Edward J. Kane

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04-6

• Understanding and Measuring FSF Capital
• Basel Capital Requirements
• Limitations of Value at Risk

• Edward J. Kane
• Boston College

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Ownership Capital acts as a shield against loss
for nonowner stakeholders, including guarantors.
Its thickness protects them as long as it retains
positive value.
I. MEASURING CAPITAL

• When losses move through the Chain of Corporate
  Stakeholders in a workout situation, source of
  capital transitions from original owners to less
  and less senior creditors.
• The Transitioning is governed by Enforceable
  Contracting Protections subordination
  covenants collateral escrowed balances.
  Enforceability varies across jurisdictions and
  contracting protocols.

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A bank needs to post enough capital to support
its unhedged risks. Its depositors and other
stakeholders must be satisfied with the
combination of enterprise-contributed and
taxpayer risk capital that cushions or buffers
the net or enterprisewide risk exposure the bank
passes through to them.
Megatheme Risks that are Not Perfectly Hedged
Need Capital Support
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In Oct. 1999, John Reed, then-CEO of Citigroup
said Our objective is to operate with more
capital than were going to need --ever- -so that
you never have to deal with the markets
perception of not having enough capital. Let me
tell you, Im going to be long dead before were
ever undercapitalized again.Lesson he learned
from the near-failure of a major hedge fund
concerns the necessity of looking at
second-order exposures to risks taken by the
banks counterparties Necessary capital is
that which is necessary to take a hit and still
be able to operate effectively within the
marketplace... Citicorp had no direct exposure
to Long-Term Capital Management, the hedge fund
that flirted with a failure in 1998. But
Citibank was the primary lender to half the
companies that came to Long-Term Capitals
rescue... None of these firms had the capital
to sustain the losses.
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The Size of the Capital Shield Differs for
Different Stakeholders. Rules for Calculating
Thickness of Protection Vary for Differently
Prioritized Stakeholders in a Bank.

• 1. For subordinated debtholders
• 2. For foreign branch depositors and uninsured
  domestic depositors
• 3. For FDIC.

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WORKOUT EXAMPLE Crippled
Bank shows the following tangible Balance Sheet,
constructed according to GAAP.
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• Exercise Lets calculate the Capital Shield
  protecting various stakeholders (subordinated
  debtholders, uninsured depositors, BIF) assuming
  net intangible assets are worth 15 in market
  value and all tangible items are booked at market
  value
• a. according to GAAP?
• b. according to market-value accounting
  principles?
• Suppose regulators apply an average risk weight
  of 90 percent to the banks tangible assets.
  Would the banks capital be adequate?
• Suppose that the Market Value of the Banks
  assets is only 75.
• How much of the banks GAAP assets would have to
  be sold to cover a 100 run by the uninsured
  depositors?
• b. What would the banks GAAP balance sheet
  look like after paying off all uninsured
  deposits?
• Under what circumstances would new stockholders
  be willing to invest in a bank that has fallen
  into tangible insolvency?

100 - 95
115 - 95
ANS. Each dollar of book value sold generates on
75, so 4(25)/3 in GAAP assets have to be sold.
ANS. Assets 66.67.TNW -3.33
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Creditors May be Fooled by Accounting Façade that
Weak Banks Erect to Keep Capital Looking Good
Long After it is First Exhausted
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Evidence on How Fast Capital Position Can Change
1999
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FDIC Guarantees and other elements of the
Government Safety Net absorb some of each banks
risk Creditor protection KtKEtKGt.To
protect FDIC reserves and taxpayer wealth from
bank risk-shifting, government regulators engage
in various supervisory activities monitoring
(including on-site examinations) enforcing
risk-based requirements for minimum capital and
dividend restrictions issuing cease-and-desist
orders for unsafe and unsound practices
replacing poor or dishonest managers.
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Both government and stockholder components of
Bank Capital lack transparency. We have covered
many ways FSFs can use accounting leeway to
confuse regulators and lessen the observability
of adverse changes in net worth

• 1. Delay asset writedowns restructure hopeless
  loans
• 2. Employ optimistic loss reserving
• 3. Engage in gains trading or book nonrecurring
  items
• 4. Deny materiality of adverse events
• 5. Use residual Z tranches of securitizations
  and structured derivative transactions to mask
  losses and risk exposures.

