1. Managing Interest Rate Risk and Insolvency Risk on the Balance Sheet
Chapter Twenty-Two
Managing Interest Rate Risk and Insolvency Risk on the Balance Sheet

2. Interest Rate Risk
The asset transformation function performed by financial institutions (FIs) often exposes them to interest rate risk
FIs use two main 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. Interest Rate Risk
The Federal Reserve’s monetary policy is the most direct influence on the level and movement of short-term interest rates
Changes in the Federal Reserve’s target fed funds 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 3

4. 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 4

5. The Repricing Model
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

6. 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 6

7. The Repricing Model
The change in net interest income for any given bucket i (ΔNIIi) is measured as:
ΔNIIi = (GAPi)ΔRi = (RSAi – RSLi)ΔRi
where GAPi = the dollar size of the gap between the book
value of rate-sensitive assets and rate-sensitive
liabilities in maturity bucket i
ΔRi = the change in the level of interest rates
impacting assets and liabilities in the ith
maturity bucket 7

8. 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 ΔRi 8

9. 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
ΔNIIi = (RSAi x ΔRRSA) – (RSLi x ΔRRSL) 9

10. The Repricing Model
Ignoring the spread effect for simplicity (highlighted rows):
For a positive repricing gap, interest rates and profitability move in the same direction
For a negative repricing gap, interest rates and profitability move in the opposite direction
The four highlighted rows ignore the spread effect. In each of these cases the effect of the spread effect is the same as the effect of the interest rate change. 10

11. The Repricing Model The repricing model has some major weaknesses
The repricing model (RPM) measures only short-term profit changes, not shareholder wealth changes
The maturity buckets are arbitrarily chosen
All assets and liabilities that mature within the maturity bucket are considered equally rate-sensitive; this is defacto, not true if a spread effect exists
The repricing model (RPM) measures only short term profit changes, not shareholder wealth changes. As such it suffers from the same problems as the goal of maximizing profits. In particular the RPM ignores cash flows changes that occur outside the maturity bucket and ignores the change in current value of future cash flows as interest rates change.
The maturity buckets are arbitrarily chosen and can be difficult to manage. It is possible to have a positive 3 month RS gap, a negative 6 month RS gap and a positive 1 year RS gap. Managing this requires detailed forecasts of interest rate changes over the various arbitrarily chosen time periods.
All assets and liabilities that mature within the maturity bucket are considered equally rate sensitive. This is defacto not true if a spread effect exists.
The RPM ignores runoffs. Runoffs are receipts of cash on FRA or payments due on FRLs that occur during the maturity bucket period. This cash must be reinvested by the intermediary and it is rate sensitive. Runoffs are not calculated in the basic version of the RPM presented here.
The RPM ignores prepayments. Prepayment patterns are affected by changing interest rates and are difficult to predict. Prepayments increase with declining rates so assets that were considered fixed rate may become rate sensitive by being prepaid within the maturity bucket.
The RPM ignores cash flows generated from off balance sheet activities. These cash flows are also often sensitive to the level of interest rates, so the RPM underestimates the interest rate sensitivity of the institution. Payments on FRLs that require additional borrowing would result in a change in interest expense on a given account, making it rate sensitive. Similarly, if the bank had to liquidate part of a fixed rate asset to pay the liability, this would change the income on fixed rate assets. 11

