Prof. Dr. Rainer Stachuletz Banking Academy of Vietnam
Published byModified over 6 years ago
Presentation on theme: "Prof. Dr. Rainer Stachuletz Banking Academy of Vietnam"— Presentation transcript:
1 Prof. Dr. Rainer Stachuletz Banking Academy of Vietnam Based upon: Bank Management, 6th edition. Timothy W. Koch and S. Scott MacDonaldManaging Interest Rate Risk: Duration GAP and Economic Value of EquityChapter 6Prof. Dr. Rainer Stachuletz – Banking Academy of Vietnam - Hanoi
2 Measuring Interest Rate Risk with Duration GAP Economic Value of Equity AnalysisFocuses on changes in stockholders’ equity given potential changes in interest ratesDuration GAP AnalysisCompares 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.
3 Recall from Chapter 4Duration 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.
4 Duration and Price Volatility Duration as an Elasticity MeasureDuration versus MaturityConsider the cash flows for these two securities over the following time line
5 Duration versus Maturity The maturity of both is 20 yearsMaturity does not account for the differences in timing of the cash flowsWhat is the effective maturity of both?The effective maturity of the first security is:(1,000/1,000) x 1 = 20 yearsThe effective maturity of the second security is:[(900/1,000) x 1]+[(100/1,000) x 20] = 2.9 yearsDuration is similar, however, it uses a weighted average of the present values of the cash flows
6 Duration versus Maturity Duration is an approximate measure of the price elasticity of demand
7 Duration versus Maturity The longer the duration, the larger the change in price for a given change in interest rates.
8 Measuring DurationDuration is a weighted average of the time until the expected cash flows from a security will be received, relative to the security’s priceMacaulay’s Duration
9 Measuring Duration Example What is the duration of a bond with a $1,000 face value, 10% annual coupon payments, 3 years to maturity and a 12% YTM? The bond’s price is $
10 Measuring Duration Example What is the duration of a bond with a $1,000 face value, 10% coupon, 3 years to maturity but the YTM is 5%?The bond’s price is $1,
11 Measuring Duration Example What is the duration of a bond with a $1,000 face value, 10% coupon, 3 years to maturity but the YTM is 20%?The bond’s price is $
12 Measuring Duration Example What is the duration of a zero coupon bond with a $1,000 face value, 3 years to maturity but the YTM is 12%?By definition, the duration of a zero coupon bond is equal to its maturity
13 Duration and Modified Duration The greater the duration, the greater the price sensitivityModified Duration gives an estimate of price volatility:
14 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.
15 Effective Duration Where: Pi- = Price if rates fall Pi+ = Price if rates riseP0 = Initial (current) pricei+ = Initial market rate plus the increase in ratei- = Initial market rate minus the decrease in rate
16 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.
17 Effective Duration Example Assume, instead, that the bond is callable at par in the near-term .If rates fall, the price will not rise much above the par value since it will likely be calledIf rates rise, the bond is unlikely to be called and the price will fall
18 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
19 Duration GAP Duration GAP Model Focuses on either managing the market value of stockholders’ equityThe bank can protect EITHER the market value of equity or net interest income, but not bothDuration GAP analysis emphasizes the impact on equity
20 Duration GAP Duration GAP Analysis Compares the duration of a bank’s assets with the duration of the bank’s liabilities and examines how the economic value stockholders’ equity will change when interest rates change.
21 Two Types of Interest Rate Risk Reinvestment Rate RiskChanges in interest rates will change the bank’s cost of funds as well as the return on invested assetsPrice RiskChanges in interest rates will change the market values of the bank’s assets and liabilities
22 Reinvestment Rate Risk If interest rates change, the bank will have to reinvest the cash flows from assets or refinance rolled-over liabilities at a different interest rate in the futureAn increase in rates increases a bank’s return on assets but also increases the bank’s cost of funds
23 Price RiskIf interest rates change, the value of assets and liabilities also change.The longer the duration, the larger the change in value for a given change in interest ratesDuration GAP considers the impact of changing rates on the market value of equity
24 Reinvestment Rate Risk and Price Risk If interest rates rise (fall), the yield from the reinvestment of the cash flows rises (falls) and the holding period return (HPR) increases (decreases).Price riskIf interest rates rise (fall), the price falls (rises). Thus, if you sell the security prior to maturity, the HPR falls (rises).
