David C. Shimko

1
RAROC, Credit and Corporate Growth

• David C. Shimko
• Harvard University and
• Risk Capital Mgmt, Inc.
• Risk Management Workshop
• Hebrew University
• November 10, 1999

2
OUTLINE OF SEMINARS

• Part I
• Theoretical foundations of RAROC as a determinant
  of discount rates
• Part II
• Application of VAR and RAROC to nonfinancial
  firms
• BREAK (required by Geneva Convention Rules)
• Part III
• Paradoxes in counterparty credit risk management

3
Part I Theoretical foundations of RAROC as a
Determinant of Discount Rates
4
CAPM Approach Simplified

• Everyone prefers to avoid risk.
• When risk reduction costs nothing, as in the case
  of diversification, people diversify as much as
  possible.
• Some risks, called systematic risks, can never be
  diversified, because they affect such a large
  number of investments.
• Whenever a risk cannot be diversified, investors
  must be paid a price to bear the risk.
• Consequently, any diversifiable risk has no price
  in the CAPM
• Capital markets are competitive (an assumption)
• Capital is never scarce at the right price (an
  assumption)
• Any temporary risk premium for diversifiable risk
  is eliminated by competition among investors

5
Components of the CAPM return

• ri rf ?i(rm - rf) 0

Diversifiable risk premium
Risk-free return
Market risk premium
Expected return on any asset i
Scaled covariance between asset risk and
systematic risk
6
Generalizations to the basic CAPM

• Most empirical tests reject the basic form of the
  CAPM
• Robert Merton (Nobel prize winner with Fischer
  Black) developed the intertemporal CAPM in 1973
• This model allows for nondiversifiable changes in
  investment opportunities
• This creates a larger set of nondiversifiable
  risks
• Each of these risks earns its own risk premium
• There is still no compensation for diversifiable
  risk
• Steve Ross (future Nobel prize winner) developed
  the Arbitrage Pricing Theory (APT) in 1976
• The APT does not explain the source of risk
  premia
• But the APT (in portfolio form) does rely on
  asset diversification and a zero risk premium for
  diversifiable risk

7
Conclusion for CAPM and related models

• None of these models allows a risk premium for
  diversifiable risk
• The financial models as a class differ from
  insurance models of risk pricing
• Select any introductory insurance textbook (e.g.
  Goovaerts et al)
• Typical expression of the pricing of risk for an
  insurance company
• (on a single policy)
• ri ? k?

Volatility of loss
Scaled by diversifiability Scaled by size of
portfolio Scaled by concentration
Required reserve on a liability
Capital availability factor
Expected loss
Are the insurance models completely wrong?
8
What is risk capital, and how is it measured?

• CONCEPTS DEFINITIONS
• Risk capital is the amount of money one is
  prepared to lose on a trade, portfolio, or
  strategy
• Often termed value-at-risk (VAR)
• VAR is a better measure of capital than capital
  itself
• RAROC (risk-adjusted return on capital) is simply
  return on risk capital, or return on VAR
• Definition RAROC PL/VAR
• COMPARISON TO THE SHARPE RATIO
• RAROC is similar to the Sharpe Ratio (invented by
  William Sharpe)
• RAROC can be applied more broadly than the Sharpe
  Ratio

9
Whats a good RAROC?
Historical performance of SP 500
Typical hedge-fund ex-ante investment criterion
RAROC Sharpe x (?t)/z t VAR period in
years z std devs in VAR
10
Components of the RAROC return

• ri rb k?

Return on any asset
Marginal risk of asset relative to benchmark
Capital scarcity factor (RAROC)
Return on benchmark
11
Can RAROC be reconciled with the CAPM?

• Loosen one of the CAPM assumptions
• What if capital is somehow constrained in a
  market?
• Legal constraints such as bank regulations
• Psychological constraints such as fears of
  emerging market investments or commodities
• Asymmetric information constraints
• Corporations cannot fully/credibly communicate
  investment prospects
• Investors restrict capital they will invest
• When capital is constrained
• The unconstrained investors are relatively
  over-exposed to the constrained asset
• They demand a risk premium because of their
  concentrated, undiversified positions
• Competitive forces fail to eliminate the risk
  premium

12
How is the RAROC risk premium determined?

• Assume investors will invest in a passive
  benchmark
• (This is a recursive process the benchmark
  investors may also earn a premium for
  diversifiable risk)
• Also assume that capital available to take
  nonbenchmark risks is further constrained
• Then investors will diversify nonbenchmark risks
  to the degree possible
• But they will not be able to diversify fully
• Hence they demand a risk premium for these risks
• Competition cannot eliminate this risk premium

