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©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

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©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

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©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

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©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

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©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

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©2009, The McGraw-Hill Companies, All Rights Reserved 9-6 McGraw-Hill/Irwin

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©2009, The McGraw-Hill Companies, All Rights Reserved 9-7 McGraw-Hill/Irwin Management of interest rate risk of the Banking Book is primarily focused on interest and fair value through Re-pricing Gap Analysis, Analysis of the Net Interest Income Sensitivity, Duration and Fair Value Sensitivity. The management of interest risk of the trading book is achieved through mark-to-market practice and exposure analysis. On a periodical basis, risk monitoring reports are prepared for senior management to gain an accurate understanding of Bank's risk position. Mathematical model like Stress-Testing is carried out at least biannually.

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©2009, The McGraw-Hill Companies, All Rights Reserved The Repricing Model 9-8 McGraw-Hill/Irwin AssetsLiabilities Rate Sensitive Assets (RSAs) $100Rate Sensitive Liabilities (RSLs) $ 50 Fixed Rate Assets (FRAs)$206Fixed Rate Liabilities (FRLs)$256 Nonearning Assets (NEAs)$ 34Equity$ 34 Total$340 Total$340 There is a little risk from an interest rate change on the $34 of NEA financed by equity There is a little profit risk from the $206 FRAs financed by FRLs This leaves $50 in FRLs not yet accounted for. There should not be an excessive amount of risk for the amount of RSAs financed by RSLs, because both are rates sensitive ($50 of the total $100). The remaining $50 in RSAs that are financed by the remaining $50 in FRA, is a major source of interest rate risk because one side (the assets) is rate sensitive and the other side is not. This category is called the repricing ‘GAP’ in the repricing model If the spread changes this is termed a ‘spread effect’ (as described below).

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-9 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

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-10 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

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-11 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

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©2009, The McGraw-Hill Companies, All Rights Reserved Summary of Spread Effects: 9-12 McGraw-Hill/Irwin Dollar GAPSpread Effect RR Direction of NII Positive Increase NegativeIncreaseAmbiguous PositiveDecreaseAmbiguous NegativeDecrease NegativePositiveIncreaseAmbiguous NegativeIncreaseDecrease PositiveDecreaseIncrease NegativeDecreaseAmbiguous

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©2009, The McGraw-Hill Companies, All Rights Reserved Paradigm For Measuring The Repricing Gap 1. Classify each asset on the balance sheet as either: RSA, FRA, NEA 2. Classify each liability/equity account: RSL, FRL, Equity 3. Group assets and liabilities into the following groups: –RSAs financed by RSLs –FRAs financed by FRLs –NEA financed by Equity Gap: Positive dollar RS Gap: Indicates that excess RSAs financed by remaining FRLs Negative dollar RS Gap: Excess FRAs financed by remaining RSLs Whatever is leftover is financed by equity 4. Calculate the average annual % rate of return on each asset category and the average annual % cost rate on each liability category and then calculate the spreads. 5. Calculate the dollar contribution to profit from each category as the product of the amount times the spread. 6. Add up the profits. The banker is now in a position to both understand the major sources of profitability and compare pricing with other institutions. One can also easily forecast changes in profitability for various projected changes in interest rates. 9-13 McGraw-Hill/Irwin

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©2009, The McGraw-Hill Companies, All Rights Reserved Example 9-14 McGraw-Hill/Irwin Assets ($ Mill)Liabilities & Equity Investments under 1 year @ 5%$ 100Deposits < 1 year @ 4%$ 900 Loans < 1 year @ 7%$ 350All Long Term Liabilities @ 7%$ 500 Variable rate loans (rate reset in 6 months) @ 6.5%$ 300Equity$ 200 Fixed Rate Assets > 1 year maturity @ 8%$ 850 Total$1,600 Total$1,600

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©2009, The McGraw-Hill Companies, All Rights Reserved 9-15 McGraw-Hill/Irwin Rate Sensitive AssetsRate Sensitive Liabilities AmntIncomeAmntCost Investments under 1 year @ 5%$ 100$ 5.00Deposits < 1 year @ 4%$ 900$ 36.00 Loans < 1 year @ 7%$ 350$24.50 Variable rate loans (rate reset in 6 months) @ 6.5%$ 300$19.50 Total RSAs$ 750 Total$ 900 Total Income$49.00 Total Cost$ 36.00 NII from this category$13.00 Average rate of return6.533%Average cost rate4.000% Spread on RSAs financed by RSLs =2.533% (6.533% - 4%) The spread indicates the contribution to profit from this category per dollar invested (ignoring noninterest income and costs.) Note that some RSLs are used to finance something other than RSAs since there are only $750 RSAs but $900 RSLs. Dollar Gap = RSAs – RSLs = -$ 150 Percentage Gap = -$150 / $1,600 = -9.375% Gap ratio = $750 / $900 = 0.833 The negative dollar gap indicates that some fixed rate assets are financed by rate sensitive liabilities. The ‘gap’ indicates the imbalance in sensitivities of the liabilities that are funding the assets.

