bearingTotal liabilitiesTotal equityTotal liabs & equity 620 300 920 920 80 1,000 100YTMMarketValue Dur.10012.00% 7008.00% 200700 3 90011.11% (1.12)3 10.00% 1,0002.694.995.00% 6207.00% 3005.65% 920 5.65% 920 80 1,0001.002.812.887005.00%7.00%131.59
Calculating DGAP DA ( 700/ 1000)*2.69 ( 200/ 1000)*4.99 2.88 DL ( 620/ 920)*1.00 ( 300/ 920)*2.81 1.59 DGAP 2.88 - (920/1000)*1.59 1.42 years What does this tell us? The average duration of assets is greater than theaverage duration of liabilities; thus asset valueschange by more than liability values.
1 percent increase in all rates.1Par 1,000 % CoupYearsMat.YTMMarketValueAssetsCash 100 Earning assets3-yr Commercial loan 700 12.00%313.00% 6-yr Treasury bond 2008.00%69.00% Total Earning Assets 90012.13% 384700 Non-cash earning assets PV tt 1Total assets 1,00010.88%3 1.131.13 LiabilitiesInterest bearing liabs.1-yr Time deposit3-yr Certificate of depositTot. Int Bearing Liabs.Tot. non-int. bearingTotal liabilitiesTotal equityTotal liabs & equity 620 300 920 920 80 1,0005.00%7.00%136.00% 8.00% 6.64% 6.64% 812.861.58
Calculating DGAP DA ( 683/ 974)*2.68 ( 191/ 974)*4.97 2.86 DA ( 614/ 906)*1.00 ( 292/ 906)*2.80 1.58 DGAP 2.86 - ( 906/ 974) * 1.58 1.36 years What does 1.36 mean? The average duration of assets is greater than theaverage duration of liabilities, thus asset valueschange by more than liability values.
Change in the Market Value of Equity yΔEVE - DGAP[]MVA(1 y) In this case:.01ΔEVE - 1.42[] 1,000 12.911.10
Positive and Negative Duration GAPs Positive DGAP Indicates that assets are more price sensitivethan liabilities, on average. Thus, when interest rates rise (fall), assets willfall proportionately more (less) in value thanliabilities and EVE will fall (rise) accordingly. Negative DGAP Indicates that weighted liabilities are moreprice sensitive than weighted assets. Thus, when interest rates rise (fall), assets willfall proportionately less (more) in value thatliabilities and the EVE will rise (fall).
DGAP SummaryDGAP SummaryPositivePositiveChange inInterestRatesIncreaseDecreaseDecrease Decrease DecreaseIncrease Increase IncreaseNegativeNegativeIncreaseDecreaseDecrease Decrease IncreaseIncrease Increase DecreaseZeroZeroIncreaseDecreaseDecrease Decrease Increase Increase DGAPAssetsLiabilitiesEquityNoneNone
An Immunized Portfolio To immunize the EVE from ratechanges in the example, the bankwould need to: decreasethe asset duration by 1.42years or increase the duration of liabilities by1.54 years DA / ( MVA/MVL) 1.42 / ( 920 / 1,000) 1.54 years
Immunized Portfolio1ParYears 1,000 % Coup Mat.AssetsCash 100Earning assets3-yr Commercial loan 7006-yr Treasury bond 200Total Earning Assets 900Non-cash earning assets Total assets 1,000LiabilitiesInterest bearing liabs.1-yr Time deposit 3403-yr Certificate of deposit 3006-yr Zero-coupon CD* 444Tot. Int Bearing Liabs. 1,084Tot. non-int. bearing Total liabilities 1,084Total equity 80YTMMarketValue 12.00%8.00%5.00%7.00%0.00%3613610012.00% 7008.00% 20011.11% 900 10.00% 1,0005.00%7.00%8.00%6.57% 6.57% DGAP 2.88 – 0.92 (3.11) 0Dur.340300280920920802.694.992.881.002.816.003.11
Immunized Portfolio with a 1% increase in rates1Par 1,000AssetsCash 100.0Earning assets3-yr Commercial loan 700.06-yr Treasury bond 200.0Total Earning Assets 900.0Non-cash earning assets Total assets 1,000.0LiabilitiesInterest bearing liabs.1-yr Time deposit 340.03-yr Certificate of deposit 300.06-yr Zero-coupon CD* 444.3Tot. Int Bearing Liabs. 1,084.3Tot. non-int. bearing Total liabilities 1,084.3Total equity 80.0Years% Coup Mat.YTMMarketValueDur. 100.012.00%8.00%5.00%7.00%0.00%3613613.00% 683.59.00% 191.012.13% 874.5 10.88% 974.56.00%8.00%9.00%7.54% 336.8 292.3 264.9 894.0 7.54% 894.0 80.52.694.972.861.002.816.003.07
Immunized Portfolio with a 1% increase in rates EVE changed by only 0.5 with theimmunized portfolio versus 25.0when the portfolio was not immunized.
Economic Value of Equity Sensitivity Analysis Effectively involves the same steps asearnings sensitivity analysis. In EVE analysis, however, the bankfocuses on: Therelative durations of assets andliabilities How much the durations change indifferent interest rate environments What happens to the economic value ofequity across different rate environments
Embedded Options Embedded options sharply influence theestimated volatility in EVE Prepaymentsthat exceed (fall short of)that expected will shorten (lengthen)duration. A bond being called will shorten duration. A deposit that is withdrawn early willshorten duration. A deposit that is not withdrawn asexpected will lengthen duration.
