The Methodology of Value-at-Risk for the Retail Banking Sector

Fred Poorman, Jr., CFA

email: fpoorman@almnetwork.com

Disclaimer & Reminder

• The opinions are solely those of the author, as such, they do not represent the views of Deutsche Bank. Disclaimer:

This information has been prepared solely for information purposes. It is not an offer, recommendation, or solicitation to buy or sell, nor is it an official confirmation of terms. It is based on information generally available to the public from sources believed to be reliable. No representation is made that it is accurate or complete or that any returns will be achieved. Changes to assumptions may have made a material impact on any returns detailed. Past performance is not indicative of future returns. Price and availability are subject to change without notice. Additional information is available upon request.

• Portions of this publication are used with the express permission of the copyright owners (the author and his publishers):

• Bank Accounting and Finance, published by Institutional Investor, Inc. and Aspen Publishers, Inc.

• Bank Asset/Liability Management, published by A.S. Pratt/Thomson Financial

• see Appendix A for additional information

• No part of this presentation may be reproduced in any form without the written permission of the copyright owner.

Presentation outline

• Applicability of VaR methodologies in the retail banking sector

• Stochastic rate generation processes in retail bank A/LM

• Efficient selection of portfolio-specific stress tests

• Utility of Earnings- and Value-at-Risk approaches

• Tradeoffs of EaR and VaR in retail banking

• Approach for management and disclosure of market risk for retail banks

Presentation considerations

• Questions: – Who uses VAR at their bank?

– For the trading book or structural or retail bank?

– Why do banks use this methodology?

– Why don’t banks use this methodology?

• Questions are welcome!

• Please note: – Based, in part, on data from U.S. retail banks

– Endnotes are available in attached article

U.S. SEC market risk disclosure formats (also retail bank market risk approaches)

1. Cash flow table, or Liquidity GAP, with Fair Value disclosures

• Circa 1980s

2. Sensitivity analysis of earnings, cash flow, or values based on hypothetical rate changes

• Usually +/- 100, 200, 300 bp or some variant

• Circa 1990s

• Still standard retail banking approach

3. Probabilistic analysis disclosing earning, cash flow, or value (Value at Risk) changes emanating from market movements

• Circa 2000s

Obiligatory VaR benefits slide

• Standard line - The VaR approach has benefits that surpass regulatory compliance:

1. A way to describe the magnitude of likely losses in a portfolio.

2. The likelihood of those losses.

3. A method to monitor, manage and control risk.

4. Efficient selection of portfolio- (or bank-) specific risk scenarios. This is an elusive goal of stress-test analysis.

Additional VaR benefits slide

• Also consider these benefits:

1. Efficient selection of portfolio-specific “worst case” stress test.

1. This benefit deserves additional attention

2. Determination of directionality in interest rate risk management

1. Useful for active risk management

2. Clarify investor expectations

Additional VaR benefits slide

• EaR is equally important

– A way to describe the magnitude of fluctuations in earnings.

– What are chances of realising budgeted income given market conditions

– In what scenarios do you make budget?

– What scenarios should be hedged?

Requisite VaR methodologies slides

1) Parametric methods variously referred to as the correlation-covariance method, or the delta-normal or delta–gamma approaches. J.P. Morgan standardized this as RiskMetrics in 1994. This is typically a closed-form process and is used by some financial firms to analyze and disclose market risk.

Requisite VaR methodologies slides

2) Historical simulation, or extreme event stress tests. This methodology replicates market risk factors.

• The 1987 U.S. equities market crash.

• The 1998 Russian, Asian, and Long Term Capital Management crises.

• Rapid interest rate increases, in the following years:

– 1994, when the Fed Funds rate increased 250 bps.

– 1977-1981, when the Fed Funds rate increased over 1500 bps in forty-eight months.

• Rapid interest rate decreases, in the following years:

– 2001, when the Feds Fund rate decreased by 475 bps.

– 1991-93, when the Fed Funds rate decreased 500 bps in twenty-four months.

Requisite VaR methodologies slides

3) Monte Carlo or Quasi- Monte Carlo methods, perhaps more correctly a stochastic process. At its simplest, Monte Carlo simulation is the procedure by which random future rate paths are generated and used to derive path dependent cash flow schedules. It uses stochastically generated rate paths and associates cash flows to value interest rate contingent financial instruments (Linsmeier, 2000 and Rahl, 2000).