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Government Guarantees Negate the Pin-Prick Test
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II. Basel Protocols Buy into a Dangerously
Inflexible Way to Assess Capital Adequacy

• To keep government-contributed capital from
  trending upward, Regulators and Supervisors must
  continually adapt their rules, monitoring,
  penalties, and administrative procedures to
  overcome clients political clout and innovations
  in bank concealment capabilities.
• RBC supervision has proved highly vulnerable to
  dynamic deterioration risk

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Capital Regulation uses the Metaphor of a RISK
BUDGET that is Distributed over a series of RISK
BUCKETS

• What is budgeted is ownership capital.
• To support their net risks, management must hold
  sufficient capital and allocate it across the
  specific positions that expose the institution
  and its stakeholders to loss.
• Modern regulators double-check the adequacy of a
  banks budget. They set and enforce risk-based
  minimum requirements for ownership capital.

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• In principle, the amount of an institutions
  enterprisewide exposure to loss in any asset or
  liability position (Ai or Lj) that capital
  should be asked to cover varies with the loss
  exposure of the asker. Each stakeholder may
  express its requests as fractions (wi) of each
  positions value 0?wi ?1.
• Capital is adequate for a given stakeholder when
  
• In practice, weights and position values are
  sensitive to correlations and hard-to-observe
  Information Events.

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Besides Credit Risk, Capital Needs to Cover Other
Kinds of FSF Risks

• CREDIT Risk that borrower will default.
• LIQUIDITY Risk that bank wont meet its
  obligations without selling assets at
  below-market prices.
• MARKET Risk from shifts in interest rates and
  foreign exchange rates.
• PRICE Risk from changing values in securities
  portfolio
• REPUTATION Risk of bad publicity.
• STRATEGIC Risk of making bad business decisions.
• OPERATIONAL Risk of trouble from inadequate or
  failed internal processes, people, and systems or
  from external events.
• REGULATORY Risk of adverse changes in the Rules
  of the game

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Shaping a Standard How the Basel II capital rule
has evolved
1999
2000
2001
2002
2003
July
April
June
Jan.
Final rule pushed back to yearend 03,
with implementation set for yearend 06
Third proposal released
First broad outline proposed
Second, more detailed plan released. Final rule
due yearned, to take effect in 04
Oct.
Final rule pushed back to mid-04, but late
06 effective date confirmed
April
First study of potential impact conducted
Oct.
June
Third impact study launched
Basel announces plans for a third proposal,
expected in early 02, and postpones
Source American Banker Online (10-21-03)
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Final outline of the new rules
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• Basel I and II require internationally active
  banks to set aside specified capital amounts to
  support their on-balance-sheet and
  off-balance-sheet risk exposures. BIS system
  seeks

• (1) to impose comprehensive capital
  requirements (i.e., to factor in off-balance
  sheet risks) and
• (2) to do so globally in standardized (i.e.,
  equal-opportunity) fashion in all major
  financial environments.
• Previously, capital requirements had been linked
  exclusively to accounting measures of a banks
  total on-balance-sheet assets so that
  Off-Balance-Sheet items expanded.
• Regulatory Intervention System of Risk-Based
  Capital Requirements (RBCR). Prior to RBC
  requirements, off-balance sheet activity avoided
  the burden of capital requirements on the
  business and the risks not being booked on
  balance sheet.

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RBCR use simplistic ad hoc weights -- not
market-based weights

• Authorities assigned a unit risk weight to
  ordinary private loans.
• Judgmentally assign weights for other positions
  (vi) as fractions.
• Risk-Weighted Assets (RWA)
• Two-Tier RBCR w1 (RWA) and w2(RWA)

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• To risk-weight derivatives positions, a two-part
  method was used
• 1) Choose a conversion factor, (ci) converting
  each OBS position to an on-balance-sheet credit
  equivalent.
• 2) Then apply a judgmental credit-risk weight
  (vi) that determines a capital requirement
  appropriate for the credit-equivalent amount.

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• Except for swaps, conversion factors and risk
  weights are limited to 0, 20, 50, and 100.
• No formal market testing is done to justify
  these conversion factors and risk weights.
• Lack of accountability lets political pressure
  influence weighting. E.g., risk weights for
  subprime mortgages and for securities issued by
  national governments are kept unduly light.
• RBCR are so simplistic that their burden is so
  easily circumvented that one has to challenge
  either the honesty or the competence of officials
  willing to rely predominantly on this supervisory
  protocol.

