1. FHLB Income-Based IRR Measurement: Alternative Approaches and Issues
- Potentially Useful Lessons from the Private Sector -

2. Classification of IRR Measurement Techniques
Agenda
Background
Classification of IRR Measurement Techniques
Opportunities and Challenges of:
Stochastic income measures
Earnings-at-Risk (EaR)
Background: Citicorp’s Risk Measurement Challenge ~1987
Background: Citicorp’s Solution
Application to Income Output from an FHLB using QRM or BancWare
Applications
Risk Limits
Decomposition of the IRR Measure: Improved Understanding and Management
Hedging both Income and Value
Regulatory

3. Background
IRR measurement and management in private banks is largely focused on reported income
Mortgage banks more oriented toward value because accounting is closer to market value accounting
Bank America implemented an IRR measurement solution to hedge earnings and value simultaneously in 1990s
IRR measurement in many FHLBs has focused on controlling value-based risk measures
FHLBs and its regulators are starting to place more emphasis on income-based risk measures and effects on retained earnings
The private sector has implemented methodologies that are potentially useful to FHLBs and their regulators

4. Background
Some methodological issues that arise in private banks when measuring income-at-risk:
Which definition of “income” to model
How to simulate interest rates
Whether to include new business assumptions and how to vary new business assumptions in different rate scenarios
Over what period to model income-based risk (a.k.a., the “time horizon” problem)
How to set risk limits for income-based IRR
All of these questions are relevant when designing income-based risk measures

5. Three Dimensions of IRR Measurement Methodologies
Time Horizon
Existing Only vs. Existing + New
Deterministic vs. Stochastic
Both value and income based IRR measures can be categorized using this three dimensional framework

6. Three Dimensions of IRR Measurement Methodologies
Deterministic
Income Based
Stochastic
Existing Business Only
Existing + New Business
Deterministic
Value Based
Existing Business Only
Stochastic
12 – 18 Months
18 Months to ~5 Yrs
360 Months
Short Term Medium Term Long Term
Time Horizon

7. Income Based IRR Measurement Methodologies
Existing Business Only
Deterministic
Income Based IRR
Stochastic
Existing + New Business
12 – 18 Months
18 Months to 5 Yrs
360 Months
Income Based Methodologies

8. Classification of Income Based IRR Measurement

9. Classification of Useful Income Based IRR Measurement
Opinion: There are only three approaches to measuring income at risk that offer risk managers much value added and one of them is very complicated and beyond the capabilities of vendor based ALM systems.

10. Opportunities and Challenges of Stochastic Income Measures
When used with the right software it’s the only methodology available to optimize hedges when hedging from both a value and income perspectives using stochastic methodologies
For portfolios where value and income accounting are aligned then the potential issues are minimized
When mortgage bankers use value based stochastic risk measurement tools they are also approximately hedging income

11. Opportunities and Challenges of Stochastic Income Measures
Difficult to compute:
New business equations are difficult to specify and results are sensitive to these assumptions
Excluding new business helps, but in private sector defining new business for core deposits is assumption intense
Most balance sheets requires two yield curves to simulate unless basis risk is ignored or work-arounds applied
Resource intensive to get a credible measure
Not easy to produce a validated measure in QRM.
BW’s stochastic model is inferior
Not available in trading models with superior stochastic engines that focus on value based risk measurement
Not aware of any commercial bank that is using stochastic income for hedge design.

12. Opportunities and Challenges of EAR
Scenarios can be predefined shocks of almost any form or “what if” scenarios
ALM models are built for this type of analysis
Very useful for short term analyses
Easy to understand and communicate results
Risk attributes can be computed

13. Opportunities and Challenges of EaR
Can be misused
ALM models allow targeting balancing procedures, which can mask risk
Limited time horizon for analysis allows risks to be pushed “beyond the radar”
Hedging transactions often beyond the time horizon
Not useful for assessing long term and strategic risks
Risk limits are not applicable when new business sensitivities are included
Many users do not know how to decompose risk into characteristics and can generate “non-actionable” results