13
Implications for corporate investment

• Every project has benchmark and non-benchmark
  risks
• Determine scaled benchmark return
• Is RAROC appropriate?
• Compare firms investment opportunities to its
  asset base
• Examine competitor financial strength
• Assess markets appetite for risks associated
  with the project
• Identify external investment constraints, legal,
  psychic or structural
• If yes
• Determine appropriate RAROC
• Assess volatility due to non-diversifiable
  non-benchmark risks
• If no
• Use CAPM-style approach
• But please note
• The CAPM is a special case (or limiting case) of
  the RAROC approach

14
Part II Application of VAR and RAROC to
Nonfinancial Firms
15
Introduction

• What is enterprise-wide risk management?
• A computer system that tracks and measures
  business risks for management reporting
• A conceptual framework for risk-based
  decision-making across the firm
• Some large users of EWRM
• Bankers Trust
• Enron
• Microsoft
• Different applications, common goals
• A price for risk
• A way to trade off one risk against another
• Comparisons between different risk-mitigation
  alternatives
• Achieving the proper balance between risk and
  return

16
An example of risk-based decision-making

• The basic NPV rule (accept all trades with
  positive NPV) often leads to underperformance
• Positive NPV is neither necessary nor sufficient
  condition for the acceptance of a project or
  activity
• Scarce resources must be properly deployed
• People
• Market Coverage
• Risk capital

Is the firm using risk capital INEFFICIENTLY? or
EFFICIENTLY?
Maximum NPV
Cumulative profitability
Max resource
Use of resource
17
Optimizing with scarce resources A mathematical
view

• Problem Maximize expected NPV over time
  (Objective)
• Subject to a constraint on resource use
  (Resource use ? Available)
• Equivalent to
• Maximize Objective minus Multiplier x (Unused
  resource level)
• s.t. Multiplier x Unused resource 0
• Interpretation of the (LaGrange) multiplier
• Value of relaxing the constraint
• Shadow price of the scarce resource
• Interpretation in management
• Multiplier Optimal transfer price
• Apply NPV rule with transfer price
• Noncash charge to projects
• Insures projects are adopted optimally
• Does it matter if your scarce asset is labor or
  risk capital?

18
Opening Pandoras box

• What is the right RAROC for a nonfinancial firm?
• Does this change the way we look at capital?
• Can RAROC ever have an effect on shareholder
  value?
• A CASE STUDY IN ENERGY

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Determining the right RAROC for a firm

• Constructive approach
• Closed form is hopeless
• Simulate different acceptance rules
• Requires knowledge of stochastic and dynamic
  opportunity set of investments available to the
  firm over time
• Comparison to peers
• Pure plays (in and outside the industry)
• Integrated energy firms
• An internal risk capital market
• Business units trade risk capital with each other
• RAROC is the clearing price
• We chose the comparison to peers approach

20
A sample of 1998 energy peer RAROCs
1998 RAROC
Company
RAROC
Enron
93
Duke
53
Williams
75
Annualized
Trading Gains

Reliant
53
99 VaR
(MM)
Utilicorp/Aquila
55
KN Energy
92
DTE Energy
22
Sempra
-19
PGE
-4
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Risk-Return Relationship
Relationship Between Risk and Trading Gains in
1998
Increasing RAROC
Enron
Annual Trading Gains (MM)
Duke
Williams
KN Energy
Reliant
Aquilla
DTE
0
PGE
Sempra
0
Annual Value at Risk, 99 Conf (MM)
22
Separating capital and risk capital charges
Example
OLD WAY OF THINKING
NEW WAY OF THINKING
100 in SP
100 in SP
100 risk-free cash investment (6)
Expected return on SP 12
Expected return on T-bills 6
25 risk capital (24 RAROC)
Worst case loss (1 yr) 25
6
6
Expected cash return 12
Expected cash return 12
23
Real Example How Enron evaluates a tolling deal
Forecast NPV _at_ 10.6
Frequency Chart
5,000 Trials
63 Outliers
.025
125
.019
93.75
.013
62.5
.006
31.25
.000
0
-150,000
0
150,000
300,000
450,000
Certainty is 79.16 from 0 to Infinity
Worst case loss ? 90,000
Expected NPV ? 105,000
Not bad
INVESTMENT
YIELD
Cash 380,000
IRR 16.5
RAROC 52.3
Risk Capital 90,000
Yowza!
24
How can RAROC lead Enron to better decisions?

