Transcript No Slide Title

David C. Shimko
Harvard University and
Risk Capital Mgmt, Inc.
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Risk Management Workshop
Hebrew University
November 10, 1999
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
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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
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Components of the CAPM return
• ri = rf+ i(rm - rf) + 0
Diversifiable
risk premium
Risk-free
return
Expected return
on any asset i
Market risk
premium
Scaled covariance
between asset risk
and systematic risk
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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
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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
Required reserve
Capital availability
on a liability
factor
Expected loss
Scaled by diversifiability
Scaled by size of portfolio
Scaled by concentration
Are the insurance models completely wrong?
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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 = P&L/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
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What’s a good RAROC?
RAROCS*
Sharpe
Ratio
95% confidence interval
1-day
99% confidence interval
30-day
1-yr
1-day
30-day
1-yr
S=0.60 2%
9%
31%
1%
7%
26%
S=1.00 3%
15%
51%
2%
12%
43%
S=2.00 5%
29%
102%
4%
25%
86%
Historical performance of S&P 500
Typical hedge-fund ex-ante investment criterion
*RAROC = Sharpe x (t)/z
t = VAR period in years
z = # std devs in VAR
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Components of the RAROC return
• ri = rb + k
Return on
any asset
Capital scarcity
factor (RAROC)
Marginal risk
of asset relative to
benchmark
Return on
benchmark
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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
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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
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Implications for corporate investment
• Every project has benchmark and non-benchmark risks
– Determine scaled benchmark return
• Is RAROC appropriate?
–
–
–
–
Compare firm’s investment opportunities to its asset base
Examine competitor financial strength
Assess market’s 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
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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
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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
Maximum NPV
Cumulative
profitability
INEFFICIENTLY?
or
EFFICIENTLY?
Max resource
Use of resource
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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?
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Opening Pandora’s 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
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A sample of 1998 energy peer RAROCs
1998 RAROC
Company
Enron
Duke
Williams
Reliant
Utilicorp/Aquila
KN Energy
DTE Energy
Sempra
PG&E
Trading Gains
($MM)
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÷
RAROC
93%
53%
75%
Annualized
53%
99% VaR
55%
92%
22%
-19%
-4%
Risk-Return Relationship
Relationship Between Risk and Trading Gains in 1998
Annual Trading Gains ($MM)
Increasing RAROC
KN Energy
Enron
Williams
Duke
Reliant
Aquilla
DTE
$0
0
Sempra
PG&E
Annual Value at Risk, 99% Conf ($MM)
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Separating capital and risk capital charges: Example
OLD WAY OF THINKING
NEW WAY OF THINKING
$100 in S&P
$100 in S&P
Expected return on S&P = 12%
$100 risk-free cash investment (6%)
Expected return on T-bills = 6%
$25 risk capital (24% RAROC)
“Worst case” loss (1 yr) = 25%
$6
Expected cash return
Expected cash return
= $12
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$6
= $12
Real Example: How Enron evaluates a tolling deal
Forecast: NPV @ 10.6%
5,000 Trials
Frequency Chart
63 Outliers
.025
125
.019
93.75
.013
62.5
.006
31.25
.000
0
-150,000
0
150,000
Certainty is 79.16% from 0 to +Infinity
300,000
450,000
“Worst case” loss  $90,000
Expected NPV  $105,000
INVESTMENT
Cash
Risk Capital
$380,000
$90,000
YIELD
IRR
16.5%
RAROC
52.3%
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Not bad
Yowza!
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?
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RAROC answers the question: “Should I hedge?”
Expected Profitability
RAROC Rule
NPV Rule
Unhedged deal
Hedge market risk
Hedge credit risk
0
Insure all risks
Value-at-risk (all sources)
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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
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Main reasons banks and energy firms use RAROC
• Proper RAROC analysis prevents wasting risk capital on lowvalue (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
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How does Microsoft’s 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
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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%
•
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
Banks tend to find this
implementation easier
•
•
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Risk-adjusted NPV or Riskadjusted EVA
Energy firms tend to find this
implementation easier
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
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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
• CRO’s office contains the following functions (large org.)
– Head of compliance
– Head of risk operations
– Head of research/analytics
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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
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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)
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Incorporating VaR into swap bid/offer
• Case I: Bid/offer for a single undiversified trade
– Fixed price firm:
– With option:
25±15(0.20) = {22,28}
25+1±18(0.20) = {22.4,29.6}
• Case II: Warehousing period of one week
– Fixed price firm:
– With option:
25±15(0.20)0.25 = {23.5,26.5}
25+1±18(0.20)0.25 = {24.2,27.8}
• Case III: Small trade, fully diversified
– Fixed price firm:
– With option:
{25,25}
{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.
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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 counterparty’s 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
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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
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You could build a great model...
•
•
Bid = Q
–(C+u)C(XC)
•
•
•
+SP(XS)
•
•
•
a
–k IV(XS,XC)
•
•
•
–  IXS
•
NOTES:
•
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
– 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
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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 counterparty’s cost of credit
• INEFFICIENCY #2
– One can never know one’s counterparty’s nondisclosed risks
• Market risks (LTCM)
• Credit risks (The US Power Industry)
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What’s wrong with paying the other guy’s 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. Don’t trade
– C. Don’t charge traders for credit risk
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Can’t 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
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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
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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
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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 participant’s 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
• CoVar’s secret
• Collateral solutions imply credit solutions
• For more information
– www.COVAR.com
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