12. The Repricing Model The repricing model has some major weaknesses
The RPM ignores runoffs
Runoffs are receipts of cash on FRA or payments due on FRLs that occur during the maturity bucket period. This cash must be reinvested by the intermediary and it is rate sensitive
The RPM ignores prepayments
The RPM ignores cash flows generated from off-balance-sheet activities
The repricing model (RPM) measures only short term profit changes, not shareholder wealth changes. As such it suffers from the same problems as the goal of maximizing profits. In particular the RPM ignores cash flows changes that occur outside the maturity bucket and ignores the change in current value of future cash flows as interest rates change.
The maturity buckets are arbitrarily chosen and can be difficult to manage. It is possible to have a positive 3 month RS gap, a negative 6 month RS gap and a positive 1 year RS gap. Managing this requires detailed forecasts of interest rate changes over the various arbitrarily chosen time periods.
All assets and liabilities that mature within the maturity bucket are considered equally rate sensitive. This is defacto not true if a spread effect exists.
The RPM ignores runoffs. Runoffs are receipts of cash on FRA or payments due on FRLs that occur during the maturity bucket period. This cash must be reinvested by the intermediary and it is rate sensitive. Runoffs are not calculated in the basic version of the RPM presented here.
The RPM ignores prepayments. Prepayment patterns are affected by changing interest rates and are difficult to predict. Prepayments increase with declining rates so assets that were considered fixed rate may become rate sensitive by being prepaid within the maturity bucket.
The RPM ignores cash flows generated from off balance sheet activities. These cash flows are also often sensitive to the level of interest rates, so the RPM underestimates the interest rate sensitivity of the institution. Payments on FRLs that require additional borrowing would result in a change in interest expense on a given account, making it rate sensitive. Similarly, if the bank had to liquidate part of a fixed rate asset to pay the liability, this would change the income on fixed rate assets. 12

13. 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 (DA) (or liabilities (DL)) 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 13

14. The Duration Model 14

15. 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: 15

16. The Duration Model
Finally, the change in the market value of equity of an 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 16

17. 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 = (DA – kDL)
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 17

18. Duration Gap Example 18

19. The Duration Model
Difficulties emerge when applying the duration model to real-world FI balance sheets
Duration matching (immunization) 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 19

20. Duration and Convexity (Curvature)20

21. 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 21

22. Insolvency Risk
The Capital Purchase Program (CPP) was part of the TARP funding in
The Treasury purchased over $200 billion of senior preferred equity under the program
The CPP was designed to help FIs increase their capital with the aim of increasing lending to the general public
Lending fell in 2008, 2009, and 2010, so in this sense, the program was a failure, although presumably lending would have fallen even farther without it and more failures may have occurred
The program came with stipulations on maximum executive pay, golden parachutes and clawback provisions on executive pay based on earnings and limits on tax deductions associated with executive compensation. 22

23. 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) 23

24. Insolvency Risk The market value of capital and credit risk
Decreases in current and expected future cash flows on loans lowers the MV of an FI’s assets
Decreases in the MVs of assets are 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 FI’s balance sheet is positive
Losses are first charged against equity capital 24

25. Interest Rate Changes and Equity Value25

26. Insolvency Risk
The book value of equity capital is the difference between the BV of assets and the BV of liabilities
BV of equity is usually composed of the par value of equity shares, the surplus value of equity shares, and retained earnings
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)
Selectively selling assets to inflate reported earnings (and thus capital) is called ‘gains trading.’ 26

27. 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 27

28. Market-to-Book Ratios
Data is from 2010. 28

29. Insolvency Risk
Arguments against using market value accounting include:
It is difficult to implement
especially for small FIs that are not publicly traded
It introduces variability into reported earnings
FIs claim they may be less willing to accept longer-term asset exposures if they must be continually marked-to-market 29

30. Insolvency Risk
The industry argues the lack of liquidity in the recent crisis led to unrealistically low market values of assets and marking to market imposed excessive losses on institutions
Consequently, the Financial Accounting Standards Board (FASB) allows management to rely on internal estimates of cash flows to estimate fair value
As of April 2009, FASB allows DIs to not recognize losses in earnings and regulatory capital on accounts that are a) designated as held for investment rather than sale and b) temporarily impaired in value due to market conditions rather than underlying credit deterioration
This is referred to as ‘marking to model’ rather than ‘marking to market.’ This makes sense in a non-functioning market environment but it still allows FIs to not update the value of assets and liabilities to current market conditions and adds subjectivity that is likely to be manipulated by management.
The April 2009 FASB ruling:
The losses must be accounted for and revealed separately. This again adds subjectivity that can be used to hide losses. The new rules imply that regulators will be able to evaluate these issues and will be willing to do so. 30