• Pricing strategy
• RAROC criterion provides more pricing flexibility
  in a competitive market (in this case)
• Hedging strategy
• Under a RAROC criterion,
• hedges may sacrifice NPV...
• but increase returns by reducing dependence on
  risk capital
• Under traditional capital budgeting, hedges are
  never worthwhile unless they have positive NPV
• Traders will be rewarded for putting on efficient
  futures hedges and offsetting OTC deals --- this
  increases RAROC
• Comparables
• With a RAROC criterion, the tolling deal can be
  compared on equal footing to any trade or asset
  deal
• Example How would the the tolling deal have
  compared with purchasing a gas-fired power plant?

25
RAROC answers the question Should I hedge?
NPV Rule
RAROC Rule
Unhedged deal
Expected Profitability
Hedge market risk
Hedge credit risk
0
Insure all risks
Value-at-risk (all sources)
26
Prepay deal

• Typical industry view No hedge, no deal
• Prepay valued as debt substitution
• May crowd out balance sheet to the extent ratings
  agencies impute operational risk
• Otherwise, no additional capital costs required
• How could RAROC help on a prepay?
• Deciding whether to hedge and how to hedge
• Prepays may be a more efficient means to obtain
  long-term exposures
• Deciding when to purchase others prepay
  contracts
• Integrating credit and market risk
• Major competitive advantage Linking financing
  to sellers

27
Main reasons banks and energy firms use RAROC

• Proper RAROC analysis prevents wasting risk
  capital on low-value (but positive NPV) deals
• VAR is the best (sometimes only) way to measure
  capital
• RAROC can be applied consistently across trading
  and asset businesses to ensure optimal capital
  allocation
• RAROC can be applied within a trading business to
  grow profitable activities at the expense of less
  profitable ones
• Risk control allows firms to leverage more of
  their core expertise in origination, marketing,
  and market development
• Investors evaluate banks energy company
  performance relative to peers partly on RAROC
  analysis

28
How does Microsofts risk analysis differ from
others?

• Bankers Trust and Enron have similar risks
• Market risk
• Liquidity risk
• Credit risk
• For Microsoft, other risks are more important
• Competitive risks
• Operational risks
• Legal risks
• Should Microsoft use RAROC?
• In EWRM, all risks are treated equally to the
  extent they risk the same amount of capital
• A common language for risk and risk measurement
  leads to better decision-making
• Pricing, project origination and performance
  measurement

29
Two uses of RAROC

• As a ratio
• RAROC ranks relative performance
• Trading desk makes 50 MM and risks 80 MM for a
  RAROC of 62.5
• Asset business makes 30 MM on a 100 MM
  investment that can be sold for 60 MM in the
  worst case RAROC 75
• Banks tend to find this implementation easier

• As a measure of value-added
• NPV Usual NPV minus risk charges
• Risk charges Corporate RAROC x VAR
• Suppose corporate RAROC 40
• Trading desk adds
• 50 - 40 of 80 18 MM
• Asset business adds
• 30 - 40 of 40 14 MM
• Risk-adjusted NPV or Risk-adjusted EVA
• Energy firms tend to find this implementation
  easier

30
What do firms need to do to establish EWRM?

• LAY THE FOUNDATIONS...
• Analytical risk assessment systems are needed
• High quality analytic staff
• AND ERECT THE STRUCTURE
• Integrated VAR framework for all trades,
  financing and asset deals
• Market risk (paper/physical)
• Credit risk
• Operational risk and competitive risk
• VAR-based risk reporting (usu. daily frequency)
• VAR-based trading limits and capital allocation
• Establishing a culture of efficient risk-taking
• Exposure at all levels of management
• Risk-based decision-making
• RAROC-based performance measurement and
  compensation

31
A successful organizational structure

• Chief Risk Officer independent of business
• Head of risk management committee
• Report to CEO (in some cases, the Board of
  Directors)
• Responsible for
• Capital allocation/budgeting of risk capital
• Trading and non-trading businesses
• Establishment of benchmarks
• Integrity of risk systems
• Performance measurement
• Risk and performance reporting
• CROs office contains the following functions
  (large org.)
• Head of compliance
• Head of risk operations
• Head of research/analytics

32
Recommended next steps for EWRM implementers

• This presentation discussed the whats and whys
• Next examine the hows carefully
• Measuring VAR in the trading books and asset
  businesses
• Reporting
• Applying asset allocation to risk limits
• Applying RAROC consistently to project evaluation
• Establishing benchmarks by business
• Ensuring systems efforts are consistent with
  long-term organizational goals
• Expose decision-makers at all levels to RAROC and
  risk-aware decision-making

33
Part III Paradoxes in Counterparty Credit Risk
Management
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Example Pricing options into swap contracts

• Assumptions (using an electric power example)
• Fixed price power contract with no options is
  worth 25/MWh
• Independent modeling suggests option is worth
  1/MWh
• Value-at-risk on the fixed price contract is
  15/MWh
• Value-at-risk on the fixed price contract with
  swings is 18/MWh
• Required return on risk capital of 20 (30-day
  VaR)