14. Citicorp’s Risk Measurement Challenge ~ 1987
Background:
7 retail banks, 3 thrifts, a mortgage bank, and large credit cards businesses with decentralized management structure
Corporate management was concerned that smaller thrifts could take a risk position and bankrupt the corporation
Perceived need to develop common, understandable, and actionable risk management metrics and language across multiple management units
Requirement to understand risk of the combined units
Risk measures were needed to limit risk in a way that could not be “gamed” by new business assumptions
No vendor solutions were available

15. Citicorp’s Solution
“SMEAR”: Spot Measure of Earnings-at-Risk
Designed by Gary Lachmund, former President of National Asset Liability Management Association (NALMA) and then head of ALM at Citibank
Originally developed proprietary model in-house; Can (now) be easily generated in vendor ALM models
Complementary to analyses of risk that do include new business sensitivities
Addresses several of the issues relevant to measuring income-based IRR in the FHLBs by the regulators
Was utilized to limit risk of short- and long-term earnings sensitivity

16. Application to FHLBs and FHFB
Provides method a solution to “time horizon problem”
Easily produced in BancWare and QRM
Measures are complementary to income-based risk measures that include new business
Potential to creates common methodology across 12 regulated banks so risk measures can be consolidated and compared
Regulators can measure position of system
Regulators can rank order positions of individual FHLBs

17. SMEAR Procedures Start with current balance sheet
Shock interest rates instantaneously, by multiple increments
May use flat rates or forwards, but forwards are preferred
Key: all rates shocked same amount*
Run-off balances based on contractual maturity- or model-based prepayment in each scenario
As balances run-off replace with overnight funding or placements (a.k.a. the balancing item) at scenario- dependent rate
For repricing assets and liabilities reprice according to contractual rules
Allow no new business
* i.e parallel shocks; This assumption eliminates repricing effects from analysis

18. SMEAR Procedures Treat equity as an indefinite term maturity item
Compute “Pretax Rate Sensitive Earnings” (PRSE) in each scenario and as many time periods as relevant
This allows for fee income, direct expenses, and gains-on-sale
Generates a matrix of solutions for each time period and shock
Calculate differences in each time period relative to the base case
Graph the calculated differences

19. Definition of Income Applicable to an FHLB Risk Measure
Income measure = the net revenues in each time period associated with the book of existing business (i.e. “the risks you already own”) or “NII associated with Existing Book of Business” (NII-EBS)
Gains-on-sale are not currently a component of income sensitivity
Since this measure explicitly excludes net revenues associated with new business, it does not fall into one of the standard income definitions
FHLBs have derivatives that do not qualify for hedge accounting. The NII-EBS incorporates these obligations by calculating net cash flow differences as their contribution to the income-based risk measure
In order to accommodate a GAAP earnings measure, market value sensitivity of derivative instruments not qualified for hedge accounting treatment can be added back into the analysis separately
Using a blend of market-value accounting and accrual accounting in an income-based risk measure can lead to non-economic risk management decisions

20. Notes on Long Term Earnings at Risk Measure
Focus is on “the risks you own” (certainty) vs. risks you only incur over time in an uncertain future
Ignorance of long term earnings effects can lead to risk positions that increase longer-term exposures that are off the radar screen
Market value sensitivity analyses is not a substitute for longer term earnings exposures

21. SMEAR Calculation Steps
Step 1: Calculate NII-EBS in each period for the base (“expected” or forward curve) scenario and for each “rate shock” (or “stress”) scenario
Step 2: Subtract NII-EBS shock scenario values from those of the FWD case
Step 3: Plot the value changes for each stress scenario
Step 4: Connect the dots

22. SMEAR Example: Income-Based Simulation Results
Step 1: Calculate NII-EBS in each scenario and period

23. Transforming Income Simulations to Risk Measures
Step 2: Calculate DNII-EBS relative to FWD case

24. Transforming Income Simulations to Risk Measures
Step 3: Plot the relative values

25. Transforming Income Simulations to Risk Measures
Step 4: Connect the dots

26. We’ve transformed tables to graphs.
Summary
So far:
We’ve transformed tables to graphs.
We’ve extended the time horizon for income-based risk analyses.
Time horizon can be extended as far into the future as needed for controlling longer term earnings sensitivity associated with the existing balance sheet.
Number of shocks can be added so that a broader range of rate shocks is applied as the time horizon is extended