Applicability of VaR for retail banks

• Trading portfolio assets tend to have well-defined cash flow characteristics, with standardized cash flow mapping, and readily available correlations and cross-correlations

• Retail bank balance sheets, in comparison, are replete with financial instruments with either indeterminate and/or interest rate contingent cash flows

• More intricate examples include credit card and line of credit loan types, also seen in investment portfolios in securitized equivalents and non-maturity deposits

• Due to the predominance of option-laden instruments on bank balance sheets, closed-form solutions are not typically used for the structural bank, except in stylized examples (Ho, 1999).

Applicability of VaR for retail banks

• Extensive discussions of instrument-level modeling specifics are outside the scope of this paper, but a brief explication of the approach rendered is germane.

• Modeling and valuing structural balance sheets can be problematic, as one class of financial instruments, non-maturity deposits (e.g. demand, savings, and money market deposit types) comprise up to fifty percent of bank liabilities.

• Lacking a public market, there is no general consensus regarding appropriate modeling and valuation methodologies among marketplace participants, regulators and academia for non-maturity deposits.

• See appendix for VaR for Core deposits slides

A/LM & VaR

• Within the banking sector, the primary method for analyzing and managing market risk is usually referred to as Asset/Liability Management (A/LM).

• The goal of successful A/LM is seen as “ensuring that net interest income and the net economic value of the balance sheet remain positive and stable under all probable scenarios (Essert, 1997)”

• For retail banks, use risk to economic capital, referred to as Economic Value of Equity (EVE)

• Advanced vendor-built A/LM models used by the banking sector are capable of producing VaR analyses utilizing historical and/or stochastic process approaches

A/LM & VaR

• A necessary and integral component of a VaR-based bank A/LM approach is a suitable interest rate model.

• Minimum requirements for utilization of a stochastic interest rate model include: – Creation of arbitrage-free forward term

structures of interest rates.

– Capability of utilizing historical or implied market volatilities.

Stochastic rate generation processes in retail bank A/LM

• Numerous interest rate models have been proposed for evaluating rate-contingent financial instruments

• The model used and discussed herein is the well-known continuous single factor Black-Derman-Toy (B-D-T) model (Black, 1990)

• In the following analysis, the B-D-T model is implemented with user-defined selection of: – Short volatility – Speed of the reversion process, via selection of the

long and short periods.

Stochastic rate generation processes in retail bank A/LM

• The selection of a stochastic rate component is important in generating and valuing rate-contingent cash flows, primary choices include:

• A Monte Carlo simulator – Random

– Structured

• A lattice based model, primarily: – Binomial (rates go up or down)

– Trinomial (rates go up, down, or remain stationary).

Other rate considerations

• Historical vs. Implied volatility

• Which volatility?

– Treasury

– Agency / Corporate

– Mortgage

– Swaps / Swaption (current vol. choice of many)

• What type of volatility model?

– Normal / Lognormal

– Curve / Mean reversion

Interest rates change

• Interest rates change

• Not all rates move together

– Short-term rates and long-term rates may move in different directions

– Key rate durations from the swap curve serve as a good bank risk proxy

Rate scenario generation

• Linear Path Space (LPS) is a sampled binomial tree imposed on a trinomial lattice

– Key rate duration approach, with seven points on yield curve

– Seven sources of IRR, based on key rate durations, may be bank specific

– All points may have unique volatility

– Compare to sensitivity analysis, usually one IRR source, parallel shift

Rate scenario considerations

• For retail bank A/LM, prefer sampled lattice utlising market-based volatilities (can use vol shocks)

• Computational time is non-trivial

– 360 month binomial lattice has 2360 interest rate paths

– LPS is sample of all possible paths

– 269 scenarios covers 89.9% of these possibilities

– These are ordered in terms of likelihood

• Management time is valuable

– 101 scenarios covers 91.3% of 269 scenarios

– 89.9% * 91.3% > 80%

– 80/20 rule applies

Short rate scenarios

• Averages of 3 month rates generated (Spring 2000 displayed)

• Non-parallel yield curve shifts are the rule, not the exception

• Rate rate changes of 100 bps, over time, correspond to one std. dev.,but only for a single yield curve point