35
Incorporating VaR into swap bid/offer

• Case I Bid/offer for a single undiversified
  trade
• Fixed price firm 2515(0.20) 22,28
• With option 25118(0.20) 22.4,29.6
• Case II Warehousing period of one week
• Fixed price firm 2515(0.20)?0.25 23.5,26.5
• With option 25118(0.20)?0.25 24.2,27.8
• Case III Small trade, fully diversified
• Fixed price firm 25,25
• With option 26,26
• GENERAL STATEMENTS
• Swap bid offer must contain not only option
  values, but charges for marginal risk.
• Concentrations of unidirectional options require
  higher risk charges.

36
What does this mean for credit?

• Credit risk must be computed and charged against
  risk capital
• Same rules apply
• Single nondiversified exposure gets high charge
• Diversified credit exposures minimize credit
  charges if credit risks are independent
• Credit risk does not diversify market risk
• Risks are multiplicative, i.e. contract in the
  money together with counterparty default
• So what is a swap really?
• The agreement to exchange cash flows subject
  to...
• Each counterpartys right to default on this
  obligation along with their collective
  obligations
• Option may not be exercised optimally in the
  narrow sense
• What is collateral really?
• The striking price of the default option

37
Putting it all together

• Credit risk is a combination of two embedded
  options
• The embedded option increases value-at-risk to
  both parties to the swap
• Joint collateral holdings reduce credit risk by
  making the default options more out-of-the-money
• Hence, good collateral management at sufficiently
  high levels can hedge most of the credit risk
• And thereby reduce the necessary capital charges
  for credit risk

38
You could build a great model...

• Bid Q
• (?Cu)C(XC)
• ?SP(XS)
• ?a
• k IV(XS,XC)
• ? IXS
• NOTES
• Subscript C indicates counterparty, S indicates
  self
• Probability of counterparty default is based on a
  credit rating plus an uncertainty premium u
• The call and put options decrease in value as
  collateral X increases

• Price of default-free contract
• Probability of counterparty default x price of
  call option
• Probability of own default x price of put
  option
• Admin costs per unit
• Charges for incremental risk capital
• Charges for incremental collateral

39
But it would be wrong.

• Credit risk ultimately is extremely difficult to
  model.
• Not because of the analytic complexity of credit
  risks, fat tails, correlations and aggregation
• But because of structural inefficiencies in the
  balance sheet credit methods
• INEFFICIENCY 1
• Everyone pays his counterpartys cost of credit
• INEFFICIENCY 2
• One can never know ones counterpartys
  nondisclosed risks
• Market risks (LTCM)
• Credit risks (The US Power Industry)

40
Whats wrong with paying the other guys credit
costs?

• Trade subsidization
• Higher quality credits effectively pay for lower
  quality credits to trade with them
• Incentive for all to seek higher credit quality
  counterparty
• HOW TO AVOID PAYING THESE COSTS
• A. Price swaps to reflect counterparty credit
  quality
• B. Dont trade
• C. Dont charge traders for credit risk

41
Cant we estimate nondisclosed risks?

• That would be very difficult.
• Risks change constantly
• Risks sometimes change, unknown to counterparty
• Incentives
• A counterparty of equal credit rating should only
  trade with you if he believes his hidden risks
  are greater than you realize
• You realize this
• You resist trading with those who would trade
  with you

42
Where does this leave us?

• There are serious shortcomings of even the most
  sophisticated practices
• Inability to determine hidden credit exposures of
  counterparties
• The best credit manager and the best credit
  analytics cannot solve these problems

43
A humble suggestion

• Post collateral to cover all counterparty
  obligations to all other counterparties
• In this system, everyone pays their own credit
  costs
• Do you think collateral is expensive?
• It is under the current system
• Why is collateral so inefficient?
• Lack of uniform collateral collection
• Unnecessary transfer costs between custody banks
• Limits to rehypothecation of collateral
• Eligibility
• Permission of issuing institution
• Letters of Credit and Third Party Guarantees
• Inability to post collateral on a hedged or
  diversified basis

44
Introducing the CoVar project at Bankers Trust

• First application in the energy industry
• Solves four major collateral problems
• Lack of uniform collateral collection
• Centralized reconciliation and messaging
• Unnecessary transfer costs between custody banks
• Keeps collateral at participants custody bank
  until default
• Limits to rehypothecation of collateral
• Standardizes eligible collateral
• Retains and reassigns LCs and TPGs by book entry
• Inability to post collateral on a hedged or
  diversified basis
• CoVars secret
• Collateral solutions imply credit solutions
• For more information
• www.COVAR.com