25 Reinvestment Rate Risk and Price Risk Increases in interest rates will increase the HPR from a higher reinvestment rate but reduce the HPR from capital losses if the security is sold prior to maturity.Decreases in interest rates will decrease the HPR from a lower reinvestment rate but increase the HPR from capital gains if the security is sold prior to maturity.
26 Reinvestment Rate Risk and Price Risk An immunized security or portfolio is one in which the gain from the higher reinvestment rate is just offset by the capital loss.For an individual security, immunization occurs when an investor’s holding period equals the duration of the security.
27 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.
28 Weighted Average Duration of Bank Assets Weighted Average Duration of Bank Assets (DA)Wherewi = Market value of asset i divided by the market value of all bank assetsDai = Macaulay’s duration of asset in = number of different bank assets
29 Weighted Average Duration of Bank Liabilities Weighted Average Duration of Bank Liabilities (DL)Wherezj = Market value of liability j divided by the market value of all bank liabilitiesDlj= Macaulay’s duration of liability jm = number of different bank liabilities
30 Duration GAP and Economic Value of Equity Let MVA and MVL equal the market values of assets and liabilities, respectively.If:andDuration GAPThen:where y = the general level of interest rates
31 Duration GAP and Economic Value of Equity To protect the economic value of equity against any change when rates change , the bank could set the duration gap to zero:
33 Calculating DGAP DA DL DGAP ($700/$1000)* ($200/$1000)*4.99 = 2.88DL($620/$920)* ($300/$920)*2.81 = 1.59DGAP(920/1000)*1.59 = 1.42 yearsWhat does this tell us?The average duration of assets is greater than the average duration of liabilities; thus asset values change by more than liability values.
35 Calculating DGAP DA DGAP ($683/$974)*2.68 + ($191/$974)*4.97 = 2.86 ($614/$906)* ($292/$906)*2.80 = 1.58DGAP($906/$974) * 1.58 = 1.36 yearsWhat does 1.36 mean?The average duration of assets is greater than the average duration of liabilities, thus asset values change by more than liability values.
36 Change in the Market Value of Equity In this case:
37 Positive and Negative Duration GAPs Positive DGAPIndicates that assets are more price sensitive than liabilities, on average.Thus, when interest rates rise (fall), assets will fall proportionately more (less) in value than liabilities and EVE will fall (rise) accordingly.Negative DGAPIndicates that weighted liabilities are more price sensitive than weighted assets.Thus, when interest rates rise (fall), assets will fall proportionately less (more) in value that liabilities and the EVE will rise (fall).
39 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 orincrease the duration of liabilities by 1.54 yearsDA / ( MVA/MVL) = 1.42 / ($920 / $1,000) = 1.54 years
41 Immunized Portfolio with a 1% increase in rates
42 Immunized Portfolio with a 1% increase in rates EVE changed by only $0.5 with the immunized portfolio versus $25.0 when the portfolio was not immunized.
43 Stabilizing the Book Value of Net Interest Income This can be done for a 1-year time horizon, with the appropriate duration gap measureDGAP* MVRSA(1- DRSA) - MVRSL(1- DRSL) where:MVRSA = cumulative market value of RSAsMVRSL = cumulative market value of RSLsDRSA = composite duration of RSAs for the given time horizonEqual to the sum of the products of each asset’s duration with the relative share of its total asset market valueDRSL = composite duration of RSLs for the given time horizonEqual to the sum of the products of each liability’s duration with the relative share of its total liability market value.
44 Stabilizing the Book Value of Net Interest Income If DGAP* is positive, the bank’s net interest income will decrease when interest rates decrease, and increase when rates increase.If DGAP* is negative, the relationship is reversed.Only when DGAP* equals zero is interest rate risk eliminated.Banks can use duration analysis to stabilize a number of different variables reflecting bank performance.
45 Economic Value of Equity Sensitivity Analysis Effectively involves the same steps as earnings sensitivity analysis.In EVE analysis, however, the bank focuses on:The relative durations of assets and liabilitiesHow much the durations change in different interest rate environmentsWhat happens to the economic value of equity across different rate environments
46 Embedded OptionsEmbedded options sharply influence the estimated volatility in EVEPrepayments that exceed (fall short of) that expected will shorten (lengthen) duration.A bond being called will shorten duration.A deposit that is withdrawn early will shorten duration.A deposit that is not withdrawn as expected will lengthen duration.