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©2009, The McGraw-Hill Companies, All Rights Reserved 9-16 McGraw-Hill/Irwin Fixed Rate AssetsFixed Rate Liabilities AmntIncomeAmntCost Fixed Rate Assets > 1 year maturity @ 8%$ 850$68.00 All Long Term Liabilities @ 7%$ 500$ 35.00 Total FRAs$ 850 Total$ 500 Total Income$68.00 Total Cost$ 35.00 NII from this category$33.00 Average rate of return8.000%Average cost rate7.000% Spread on FRAs financed by FRLs = 1.000% (8% - 7%) The spread indicates the contribution to profit from this category per dollar invested (ignoring noninterest income and costs.) Note that only $500 of FRAs are actually financed by FRLs. $200 FRAs are financed by equity and the remaining $150 FRAs are financed by RSLs. Notice the GAP FRAs – FRLs

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©2009, The McGraw-Hill Companies, All Rights Reserved 9-17 McGraw-Hill/Irwin CategoryAmountSpread$ Profit RSAs financed by RSLs$ 7502.533%$19.00 FRAs financed by FRLs$ 5001.000%$ 5.00 FRAs financed by equity$ 2008.000%$16.00 The Gap: FRAs financed by RSLs$ 1504.000%$ 6.00 NII$46.00 Average rate of return per dollar invested2.875% [1] [1] FRAs financed by equity are not a part of the gap since the assets and liabilities in this category are both fixed rate. Instructors please be aware that the profit table has to be constructed based on the size of the given categories. For instance, one will not always include a line where FRA is financed by equity. If the gap had been positive the third row would have been RSA financed by equity.

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©2009, The McGraw-Hill Companies, All Rights Reserved 9-18 McGraw-Hill/Irwin CategoryAmountSpread$ Profit RSAs financed by RSLs$ 7502.233%$16.75 FRAs financed by FRLs$ 5001.000%$ 5.00 FRAs financed by equity$ 2008.000%$16.00 The Gap: FRAs financed by RSLs$ 1503.000%$ 4.50 NII$42.25 Average rate of return per dollar invested2.641% The change in ROA is 2.641% - 2.875% = - 23 basis points. If the spread effect had been positive the profit drop would have been smaller. [1] [1] FRAs financed by equity are not a part of the gap because the assets and liabilities in this category are both fixed rate. Instructors please be aware that the profit table has to be constructed based on the size of the given categories, for instance, it will not always include a line where FRA is financed by equity. If the gap had been positive the third row would have been RSA financed by equity.

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-19 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

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-20 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:

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-21 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

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-22 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

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-23 McGraw-Hill/Irwin The Duration Model

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©2009, The McGraw-Hill Companies, All Rights Reserved 9-24 McGraw-Hill/Irwin Example calculation: Suppose a bank with $500 million in assets has an average asset duration of 3 years, and an average liability duration of 1 year. The bank also has a total debt ratio of 90%. If R is 12% and the bank is expecting a 50 basis point increase in interest rates, by how much will the equity value change? Equity Value Change E = – [3 – (0.90 1)] $500 million (0.0050 / 1.12) = –$4,687,500. To find the percentage change in equity, divide both sides of the equation by E: E = $500 million (1-0.90) or E = $50 million so that: E/E = – [3 – (0.90 1)] ($500 million/$50 million) (0.0050 / 1.12) = – 9.375% or E/E may be more simply found as -$4,687,500 / $50,000,000 = -9.375%.

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©2009, The McGraw-Hill Companies, All Rights Reserved Changes in the value of equity for different duration gaps 9-25 McGraw-Hill/Irwin Duration Gap Interest Rate Change Biggest Value Change Equity Value Positive Increase AssetsDecreases DecreaseAssetsIncreases Negative IncreaseLiabilitiesIncreases DecreaseLiabilitiesDecreases

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-26 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

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-27 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

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-28 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)

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-29 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

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-30 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)

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-31 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

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©2009, The McGraw-Hill Companies, All Rights Reserved 22-32 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”

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Measuring Interest Rate Risk with Duration GAP

Measuring Interest Rate Risk with Duration GAP

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