Short rate examples

• 3 month rate examples,

– Base

– Up likely

– Down likely

– Up extreme

– Down extreme

– From last year, good for backtesting

Projected 3 month LIBOR, Mar 2000, 20% vol

%

2%

4%

6%

8%

10%

12%

14%

Apr-00

Jul-00Oct-00

Jan-01

Apr-01

Jul-01Oct-01

Jan-02

Base Case Up likely Down likely Up extreme Down extreme

Short rate examples

• 3 month rate examples,

– Base

– Up likely

– Down likely

– Up extreme

– Down extreme

– From 2000, good for backtesting

Projected 3 month LIBOR, Mar 2000, 40% vol

%

2%

4%

6%

8%

10%

12%

14%

Apr-00

Jul-00Oct-00

Jan-01

Apr-01

Jul-01Oct-01

Jan-02

Base Case Up likely Down likely Up extreme Down extreme

Sample yield curves April ‘01 base rolled to March ‘04, 20% vol.

• Projected rates, 3 years forward – Base

– Up likely

– Down likely

– Up extreme

– Down extreme

– From April 2001

Two sample banks

• Banks scaled to $20 billion in assets

• March 2001 balance sheets, rates, volatilities

• Bank 1

– Earnings at Risk exposure is to high level of rates, especially at the short end of the curve

– Core deposits < 50% of funding

• Bank 2

– Earnings at Risk exposure is to low level of rates, especially at the short end of the curve

– Core deposits > 50% of funding

Bank 1 VaR disclosure

A sample market risk disclosure should read: Our lifetime VaR limit for the Economic Value of Equity is 25% … we calculate lifetime VaR… at the 99% confidence level (two tailed). Table 2

VaR Profile: March, 2001

Lifetime VaR% Quarter-end

Interest Rate Risk 16.8%

Bank 1 VaR (EVE) profile

0%

25%

50%

75%

100%

2,323,329 2,479,811 2,636,294 2,792,776 2,949,258 3,105,740 3,262,223 3,418,705

Probability

Cumulative Probability

Standard deviations <-3 -3 to -2 -2 to -1 -1 to mean mean to +1 +1 to +2 +2 to +3 +3 to +4Market Value 2,323,329 2,479,811 2,636,294 2,792,776 2,949,258 3,105,740 3,262,223 3,418,705 Probability 1% 4% 13% 18% 46% 18% 0% 0%

Cumulative Probability 100% 96% 83% 65% 18% 0% 0% 0%

Measuring risk

• Disclosure – Trend is toward ever-increasing transparency

• Basle Principle 13

– U.S. GSEs have agreed to greater disclosure – Equity analysts need disclosure due to Reg FD – Enron and Global fiascos suggest more transparent

risk disclosures are appropriate

• Supplemental disclosure and analysis – A measure of directionality – A valuation benchmark – The goodness of fit, or R2, of the measure.

Bank 1 VaR disclosure Benchmark is 5 year swap rate

Economic Value of Equity

y = -7E-06x + 25.931R2 = 0.9354

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

2,000,000 2,250,000 2,500,000 2,750,000 3,000,000 3,250,000

EVE, data points sized based on probability

Fwd.5 year rate

Bank 1 EaR disclosure

Our EaR analysis and sample disclosures use the same format and bank previously used

for the VaR analysis. A sample EaR disclosure should read: Our first year EaR limit for

Net Interest Income (NII) is 10% … we calculate first year EaR … at the 99% confidence

level.

Table 3

EaR Profile: March, 2001

First year EaR % Quarter-end

Interest Rate Risk 5.5%

Bank 1 EaR (NII) profile

0%

25%

50%

75%

100%

583,409

594,758

606,107

617,456

628,805

640,154

651,503

662,852

P robabi l i ty

Cumulative

P robabi l i ty

Standard deviations <-3 -3 to -2 -2 to -1 -1 to mean mean to +1 +1 to +2 +2 to +3 +3 to +4Net Interest Income 583,409 594,758 606,107 617,456 628,805 640,154 651,503 662,852 Probability 1% 1% 18% 31% 28% 21% 0% 0%

Cumulative Probability 100% 99% 81% 50% 21% 0% 0% 0%

Bank 1 EaR disclosure Benchmark is 12 month LIBOR

Net Interest Income

y = -9E-05x + 63.274R2 = 0.9416

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

550,000 600,000 650,000 700,000 750,000

NII, data points sized based on probability

1 year rate

Risk highlights

• A short-term rate decrease is favorable from an earnings and a valuation standpoint. Note that this is not necessarily always the case.

