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Managing Interest Rate Risk(II): Duration GAP and Economic Value of Equity

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

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

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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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Weighted Average Duration of Bank Assets Weighted Average Duration of Bank Assets (DA) Where w i = Market value of asset i divided by the market value of all bank assets Da i = Macaulay’s duration of asset i n = number of different bank assets

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Weighted Average Duration of Bank Liabilities Weighted Average Duration of Bank Liabilities (DL) Where z j = Market value of liability j divided by the market value of all bank liabilities Dl j = Macaulay’s duration of liability j m = number of different bank liabilities

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

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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 the average duration of liabilities; thus asset values change by more than liability values.

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1 percent increase in all rates.

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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 the average duration of liabilities, thus asset values change by more than liability values.

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Change in the Market Value of Equity In this case:

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

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DGAP Summary

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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

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

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Immunized Portfolio with a 1% increase in rates

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EVE changed by only $0.5 with the immunized portfolio versus $25.0 when the portfolio was not immunized.

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

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

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

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

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

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Duration Gap for First Savings Bank EVE Duration Gap = 2.6 – ($919,400/$1,001,963)*2.0 = 0.765 years Example: A 1% increase in rates would reduce EVE by $7.2 million = 0.765 (0.01 / 1.0693) * $1,001,963 Recall that the average rate on assets is 6.93%

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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.

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Effective “Duration” of Equity By definition, duration measures the percentage change in market value for a given change in interest rates Thus, a bank’s duration of equity measures the percentage change in EVE that will occur with a 1 percent change in rates: Effective duration of equity 9.9 yrs. = $8,200 / $82,563

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

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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

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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

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

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