27. Further Application can Extend the Benefits of the SMEAR
Further Applications
Further Application can Extend the Benefits of the SMEAR
Risk Measurement Technique:
Application I: Risk limits in the SMEAR framework
Application II: Decomposition of risk
Application III: Ability to assess value-based hedging on income-based IRR
Application IV: Regulatory

28. SMEAR RISK LIMIT FRAMEWORK: Application I
Width of rate shock band can be linked to observed market volatilities
Size of rate shock may vary with the direction of shock if view is that rates are approximately log-normally distributed.
Note that the width of the limit is no longer tied to the exact rate shock used in the calculations.
Risk limit may vary by time period or direction of shock due to expected offsets in new business activity

29. SMEAR RISK LIMIT FRAMEWORK: Application I
Limit violation marked in “X” occurs when line intersects the bottom of the SMEAR “limit box”
Size of shock utilized in limit increases with time, as does size of limit
Income limits in future periods typically become less restrictive because opportunities exist to mitigate the risk
Citicorp limits were invoked out to Year 10, requiring a broader range of rate shocks than shown

30. Challenge: “Rates Don’t Move in Parallel Shocks”
Citicorp limits were invoked out to Year 10, requiring a broader range of rate shocks than shown
The purpose of risk measurement and a risk limit system is to guide risk management actions
“Actionable understanding” is critical. Graphical framework translates to a visual picture of risk components and points the way to managing risk
The actual number used to limit risk is a proxy and shouldn’t be equated with “what if” analyses
Setting of size of actual risk limit in each case (defined by direction of shock and time) is critical component of system.
The limits should take account of evolution of new business but not the evolution of new interest rate risk positions

31. Decomposing income-based Risk Measure: Application II
Why Decompose income-based IRR?
Decomposition of income-based IRR is a:
Risk communication tool, because portfolio composition effects are difficult for the non-technical audience to comprehend (e.g., some members of ALCOs)
Risk measurement validation tool, because specific risk measures can be ascribed to individual product characteristics and errors can frequently (but not always) be seen
Risk education tool, because it reduces the complexity associated with understanding complex risk characteristics and, therefore, builds broader understanding of the complexity risk management among treasury and non-treasury professional staff

32. Decomposing income-based Risk Measure: Approach
With instantaneous parallel rate shocks income-based risk can be decomposed into:
Repricing Risk: caused by mismatches in the repricing characteristics of assets and liabilities already on the balance sheet; and
Option Risk: caused by the options embedded in the structures of financial instruments (e.g., prepayment, calls, and puts)
Basis Risk can be added to option and repricing risk by shocking the CO curve by a different amount than the LIBOR curve and adding the results to those generated with parallel shocks

33. Decomposing income-based Risk Measure: Approach
Yield Curve Risk is directly calculated from product-level decompositions of option risk.
Whereas, basis risk can be added to the other risk calculations in the SMEAR framework, total calculated yield curve risk is partially duplicative and cannot be added
Repricing risk component of yield curve risk has already been calculated by shocking interest rates
Missing component is options related effects which can be discerned at the product level
If desired, income limits can be applied to options risks directly

34. Decomposing the Income-Based IRR Measure: Example
Total IRR =
Repricing Risk Options Risk
Total IRR = Repricing Risk + Options Risk

35. Decomposing income-based IRR: Repricing Risk
Repricing risk is the sum of the “implicit” repricing exposures on each product type. However, it can be calculated at any level of aggregation, including the entire balance sheet.
Aggregate measure of repricing risk includes equity.
Repricing risk is best viewed at the balance sheet level. Focusing on offsets at the product level can introduce undesired noise at the balance sheet level.
When rates are shocked by equal amounts, repricing risk is “linear” in the risk graphs
Since fix-pay (or fix-receive) swap risk profiles are also linear, the mitigating transactions that reduce pricing risk can be easily identified and calculated.
Swaps can be designed to be almost “perfect” hedges of measured repricing or “Gap” risk

