VaR for Retail Bank, Core deposits in Appendix

1. The Methodology of Value-at-Risk
for the Retail Banking Sector
Fred Poorman, Jr., CFA
email: fpoorman@almnetwork.com

2. 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.

3. 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

4. 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

5. 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

6. 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.

7. 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

8. 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?

9. 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.

10. 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.

11. 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).

12. 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).

13. 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

14. 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

15. 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.

16. 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.

17. 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).

18. 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

19. 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

20. 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

21. 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

22. 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

23. Short rate examples
Projected 3 month LIBOR, Mar 2000, 20% vol
• 3 month rate
examples, 14%
– Base 12%
– Up likely
10%
– Down likely
8%
– Up extreme
6%
– Down
extreme 4%
– From last year, 2%
good for %
backtesting
Ap
Ju
Jan
Ap
Ju
Jan
Oc
Oc
l-0
l-0
t-0
t-0
r-0
r-0
-01
-02
0
1
0
1
0
1
Base Case Up likely Down likely Up extreme Down extreme

24. Short rate examples
• 3 month rate Projected 3 month LIBOR, Mar 2000, 40% vol
examples,
14%
– Base
12%
– Up likely
– Down likely 10%
– Up extreme 8%
– Down 6%
extreme
4%
– From 2000,
good for 2%
backtesting %
Ap
Ju
Jan
Ap
Ju
Jan
Oc
Oc
l-0
l-0
t-0
t-0
r-0
r-0
-01
-02
0
1
0
1
0
1
Base Case Up likely Down likely Up extreme Down extreme

25. 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

26. 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

27. 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%

28. Bank 1 VaR (EVE) profile
100%
75%
50%
Probability
Cumulative Probability
25%
0%
2,323,329 2,479,811 2,636,294 2,792,776 2,949,258 3,105,740 3,262,223 3,418,705
Standard deviations <-3 -3 to -2 -2 to -1 -1 to mean mean to +1 +1 to +2 +2 to +3 +3 to +4
M Value
arket 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%
Cum ulative Probability 100% 96% 83% 65% 18% 0% 0% 0%

29. 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.

30. Bank 1 VaR disclosure
Benchmark is 5 year swap rate
Fwd.5 year rate
Economic Value of Equity
10.00
9.00
8.00
7.00
6.00
5.00
4.00 y = -7E-06x + 25.931
R 2 = 0.9354
3.00
2.00
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

31. 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%

32. Bank 1 EaR (NII) profile
100%
75% P ro babi l i ty
Cum ul ati ve
50%
P ro babi l i ty
25%
0%
9
8
7
6
5
4
3
2
40
75
10
45
80
15
50
85
3,
4,
6,
7,
8,
0,
1,
2,
58
59
60
61
62
64
65
66
Standard deviations <-3 -3 to -2 -2 to -1 -1 to mean mean to +1 +1 to +2 +2 to +3 +3 to +4
Net 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%

33. Bank 1 EaR disclosure
Benchmark is 12 month LIBOR
1 year rate
Net Interest Income
10.00
9.00
8.00
7.00
6.00
5.00
4.00
y = -9E-05x + 63.274
3.00 R 2 = 0.9416
2.00
550,000 600,000 650,000 700,000 750,000
N II, data points sized based on probability

34. 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.

35. EaR & VaR profiles
Comparative EaR Directional EaR R 2 VaR (99%) Directional VaR R2
Analysis (99%) risk: EaR risk: VaR
Bank A 5.5% Increasing 0.94 16.8% Increasing 0.94
short rates intermediate
over 1-year rates over
horizon long-term
horizon
Bank B 10.5% Decreasing 0.99 2.6% Uncertain 0.14
short rates
over 1-year
horizon

36. 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.

37. 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

39. 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

40. 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

41. Account-level VAR Applications
Average 3 month LIBOR
• MBS example
– Consider
value
distribution
and negatively
convex profile
– Compare to
bank and
derivative
profiles

42. Account-level VAR Applications
LIBOR CMO floater
• MBS example
– Consider
value
distribution
and negatively
convex profile
– Compare to
bank and
derivative
profiles

43. 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

44. VaR analytics for Transaction Deposits:
Industry Models: Probability
Distributions
• Transaction premium
Retail Deposit Price Distribution
is primarily comprised
of non-time deposit 100%
components
• Compare to: 75% Probability
Cum. Prob.
– MBS distributions
50%
– Loan portfolio
profile
25%
– Institution VaR
0%
104.7 105.5 106.3 107.2 108.0 108.8 109.6 110.4
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%