• The selection of risk mitigation strategies, including off-balance sheet hedging may be dependent on income/value tradeoffs.

• Different benchmarks, or key rates, may be significant for value and earnings measures, and for different banks.

• Bank A in isolation is a useful case study. Utility preferences are established within a comparative framework.

EaR & VaR profiles

Comparative

Analysis

EaR

(99%)

Directional

risk: EaR

EaR R2 VaR (99%) Directional

risk: VaR

VaR R2

Bank A 5.5% Increasing

short rates

over 1-year

horizon

0.94 16.8% Increasing

intermediate

rates over

long-term

horizon

0.94

Bank B 10.5% Decreasing

short rates

over 1-year

horizon

0.99 2.6% Uncertain 0.14

Utility preferences and optimal frontier

• Bank A would be favored over Bank B by those investors preferring less EaR volatility.

• Investors preferring less VaR volatility would prefer Bank B to Bank A.

• Short-term, earnings-focused investors with a bias towards continued decreases in short rates would, ceteris paribus, prefer Bank A to Bank B.

• Alternatively, short-term, earnings-focused investors with a bias towards increases in short rates would, ceteris paribus, prefer Bank B to Bank A.

VaR approach: conclusion

• EaR-VaR Risk benefits: – Metrics assist in identifying risk tolerances – “Best practices” approach quantifies risk – More realistic methodology for modeling interest rate

changes – Effective risk management = potentially greater earnings

for given level of risk – Enhanced disclosures – Better, more stable earnings with better risk management

practices and disclosure should, ceteris paribus, result in increased valuations

• Understand limitations of this approach

Appendix A

• See attached article for references • This paper was the winning entry in the Glenmede

Investment Insight Award (2001) of the Financial Analysts of Philadelphia, an AIMR chapter and is available at www.faphil.org

• Thanks to: – Tom Ho for comments and insights on an earlier version

of this paper – Glenmede Trust and the Philadelphia Chapter of AIMR

• e-mail your comments on this topic to: fred.a.poorman@db.com

Account-level VAR Applications

• MBS & Mortgage Accounts

– Essential prepay factor is refi advantage

– Benchmark SVAL MBS valuation to Bloomberg

– Bloomberg OAS considerations

– LPS OAV/OAS considerations

– Compare calculation of option costs

• Core & Time Deposit Accounts

– Balances driven by spread to market rates (like refi)

– Benchmark to market transactions

– Less sophisticated analytical approach

Account-level VAR Applications Average 3 month LIBOR

• MBS example – Consider

value distribution and negatively convex profile

– Compare to bank and derivative profiles

Account-level VAR Applications LIBOR CMO floater

• MBS example – Consider

value distribution and negatively convex profile

– Compare to bank and derivative profiles

VaR analytics for Transaction Deposits: Industry Models:Premium Estimates for 101 Scenarios

• Valuation is consistent with market and model results

• Extreme value scenarios are an efficient, portfolio-specific manner for stress testing

• Review zero vol scenario,capability to review full scenario detail is imperative

• Risk profile suggests hedging strategies

VaR analytics for Transaction Deposits: Industry Models: Probability

Distributions • Transaction premium

is primarily comprised of non-time deposit components

• Compare to:

– MBS distributions

– Loan portfolio profile

– Institution VaR

Std dev. <-3 -3 to -2 -2 to -1 -1 to meanmean to +1 +1 to +2 +2 to +3 +3 to +4$ Price 104.7 105.5 106.3 107.2 108.0 108.8 109.6 110.4 Probability 1% 4% 12% 19% 46% 18% 0% 0%

Cum. Prob. 99% 95% 83% 65% 18% 0% 0% 0%

Retail Deposit Price Distribution

0%

25%

50%

75%

100%

104.7 105.5 106.3 107.2 108.0 108.8 109.6 110.4

Probability

Cum. Prob.