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OBFUSCATION OF WEAKNESSES BY AUTHORITIES
WELL, YA BETTER LARN HOW IF YORE GONNA BE A
GOVERNMENT OFFICIAL !!
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VaR

• Mean-Variance Portfolio Theory has Spawned a
  Formal Theory of Risk Budgeting and Stress
  Testing whose Starting Point is a concept called
  Value-at-Risk VaR

VaR is the maximum potential loss in net
portfolio value (NW) that can occur over a
specific horizon (e.g., two weeks) at a specified
level of statistical confidence (e.g., 99) VaR
asks managers to locate a place in the negative
tail of the distribution of future returns
whose chance of occurrence is remote enough to
neglect. Idea is to capture a worst-case
scenario beyond which owners need not expect to
cover losses.
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Weekly Profits and Losses of a Hypothetical
Financial InstitutionFrequency Distribution of
Weekly Results
Query Can you locate the 5 VaR for this
example?
of weeks
-15 -10 -5 0 5 10 15 20 25 30
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Foundations

• 1. Disaggregation of components of R Managers
  distinguish N profit centers, whose returns sum
  to the aggregate FSF Return Rt.
• 2. Calculation Rt wjtRjt ideally,
  theportfolio weight wjt MVjt/MVt

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Although it is an aggressive assumption, if
returns on individual positions follow a
stationary and joint normal distribution,
defining VaR is a straightforward statistical
exerciseVaR the mean return (?) minus c
standard deviations (c?).For 5 VaR, is c
1.95 or 1.69?Self-Study Query What does
stationarity entail?
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The rub is that the true distribution of returns
is unknowable and varies over the business cycle.
At any point in time, its true mean (?) and true
standard deviation (?) can only be estimated.
Just as with Credit Scoring, the
comprehensiveness and relevance of the exercise
must be challenged.

• Estimation imposes a demand for extensive input
  data
• 1. The initial value, mean, and standard
  deviation of returns on every tangible and
  intangible position.
• 2. A correlation matrix detailing how each
  return correlates with the others.

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The methods assumptions are unduly strong and
unduly static

• When the method is accepted without question,
  historical data can be used straightforwardly to
  estimate
• Rj
• ?j
• ?ij
• The this building-block information can be
  plugged into portfolio Rt and formulas.

However, the fragility of the underlying
assumptions require users to have better
understanding, expertise, and systems than their
staff may actually possess.
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Pluses and Minuses of Using VaR?

• A framework for Risk Budgeting and Stress
  Testing (as in treadmill testing for heart
  trouble)
• VaR is an alleged bad case to worry about,
  calculated as the estimated loss that might occur
  in (say) 99 of all ten-day periods, e.g., 100
  million
• Example JP Morgan once reported that its daily
  trading VaR averaged 15 million at a 95
  confidence level, i.e., it expected to lose 15
  mil. or more on 5 of all trading days
• But it is not a worst case. It is the least of
  the worst cases. A potential source of false
  reassurance
• 1) It omits the size of the exposure in the
  tail
• 2) It neglects changes in correlations and
  volatility that might come into play
  in crisis episodes
• 3) Blindness to periods beyond the horizon
• 4) Neglects effects of collateral, insurance,
  etc.

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A stress test examines an FSFs vulnerability to
particular categories of market events. It
estimates how the value of the firms positions
would change if an exceptional but plausible
change in market conditions were to occur. Each
hypothetical shock is based on a different
scenario and most useful for products and
markets for which VaR seems inadequate. Shocks
are usually sized with reference to historical
patterns of events in past crisis episodes. For
example, movements in interest rates or
credit-swap spreads during
1. The 1998 Russian Crisis 2. The 1987
stock market crash.
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1995 Reform Basel Committee on Bank Regulation
Mandated Value at Risk (VaR) to Find Capital
Required to Cover Risk Exposure in Trading Book

• The maximum of
• the VaR computed yesterday, or
• a 60-day moving average of VaR, multiplied by a
  constant whose minimum is 3.0
• An additional charge for notable credit risks
• Plus a penalty for observed inadequacies in
  internal VaR model (Ideally, the penalty
  structure should feed explicitly into return
  distributions used in VaR calculations.)

