1. ©2009, The McGraw-Hill Companies, All Rights Reserved 8-1 McGraw-Hill/Irwin Chapter Twenty-Two Managing Interest Rate Risk and Insolvency Risk on the Balance Sheet

2. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-2 McGraw-Hill/Irwin Interest Rate Risk The asset transformation function performed by financial institutions (FIs) often exposes them to interest rate risk FIs use (at least) two methods to measure interest rate exposure –the repricing model (a.k.a. the funding gap model) examines the impact of interest rate changes on net interest income (NII) –the duration model examines the impact of interest rate changes on the overall market value of an FI and thus ultimately on net worth The asset transformation function performed by financial institutions (FIs) often exposes them to interest rate risk FIs use (at least) two methods to measure interest rate exposure –the repricing model (a.k.a. the funding gap model) examines the impact of interest rate changes on net interest income (NII) –the duration model examines the impact of interest rate changes on the overall market value of an FI and thus ultimately on net worth

3. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-3 McGraw-Hill/Irwin Interest Rate Risk The U.S. central bank’s (the Federal Reserve’s) monetary policy is the most direct influence on the level and movement of interest rates Changes in the Federal Reserve’s fed funds target rate affect all interest rates throughout the economy –expansionary monetary policy involves decreases in the target fed funds rate –contractionary monetary policy involves increases in the target fed funds rate The U.S. central bank’s (the Federal Reserve’s) monetary policy is the most direct influence on the level and movement of interest rates Changes in the Federal Reserve’s fed funds target rate affect all interest rates throughout the economy –expansionary monetary policy involves decreases in the target fed funds rate –contractionary monetary policy involves increases in the target fed funds rate

4. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-4 McGraw-Hill/Irwin The Repricing Model The repricing or funding gap is the difference between those assets whose interest rates will be repriced or changed over some future period and liabilities whose interest rates will be repriced or changed over some future period Quarterly reporting of commercial bank assets and liabilities is detailed by maturity bucket (or bin) –one day –more than one day to 3 months –more than 3 months to 6 months –more than 6 months to 12 months –more than 1 year to 5 years –more than 5 years The repricing or funding gap is the difference between those assets whose interest rates will be repriced or changed over some future period and liabilities whose interest rates will be repriced or changed over some future period Quarterly reporting of commercial bank assets and liabilities is detailed by maturity bucket (or bin) –one day –more than one day to 3 months –more than 3 months to 6 months –more than 6 months to 12 months –more than 1 year to 5 years –more than 5 years

5. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-5 McGraw-Hill/Irwin The Repricing Model The gap in each bucket or bin is measured as the difference between the rate-sensitive assets (RSAs) and the rate-sensitive liabilities (RSLs) –rate-sensitivity measures the time to repricing of an asset or liability The cumulative gap (CGAP) is the sum of the individual maturity bucket gaps The cumulative gap effect is the relation between changes in interest rates and changes in net interest income The gap in each bucket or bin is measured as the difference between the rate-sensitive assets (RSAs) and the rate-sensitive liabilities (RSLs) –rate-sensitivity measures the time to repricing of an asset or liability The cumulative gap (CGAP) is the sum of the individual maturity bucket gaps The cumulative gap effect is the relation between changes in interest rates and changes in net interest income

6. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-6 McGraw-Hill/Irwin The Repricing Model The change in net interest income for any given bucket i (ΔNII i ) is measured as: ΔNII i – (GAP i )ΔR i = (RSA i – RSL i )ΔR i whereGAP i = the dollar size of the gap between the book value of rate-sensitive assets and rate-sensitive liabilities in maturity bucket i ΔR i = the change in the level of interest rates impacting assets and liabilities in the ith maturity bucket The change in net interest income for any given bucket i (ΔNII i ) is measured as: ΔNII i – (GAP i )ΔR i = (RSA i – RSL i )ΔR i whereGAP i = the dollar size of the gap between the book value of rate-sensitive assets and rate-sensitive liabilities in maturity bucket i ΔR i = the change in the level of interest rates impacting assets and liabilities in the ith maturity bucket

7. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-7 McGraw-Hill/Irwin The Repricing Model A common cumulative gap of interest to commercial bank managers is the one-year repricing gap estimate: where ΔNII is the cumulative change in net interest income from all rate-sensitive assets and liabilities that are repriced within a year given a change in interest rates ΔR i A common cumulative gap of interest to commercial bank managers is the one-year repricing gap estimate: where ΔNII is the cumulative change in net interest income from all rate-sensitive assets and liabilities that are repriced within a year given a change in interest rates ΔR i

8. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-8 McGraw-Hill/Irwin The Repricing Model The spread effect is the effect that a change in the spread between rates on RSAs and RSLs has on net interest income as interest rates change ΔNII i = (RSA i x ΔR RSA ) – (RSL i x ΔR RSL ) The repricing model has four major weaknesses –it ignores market value effects of interest rate changes –it ignores cash flow patterns within a maturity bucket –it fails to deal with the problem of rate-insensitive asset and liability runoffs and prepayments –it ignores cash flows from off-balance-sheet activities The spread effect is the effect that a change in the spread between rates on RSAs and RSLs has on net interest income as interest rates change ΔNII i = (RSA i x ΔR RSA ) – (RSL i x ΔR RSL ) The repricing model has four major weaknesses –it ignores market value effects of interest rate changes –it ignores cash flow patterns within a maturity bucket –it fails to deal with the problem of rate-insensitive asset and liability runoffs and prepayments –it ignores cash flows from off-balance-sheet activities

9. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-9 McGraw-Hill/Irwin The Duration Model Duration measures the interest rate sensitivity of an asset or liability’s value to small changes in interest rates The duration gap is a measure of overall interest rate risk exposure for an FI To find the duration of the total portfolio of assets (D A ) (or liabilities (D L )) for an FI –first determine the duration of each asset (or liability) in the portfolio –then calculate the market value weighted average of the duration of the assets (or liabilities) in the portfolio Duration measures the interest rate sensitivity of an asset or liability’s value to small changes in interest rates The duration gap is a measure of overall interest rate risk exposure for an FI To find the duration of the total portfolio of assets (D A ) (or liabilities (D L )) for an FI –first determine the duration of each asset (or liability) in the portfolio –then calculate the market value weighted average of the duration of the assets (or liabilities) in the portfolio

10. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-10 McGraw-Hill/Irwin The Duration Model The change in the market value of the asset portfolio for a change in interest rates is: Similarly, the change in the market value of the liability portfolio for a change in interest rates is: The change in the market value of the asset portfolio for a change in interest rates is: Similarly, the change in the market value of the liability portfolio for a change in interest rates is:

11. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-11 McGraw-Hill/Irwin The Duration Model Finally, the change in the market value of equity of a FI given a change in interest rates is determined from the basic balance sheet equation: By substituting and rearranging, the change in net worth is given as: –where k is L/A = a measure of the FI’s leverage Finally, the change in the market value of equity of a FI given a change in interest rates is determined from the basic balance sheet equation: By substituting and rearranging, the change in net worth is given as: –where k is L/A = a measure of the FI’s leverage

12. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-12 McGraw-Hill/Irwin The Duration Model The effect of interest rate changes on the market value of equity or net worth of an FI breaks down to three effects –the leverage adjusted duration gap = (D A – kD L ) measured in years reflects the duration mismatch on an FI’s balance sheet the larger the gap the more exposed the FI to interest rate risk –the size of the FI –the size of the interest rate shock The effect of interest rate changes on the market value of equity or net worth of an FI breaks down to three effects –the leverage adjusted duration gap = (D A – kD L ) measured in years reflects the duration mismatch on an FI’s balance sheet the larger the gap the more exposed the FI to interest rate risk –the size of the FI –the size of the interest rate shock

13. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-13 McGraw-Hill/Irwin The Duration Model

14. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-14 McGraw-Hill/Irwin The Duration Model Difficulties emerge when applying the duration model to real-world FI balance sheets –duration matching can be costly as restructuring the balance sheet is time consuming, costly, and generally not desirable –immunization is a dynamic problem duration of assets and liabilities change as they approach maturity the rate at which the duration of assets and liabilities change may not be the same –duration is not accurate for large interest rate changes unless convexity is modeled into the measure convexity is the degree of curvature of the price-yield curve around some interest rate level Difficulties emerge when applying the duration model to real-world FI balance sheets –duration matching can be costly as restructuring the balance sheet is time consuming, costly, and generally not desirable –immunization is a dynamic problem duration of assets and liabilities change as they approach maturity the rate at which the duration of assets and liabilities change may not be the same –duration is not accurate for large interest rate changes unless convexity is modeled into the measure convexity is the degree of curvature of the price-yield curve around some interest rate level

15. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-15 McGraw-Hill/Irwin Insolvency Risk To ensure survival, an FI manager must protect against the risk of insolvency The primary protection against the risk of insolvency is equity capital –capital is a source of funds –capital is a necessary requirement for growth under existing minimum capital-to-asset ratios set by regulators Managers prefer low levels of capital in order to generate higher return on equity (ROE) –the moral hazard problem exacerbates this tendency –the result is an increased likelihood of insolvency To ensure survival, an FI manager must protect against the risk of insolvency The primary protection against the risk of insolvency is equity capital –capital is a source of funds –capital is a necessary requirement for growth under existing minimum capital-to-asset ratios set by regulators Managers prefer low levels of capital in order to generate higher return on equity (ROE) –the moral hazard problem exacerbates this tendency –the result is an increased likelihood of insolvency

16. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-16 McGraw-Hill/Irwin Insolvency Risk The economic meaning of capital is net worth –net worth is equal to the difference between the market value (MV) of an FI’s assets and the market value of its liabilities –the market value or mark-to-market value basis uses balance sheet values that reflect current rather than historical prices Regulatory and accounting-defined capital is based in whole or in part on historical or book values (BV) The economic meaning of capital is net worth –net worth is equal to the difference between the market value (MV) of an FI’s assets and the market value of its liabilities –the market value or mark-to-market value basis uses balance sheet values that reflect current rather than historical prices Regulatory and accounting-defined capital is based in whole or in part on historical or book values (BV)

17. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-17 McGraw-Hill/Irwin Insolvency Risk The market value of capital and credit risk –declines in current and expected future cash flows on loans lowers the MV of an FI’s assets –declines in the MVs of assets is directly charged against the equity owners’ capital or net worth –liability holders are only hurt when asset losses exceed equity capital levels –thus, equity capital acts as “insurance” protecting liability holders (and guarantors such as the FDIC) against insolvency risk The market value of capital and interest rate risk –rising interest rates decrease the value of an FI’s assets more than the value of the FI’s liabilities when the duration gap of the FIs balance sheet is positive –again, losses are first charged against equity capital The market value of capital and credit risk –declines in current and expected future cash flows on loans lowers the MV of an FI’s assets –declines in the MVs of assets is directly charged against the equity owners’ capital or net worth –liability holders are only hurt when asset losses exceed equity capital levels –thus, equity capital acts as “insurance” protecting liability holders (and guarantors such as the FDIC) against insolvency risk The market value of capital and interest rate risk –rising interest rates decrease the value of an FI’s assets more than the value of the FI’s liabilities when the duration gap of the FIs balance sheet is positive –again, losses are first charged against equity capital

18. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-18 McGraw-Hill/Irwin Insolvency Risk The book value of equity capital is the difference between the BV of assets and the BV of liabilities –the BV of equity is usually composed of the par value of equity shares, the surplus value of equity shares, and retained earnings –the BV of equity does not equal the market value of equity –managers can manipulate the BV of equity by using discretion when timing the recognition of loan losses selectively selling assets to inflate reported earnings (and thus capital) The book value of equity capital is the difference between the BV of assets and the BV of liabilities –the BV of equity is usually composed of the par value of equity shares, the surplus value of equity shares, and retained earnings –the BV of equity does not equal the market value of equity –managers can manipulate the BV of equity by using discretion when timing the recognition of loan losses selectively selling assets to inflate reported earnings (and thus capital)

19. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-19 McGraw-Hill/Irwin Insolvency Risk Interest rate changes have no impact on book values of assets and liabilities –FIs can be solvent from a BV perspective, but massively insolvent from an economic perspective The degree to which the BV of equity deviates from the MV of equity depends on –interest rate volatility –examination and enforcement –loan trading The discrepancy between the MV and BV of equity is measured by the market-to-book ratio Interest rate changes have no impact on book values of assets and liabilities –FIs can be solvent from a BV perspective, but massively insolvent from an economic perspective The degree to which the BV of equity deviates from the MV of equity depends on –interest rate volatility –examination and enforcement –loan trading The discrepancy between the MV and BV of equity is measured by the market-to-book ratio

20. ©2009, The McGraw-Hill Companies, All Rights Reserved 22-20 McGraw-Hill/Irwin Insolvency Risk Arguments against using market value accounting include –it is difficult to implement especially so for small FIs that are not publicly traded –it introduces an unnecessary degree of variability into reported earnings –FIs may be less willing to accept longer-term asset exposures if they must be continually marked-to- market likely would interfere with FIs’ role as lenders and monitors and could lead to a “credit crunch” Arguments against using market value accounting include –it is difficult to implement especially so for small FIs that are not publicly traded –it introduces an unnecessary degree of variability into reported earnings –FIs may be less willing to accept longer-term asset exposures if they must be continually marked-to- market likely would interfere with FIs’ role as lenders and monitors and could lead to a “credit crunch”