47 First Savings Bank Economic Value of Equity Market Value/Duration Report as of 12/31/04 Most Likely Rate Scenario-Base StrategyAssets
48 First Savings Bank Economic Value of Equity Market Value/Duration Report as of 12/31/04 Most Likely Rate Scenario-Base StrategyLiabilities
49 Duration Gap for First Savings Bank EVE Market Value of Assets$1,001,963Duration of Assets2.6 yearsMarket Value of Liabilities$919,400Duration of Liabilities2.0 years
50 Duration Gap for First Savings Bank EVE = 2.6 – ($919,400/$1,001,963)*2.0 = yearsExample:A 1% increase in rates would reduce EVE by $7.2 million = (0.01 / ) * $1,001,963Recall that the average rate on assets is 6.93%
51 Sensitivity of EVE versus Most Likely (Zero Shock) Interest Rate Scenario Sensitivity of Economic Value of Equity measures the change in the economic value of the corporation’s equity under various changes in interest rates. Rate changes are instantaneous changes from current rates. The change in economic value of equity is derived from the difference between changes in the market value of assets and changes in the market value of liabilities.
52 Effective “Duration” of Equity By definition, duration measures the percentage change in market value for a given change in interest ratesThus, a bank’s duration of equity measures the percentage change in EVE that will occur with a 1 percent change in rates:Effective duration of equity yrs. = $8,200 / $82,563
53 Asset/Liability Sensitivity and DGAP Funding GAP and Duration GAP are NOT directly comparableFunding GAP examines various “time buckets” while Duration GAP represents the entire balance sheet.Generally, if a bank is liability (asset) sensitive in the sense that net interest income falls (rises) when rates rise and vice versa, it will likely have a positive (negative) DGAP suggesting that assets are more price sensitive than liabilities, on average.
54 Strengths and Weaknesses: DGAP and EVE-Sensitivity Analysis Duration analysis provides a comprehensive measure of interest rate riskDuration measures are additiveThis allows for the matching of total assets with total liabilities rather than the matching of individual accountsDuration analysis takes a longer term view than static gap analysis
55 Strengths and Weaknesses: DGAP and EVE-Sensitivity Analysis It is difficult to compute duration accurately“Correct” duration analysis requires that each future cash flow be discounted by a distinct discount rateA bank must continuously monitor and adjust the duration of its portfolioIt is difficult to estimate the duration on assets and liabilities that do not earn or pay interestDuration measures are highly subjective
56 Speculating on Duration GAP It is difficult to actively vary GAP or DGAP and consistently winInterest rates forecasts are frequently wrongEven if rates change as predicted, banks have limited flexibility in vary GAP and DGAP and must often sacrifice yield to do so
57 Gap and DGAP Management Strategies Example Cash flows from investing $1,000 either in a 2-year security yielding 6 percent or two consecutive 1-year securities, with the current 1-year yield equal to 5.5 percent.
58 Gap and DGAP Management Strategies Example It is not known today what a 1-year security will yield in one year.For the two consecutive 1-year securities to generate the same $120 in interest, ignoring compounding, the 1-year security must yield 6.5% one year from the present.This break-even rate is a 1-year forward rate, one year from the present:6% + 6% = 5.5% + x so x must = 6.5%
59 Gap and DGAP Management Strategies Example 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%
60 Yield Curve StrategyWhen 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 curveAs the economy contracts, the Federal Reserve typically increases the money supply, which causes the rates to fall and the yield curve to return to its “normal” shape.
61 Yield Curve StrategyTo take advantage of this trend, when the yield curve inverts, banks could:Buy long-term non-callable securitiesPrices will rise as rates fallMake fixed-rate non-callable loansBorrowers are locked into higher ratesPrice deposits on a floating-rate basisLengthen the duration of assets relative to the duration of liabilities
62 Interest Rates and the Business Cycle The general level of interest rates and the shape of the yield curve appear to follow the U.S. business cycle.TimeIntrsRa(Pc)ExpoCLg-ShkuIn expansionary stages rates rise until they reach a peak as the Federal Reserve tightens credit availability.In contractionary stages rates fall until they reach a trough when the U.S. economy falls into recession.