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• Like credit scoring and pvbp,VaR appears more
  elegant than it is. It actually represents a
  crude statistics-101 way for FSF managers to
  figure out how much capital they should hold to
  cover adverse movements in their institutions
  total return, Rt.
• It is restrictive to measure an FSFs
  enterprisewide risk as the ? of its return
  distribution, ft(Rt), over a managerially-specifi
  ed time horizon, k.

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• The stationarity assumption lets us calculate VaR
  over a period of n days as vn times the daily
  VaR.
• It is dangerous to assume that returns on every
  business day come as independent draws from the
  same distribution
• Such an assumption neglects event risk and
  evidence of day-of-the-week and intraday effects

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In practical applications, VaR focuses
principally on justifying a capital level by
itemizing and aggregating elements of credit risk
and IRR in a banks tangible positions over a
particular horizon k.

• In most uses, VaR focuses on credit or market
  risk and pvbp of tangible positions and neglects
  operational risk (including ethical risk),
  liquidity risk, and risk due to
  underdiversification (concentration risk).
• In the end, the reliability of VaR estimates
  depends on the sincerity with which data are
  collected, adjusted, and processed.
• CROs are often told what the CEO wants the VaR to
  be.

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VaR Can Measure Leverage Source Risk (July 2004)
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Steps in Implementing VaR

• Consolidate mark-to-market positions into one
  database
• Set time horizon (period over which portfolio
  composition is presumed not to change)
• Obtain necessary data
• Generate and validate a frequency distribution
  of mark-to-market returns
• Parametric (variance-covariance)
• Historical
• Stochastic simulation (Monte Carlo)
• Historical simulation
• Given confidence level, pinpoint the VaR and
  treat it as the endpoint of an out-of-sample
  fiducial interval

or combinations
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Usefulness of VaR is Challenged by Stylized Facts
of Credit Losses

• Credit loss distribution is highly asymmetric.
  Relatively fat-tailed.
• Credit portfolios hard to trade/hedge, especially
  during bad times.
• When storm comes, ride it out.
• Observable credit events arrive at low frequency.
  Data sparse and badly measured
• Implications
• Sample should cover a long horizon, but one year
  is standard.
• Direct validation of tail behavior impossible.

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• ANSWER KEY TO EXERCISE FOR WEEK 11
• Part a. Definition A quantile is a variate
  value that divides the density of a frequency or
  probability distribution of potential outcomes
  into specified proportions. For example, the 5th
  percentile of distribution is the value that
  partitions the density between the 5-percent
  lowest outcomes and the other 95 percent.
• The X-percent VaR of a portfolio with a known
  distribution is the X-percent quantile of the
  probability distribution of returns over a given
  horizon. In practice where one works with an
  unknown distribution, VaR is estimated as the
  lower bound of a one-sided confidence interval.

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Dangers in using VaR may be likened to those in
setting up a VCR to record a program on a distant
day vs. TIVO. Four items must be set, knowing
that uncontrollable events like interim schedule
changes, power failures, or burglaries may foul
up the result

• 1. A channel The frequency distribution over
  which we assume the signal of an FSFs net
  returns travel each day
• 2. A targeted number of days ahead to ask the
  mechanism to look at the signal a cumulative
  return horizon of (say) 10 consecutive days
• 3. An interval within which the channel is to be
  sampled as long as the signal remains above a
  management-selected cut-off level of tolerable
  deterioration
• 4. A safe speed (safety factor) at which to spin
  the amount of tape available (capital) so it
  doesnt run out during the program.

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Item 1. Verifying the choice of frequency
distribution assumed to govern daily returns is a
technical statistical issue.

• Verification employs simulation or estimation
  techniques
• Approximation error is inevitable and the size of
  such errors is seldom adequately researched

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Many Institutions Use Their Own Historical
Profile of Weekly Profits and Losses Frequency
Distribution of Weekly Results
of weeks
-15 -10 -5 0 5 10 15 20 25 30
35
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Item 2. In practice, choosing a return horizon
is a problem for joint managerial and regulatory
optimization. The horizon can be shorter

• a. The less risk-averse managers happen to be
• b. The more quickly and more cheaply management
  can raise outside capital to restore depletion in
  an institutions capital shield.