AssetsFirst Savings Bank Economic Value of EquityMarket Value/Duration Report as of 12/31/04Most Likely Rate Scenario-Base StrategyBook ValueMarket Value Book Yield Duration* 100,000 25,000 170,000 55,000 250,000 100,000 25,000 725,000 (15,000) 710,000 e Based LnEquity Credit LinesFixed Rate I yrVar Rate Mtg 1 Yr30-Year MortgageConsumer LnCredit CardTotal LoansLoan Loss ReserveNet LoansInvestmentsEurodollarsCMO Fix RateUS TreasuryTotal Investments 80,000 35,000 75,000 190,000 01.81.1Fed Funds SoldCash & Due FromNon-int Rel AssetsTotal Assets 25,000 15,000 60,000 100,000 02.6
First Savings Bank Economic Value of EquityLiabilitiesMarket Value/Duration Report as of 12/31/04Most Likely Rate Scenario-Base StrategyBook ValueMarket Value Book Yield Duration*MMDARetail CDsSavingsNOWDDA PersonalComm'l DDATotal DepositsTT&LL-T Notes FixedFed Funds PurchNIR LiabilitiesTotal Liabilities 050,25028,500919,400EquityTotal Liab & Equity 65,000 1,000,000 82,5631,001,963Deposits Off Balance Sheetlnt Rate SwapsAdjusted Equity 050,00030,000935,000- 1,25065,000 8.04.81.65.98.02.09.92.66.00%Notional2.8 50,0007.9
Duration Gap for First Savings Bank EVE Market Value of Assets 1,001,963 Duration of Assets 2.6years Market Value of Liabilities 919,400 Duration of Liabilities 2.0years
Duration Gap for First Savings Bank EVE Duration Gap2.6 – ( 919,400/ 1,001,963)*2.0 0.765 years Example: A1% increase in rates would reduceEVE by 7.2 million 0.765 (0.01 / 1.0693) * 1,001,963 Recall that the average rate on assetsis 6.93%
Effective “Duration” of Equity By definition, duration measures thepercentage change in market value fora given change in interest rates Thus,a bank’s duration of equitymeasures the percentage change inEVE that will occur with a 1 percentchange in rates: Effective duration of equity9.9 yrs. 8,200 / 82,563
Asset/Liability Sensitivity and DGAP Funding GAP and Duration GAP are NOTdirectly comparable FundingGAP examines various “timebuckets” while Duration GAP representsthe entire balance sheet. Generally, if a bank is liability (asset)sensitive in the sense that net interestincome falls (rises) when rates rise andvice versa, it will likely have a positive(negative) DGAP suggesting that assetsare more price sensitive than liabilities, onaverage.
Strengths and Weaknesses: DGAP and EVESensitivity Analysis Strengths Duration analysis provides acomprehensive measure of interest raterisk Duration measures are additive This allows for the matching of totalassets with total liabilities rather than thematching of individual accounts Duration analysis takes a longer termview than static gap analysis
Strengths and Weaknesses: DGAP and EVESensitivity Analysis Weaknesses It is difficult to compute durationaccurately “Correct” duration analysis requires thateach future cash flow be discounted by adistinct discount rate A bank must continuously monitor andadjust the duration of its portfolio It is difficult to estimate the duration onassets and liabilities that do not earn orpay interest Duration measures are highly subjective
Speculating on Duration GAP It is difficult to actively vary GAP orDGAP and consistently win Interestrates forecasts are frequentlywrong Even if rates change as predicted,banks have limited flexibility in varyGAP and DGAP and must oftensacrifice yield to do so
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. Incorpor
interest rate. An interest rate future is actively used to hedge against future interest rate movement, i.e., so-called interest rate market risk. Due to the varying feature of the underlying interest rates, the way to calculate the price and to quote the interest rate future varies a lot.
changes on the exchange rate. However, changes on exchange rate cause changes in the local interest rate while changes on the foreign interest rates do not cause changes in the local interest rate. In addition, changes on both the exchange rate and foreign interest rate jointly do cause changes on the local interest rate. Finally changes on
while, the difference between the ex ante real interest rate—the nominal interest rate minus expected infla-tion—and the equilibrium real interest rate is defined as the real interest rate gap. In the new Keynesian model, the real interest rate (RIR hereafter) gap is central to the determination of output and inflation.
3 A Functional Time Series Approach 16 . interest rate at which payments are made based on a notional amount. The price of an interest rate derivative depends on the level of the interest rate and its expected change in the future. To price an interest rate derivative, a common approach is to de ne the future evolution of the interest rates .
Interest rate (§ 230.2(o)) An interest rate is the annual rate of interest paid on an account and does not reflect compounding. For purposes of the account disclosures in section 230.4(b)(1)(i), the interest rate may, but need not, be referred to as the "annual percentage rate" in addition to being referred to as the "interest rate."
Lecture Notes: Interest Rate Theory Foreword Goals I Basic concepts of stochastic modeling in interest rate theory. I "No arbitrage"as concept and through examples. I Concepts of interest rate theory like yield, forward rate curve, short rate. I Spot measure, forward measures, swap measures and Black's formula. I Short rate models I A ne LIBOR models I Fundamentals of the SABR model
Stable NIM and Interest Rate Exposure of US Banks Juliane Begenau and Erik Stafford* . Bond prices fall as a consequence of unexpected increases in interest rates. In virtually all asset pricing contexts, duration risk is considered an important component of interest rate risk. Even though the cash flows on the existing bonds are not impacted .
bachelor’s degree in Mechanical Engineering from Cooper Union School of Engineering in New York. He is the author of more than 100 books in engineering and related fields. CIVIL ENGINEERING FORMULAS Tyler G. Hicks, P.E. International Engineering Associates Member: American Society of Mechanical Engineers United States Naval Institute Second Edition New York Chicago San Francisco Lisbon .
