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**FHLB Income-Based IRR Measurement: Alternative Approaches and Issues**

- Potentially Useful Lessons from the Private Sector -

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**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

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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

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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

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**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

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**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

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**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

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**Classification of Income Based IRR Measurement**

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**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.

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**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

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**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.

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**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

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**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

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**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

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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

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**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

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**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

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**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

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**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

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**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

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**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

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**SMEAR Example: Income-Based Simulation Results**

Step 1: Calculate NII-EBS in each scenario and period

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**Transforming Income Simulations to Risk Measures**

Step 2: Calculate DNII-EBS relative to FWD case

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**Transforming Income Simulations to Risk Measures**

Step 3: Plot the relative values

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**Transforming Income Simulations to Risk Measures**

Step 4: Connect the dots

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Decomposing the Income-Based IRR Measure: Example**

Total IRR = Repricing Risk Options Risk Total IRR = Repricing Risk + Options Risk

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**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

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**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.

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**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

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**Decomposing income-based IRR: Option Risk**

Classification Scheme for Graphs to Follow

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**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.

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**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.

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**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.

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**Decomposing income-based IRR: Option Risk**

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**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?

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**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

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**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

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**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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**15 Fairway Drive, Novato CA 94949**

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

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