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Item 3. Choosing the time when the machine turns
it self off is partly a technical statistical
issue and partly a matter of management tradeoffs.

• a. Statistically, the cut-off level is a
  quantile or confidence bound that is
  calculated under the (unproven) assumption that
  daily returns are independently and identically
  distributed another under-researched source of
  approximation error.
• b. The more risk averse is management and the
  higher the cost of raising additional capital
  quickly, the more conservatively the lower
  confidence bound (L) should be set
• L ? - c?

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Item 4. Regulators interpose a multiplicative
safety factor m (conventionally3) to require
capital to be several times the cutoff level of
tolerable losses over the target
horizon.Regulatory VaR
Statistical VaR
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Simplistic Version of VaR is the Delta-Normal
Method. It aggressively assumes

• 1. ft(Rt) is normal.
• 2. ft(Rt) is stationary across time periods
• ft(Rt) f(Rt)
• 3. Returns on the firms individual positions
  Rjt(j1, , n) are independently and identically
  (normally) distributed (I.I.D) across time.
• 4. Component building blocks of positions and
  activities that govern return generation are
  known and measurable.

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How to Fulfill Informational Needs of
Delta-Normal VaR?

• Query Can statistical staff estimate
• , , and from historical
  
• data?
• ANS. Yes and no.

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Why No? ANS Limitations

• 1. What to do about new products, new business
  units, new competitors, etc? Weak history of data
  points for new items.
• 2. Need to allow for known breakpoints in the
  FSFs strategy or implementation techniques.
• Need to identify and correct for variation over
  time in the applicability of VaRs
  more-aggressive assumptions.
• Limitations guarantee inaccuracy like using a
  one-inch ruler to measure a very large room.

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It is dangerous to accept the methods
assumptions even with repeated sensitivity testing

• 1. Normality econometric tests indicate that
  returns on financial instruments (esp., stock)
  are generally more fat-tailed than the normal.
• 2. Stationarity econometric tests and
  commonsense indicate that information flows can
  change the true distribution of returns sharply
  and suddenly. Even assuming ft(Rt) were normal,
  future and past means, standard deviations, and
  correlations are subject to unpredictable jump
  shifts (also called event risk).
• 3. Independence serial correlation of returns
  often exists inherent cyclicality in alternating
  gain and loss periods.
• 4. Nonlinearities caps, floors, and
  optionality. The existence of customer rights to
  prepay loans, make early withdrawals from
  deposits, and to draw down credit lines in an
  opportunistic manner undermines all three
  assumptions.

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• VaR neglects strategic risks tradeoffs between
  short-term (i.e., within the selected horizon)
  and long-term effects of managerial strategies on
  a banks creditworthiness structure and KGt.
• Lack of Robustness VaR fails to incorporate the
  exposures and penalties that arise when lower
  bound is violated.
• Scenario Analysis uses additional Ad Hoc Stress
  Tests as a crude way to address VaRs weaknesses.

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In Making VaR a Rising Star, Regulators May or
May not Have Good Intentions
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PROPERTIES THAT HAVE MADE VaR A STAR

• A single number
• Reproducible and understandable
• Quantifies the risk of entire portfolio
• Accounts for interactions among assets
• Acceptance by regulators makes it the de facto
  standard for measuring market risk

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Lets Compare it to Longins Supplement BVaR
Why VaR is also a Dim Star

• BVaR accounts for the size of expected losses
  beyond the VaR
• But BVaR is also a function of assumed
  probability density function of return fR and
  confidence level set in VaR calculation.

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• The denominator is the selected tail
  probability.
• If tail probability is low, but LGD is high,
  ranking on BVaR will be much worse than ranking
  on VaR

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• BVaR resembles (1-s) in credit-risk calculations.
  It puts the magnitude of extreme losses into the
  control strategy.
• For Fat-Tailed distributions, BVaR is critical
  because the difference between BVaR and VaR
  increases with tail thickness and may not
  disappear asymptotically with increases in the
  confidence level.