36. Decomposing income-based IRR: Option Risk
Option risk is the sum of the options exposures associated with each product.
It can be calculated at the aggregate level by subtracting repricing risk from total risk. However, graphical representations of options risk can be complicated when more than one type of option is present.
Options risks are best hedged with options, although options exposures are frequently partially hedged with swaps
Measurement of options related risks are highly model sensitive because the exact conditions determining when the option is exercised are often based on specific modeling assumptions.
Whereas repricing risk is best analyzed at the balance sheet level, options risk is better understood at the product level.

37. Decomposing income-based IRR: Option Risk
Identified Embedded Options in the Illustrative FHLB Balance Sheet
Total Option Risk equals the sum of options risks embedded in all products and derivative instruments

38. Decomposing income-based IRR: Option Risk
Classification Scheme for Graphs to Follow

39. Decomposing Options Risk : Prepayment and Call Risk
Callable Agencies have no extension risk, unless they are expected to be called in the Forward Rate shock. Mortgages have extension risk as prepayment speeds slow relative to those modeled in the Forward Rate shock.
Note: Graphs are not drawn on same scale.

40. Decomposing Options Risk: Cancelable Advances & COs
Cancellation features in CO portfolios raise the average coupon in lower rate levels. In turn, this raises income relative to the forward scenario. In the illustrative balance sheet the CO portfolio was far larger than the Advances portfolio.

41. Decomposing Options Risk: Derivatives with Options
Swaptions include options to purchase fixed receive as well as fixed pay swaps. There is greater prevalence of cancelable swaps than swaptions and caps observed on FHLB balance sheets.
Note: Graphs are not drawn on same scale.

42. Decomposing income-based IRR: Option Risk=

43. Value vs. income-based IRR Hedging: Application III
Background
Bank of America built a stochastic interest rate model that calculated both income and economic value simultaneously. The model incorporated consistent simulation of two yield curves (Treasury and LIBOR)
An optimizer was constructed to find hedges that minimized both value-based and income-based risk measures
A trade-off was calculated
Given senior management input on preferences for minimizing variances of value and income over time, an optimal hedge solution was calculated
Several FHLBs are designing hedges focused exclusively on value-based IRR measures and have asked:
How will value-based hedges impact income-based IRR measures?
What methodology can be employed to measure the impact of value-based hedges on income-based IRR measures?

44. Value vs. income-based IRR Hedging: Application III
Considerations and an Approach using SMEAR
The income-based risk measure that most coincides conceptually to the value-based risk measure includes long-term earnings and excludes new business
Bank America findings from hedging from both perspectives:
The size of hedge adjustments varied by product
Adjustments could be thought of as duration neutral adjustments to the cash flow timing
Significant improvement to reducing earnings variances that did not sacrifice value based risk measure could be determined by trial and error

45. Value vs. income-based IRR Hedging: Application III
Simple SMEAR Test on Current FHLB Positions
Calculate the SMEAR risk in two subsequent time periods
Use risk measures in each period to evaluate the effects of value based risk measures on income at risk
Subtract the risk measures
This is called “Delta SMEAR”
Use Delta SMEAR to evaluate the stability of the value based hedge in term of income based risk
Iterate the process and adjust the hedges accordingly

46. Regulatory Extensions and Applications: Application IV
Regulators Need an Income-Based IRR Methodology that Can Be:
Applied consistently across 12 independently managed FHLBs
Used to assess risk at each bank as well as all banks
Used to assess relative risk of 12 banks
Used to limit risk at individual banks
Regulatory limits can be set relative to individual FHLB’s “real” capital
Total risk of 12 FHLBs can be limited and limits can be allocated
Produced with minimum additional effort, utilizing QRM or BancWare models
Used in conjunction with FHLBs other risk measures

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Contact Information
ALCO Partners, LLC
15 Fairway Drive, Novato CA 94949
Mike Arnold, Principal (415)
Bruce Campbell, Principal (949)