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Suppose (1) The one-percent 60-day VaR for Banks
A and B is 50 mil for both banks (2) But the
conditional expectation of bank B is twice that
of Bank A. Then the BVaR of Bank B will also be
twice the BVaR of Bank A.
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IV. Three Policy Issues In Relying On This System

• Issue A Is it safe for Regulators to Allow Bank
  Discretion to Estimate own VaR?
• Historical Method
• A sample of past periods (at least one year
  according to 1995 Basel Committee)
• Empirical estimation of volatilities and
  correlations, perhaps over broad asset categories
• Prospective Method
• Forecast values of volatilities and correlations
  based on predictions from an FSFs own
  internally developed econometric model
  (required for top 10 banks and allowed for
  others).

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• Reliance on internal models puts an intolerable
  weight on individual and firm ethics.
• External credit ratings (CRt) are a
  single-dimensional proxy for an institutions
  creditworthiness structure, are produced by
  conflicted parties, and do not identify the
  relative roles played by KGt and KEt in
  supporting CRt.
• (A proxy stands in for an unobservable variable
  that it is imperfectly correlated with).

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A banks economic capital is the sum of its
enterprise-contributed capital (KEtMVTtEit) and
government-contributed risk capital (KGt).

• Neither KEt or KGt is observable without error.
• Policy Concern Banks can extract hard-to-verify
  increases in KGt by engaging in clever forms of
  dealmaking and by cooking internal models to
  plausibly understate effects on KG.

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For each future date tk, VaR analysis maps a
banks economic capital (Kt) into a particular
probability pp(k,Kt) of becoming unable to
cover its liabilities at a particular date tk
e.g., p might equal .0001 for a horizon k of 6
months.For fixed Kt, p(k,Kt) implicitly
establishes a term structure of bank default
probability over the full range of possible
horizons but incorporates no vector of LGDs.
Focus On Single Horizon Is MYOPIC
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Issues Verification and Validation

• Bank managers would prefer a particular mix of KE
  and KG. Often, this entails a higher level of KG
  than a perfectly informed regulator could or
  would openly approve Rent-seeking
• Regulators are asked to devise and enforce
  capital requirements to guard against their being
  gamed by internal models.
• Banks need only claim to have validated their VaR
  models. Regulators lack tools for verifying such
  claims.

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Issue B. Even if VaR were perfectly measured,
Does it measure what Regulators Need to
Measure?VaR is only a starting point. The
continuing challenge for regulators in this Game
of Cat and Mouse is to incent the industry and
their own staffs to devise better and better
definitions, indices, and strategies for
measuring and controlling enterprisewide risk and
KG.
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Advances in Risk Management Come from Advances in
Understanding and Measuring Risk
Level of Sophistication
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VAR stress tests
IV
Portfolio Risk/Return
Finance Theory
III
Scoring Expected Loss
II
Generators of Improvements
Information Technology
Formal Loan Rating
I
Development Path
Subjective Instincts
time
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Regulatory Dialectic continually revises the
Contractual Architecture for Distributing
Possible FSF losses.

• Persistent use of any loopholes eventually
  triggers regulatory response. Basel II proposals
  focus on revising system negotiated at the BIS in
  Basel during 1987-1988 to close some of the
  loopholes authorities have observed since.

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Reasonableness of Hoping for a Clean Getaway
Feeds Policy Delays, Creating a Long Reregulation
Lag
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Basels Reregulation Lag Not until 6-99 did
Basel Committee on Banking Supervision Formally
Propose

• to introduce external credit risk assessments
  from credit rating agencies so as to reduce risk
  weights for high-quality corporate credits
• to treat structured securitization, noncredit
  risk, and risk mitigation in a more satisfactory
  way and
• to set standards for individual-bank disclosure
  of derivative positions for internal
  capital-assessment procedures and for
  operational-risk controls.

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Issue C Three Obvious and Large Loopholes in RBCR

• 1. Risk weights focus on credit risk (rather
  than firm-wide risk) and are too few in number
  to track the capital needed to support individual
  positions.
• 2. Regulatory requirements are set much too high
  on safe instruments and much too low on very
  risky ones.
• 3. Regulatory Dialectic authorities lag behind
  the market in understanding how to analyze
  supervise the values and risks of complicated
  derivatives.
• Weaknesses in rules induce a mutation of
  derivatives that resembles mutation of bacteria
  to make antibiotics ineffective on them.

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Regulatory Arbitrage
Capital Ratio
Market vs. BIS Capital Requirements
Hypothetical Market Requirements
too low
BIS Minimum
4
too high
too high
Middle Market Business
Closely Followed Large Corporations
Prime Households
Small Business
Borrower Size
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Even with a specified horizon and confidence
level, regulatory VaR can be made as low as
managers want it to be.

• Arbitrage Opportunity No. 1 Identify and hold
  assets with low regulatory charges relative to
  the risks they pose.
• Arbitrage Opportunity No. 2 Unscrupulously
  manipulate unverifiable internal Value-at-Risk
  models for self-assessing risk exposure to
  understate need for capital. Another form of
  accounting gimmickry.

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• Imperfections in enforcement open and solidify
  Avoidance Opportunities that make the hypothesis
  that most banks would crunch profitable but
  risky opportunities seem awfully naïve.
• The naïveté lies in the twin presumptions that
  accounting ratios are difficult to misrepresent
  and that banks passively accept statutory burdens
  rather than work to adjust their risk profile to
  minimize the net effect on RBC system bank
  profits and market capitalization.

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Bank Responses to Basel I Range Across a Spectrum

• Some healthy banks held enough risky assets at
  the outset that the market made them hold ratios
  of LLR plus Book NW to Risk-Weighted Assets (kM)
  that approach the regulatory minimum kR. These
  banks increased accounting capital by reducing
  LLR.
• At the other extreme, healthy banks holding
  substantial amounts of low-risk assets did not
  need capital to close the gap between kM and kR.
  They could meet the requirements by securitizing
  safe assets and adding some risky ones. This may
  be expected to raise their loan-to-asset ratios
  (U.S.).
• N.B. If the costs of offloading safe assets and
  assuming new risks were zero, both types of banks
  would wipe out the burden of risk-based capital
  requirements completely and at no cost.

77
Proposed Basel II More Weights Categories
External Credit Rating (e.g., Standard Poors)
vs. use of internal systems to gauge risk and
set capital levels
78
HISTORICAL CORRELATION BETWEEN CREDIT RATINGS AND
DEFAULT RATES
Source Adapted by Jorion from Moodys default
rates from 1920-1998.
79
Self-Study for Ph.D Students Only Fatal Flaw
Mapping Between Capital set by VaR or BVaR Lacks
Coherence as Measure of Risk Passed Through to
Deposit Insurers
The concept of coherence of risk measures states
four desirable properties for a risk measure to
possess (Artzner et al, 1999). Let Xf represent
the amount of a banks net worth that is held in
a perfectly hedged position. With random
variables X1, X2 representing the future net
worths of two banks, the four properties can be
envisioned as tests the FDIC would ideally like
a risk measure ? to pass
Subadditivity Monotonicity Linear
Homogeneity Translation invariance
Query Which tests does VaR fail?
80
Consequences of Normality and I.I.D Assumptions
Self-Study

• 1. is a quadratic form
• 2. ?t the variance-covariance matrix of
  position returns ?t is diagonal only if returns
  are not correlated across positions

81
Consequences of Stationarity
Self-Study

• 1. One can suppress the subscript t.
• Choosing a longer decisionmaking horizon
  predictably increases the ? that applies (as
  opposed to subjectively having to make increasing
  allowances for extrapolation error).
• Permits the extrapolation VaR (n days)
• (vn) times the daily VaR.

82
VaR and Kurtosis
Self-Study

• Most VaR models conveniently and inappropriately
  assume
• normal distributions for daily returns
• stationary means, volatilities, and correlations
• Kurtosis (peakedness) unambiguously causes a
  serious understatement in VaR
• Relaxing any of the aggressive assumptions
  implies that the true tail probability and
  expected loss given VaR violation are much
  higher than the normal distribution would imply
  (Key).

83
Methods for Sensitivity-Testing VaR Models
Self-Study

• 1. Back testing of model fit against history.
• 2. Forward-looking stress testing of predicted
  responses
• a. To variation in doubtful assumptions
• b. To extreme movements in particular sources of
  risk (scenario analysis designed to identify
  potential nonlinearities)
• 3. Testing for dangerous ethical interfaces How
  can unit or division managers distort measures
  and tests in their favor?
• 4. Supplementation because VaR is not additive
  across stakeholders, shifting of risks to other
  parties needs to be assessed.