The new name for

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Alistair Milne Cass Business School amilne_at_city.ac
.uk Risk Management in Insurance and
Insolvency, The Hebrew University of
Jerusalem, October 16th-17th 2006
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Economic and Regulatory Capital Applications
in Banking and Lessons for the Insurance Industry
Alistair MilneCass Business School

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My research focus

• bank capital and shareholder value
• i.e. risk-management and corporate finance
• co-authors and papers
• Giles and Milne (2004)
• Dimou, Lawrence, and Milne (2005)
• Milne and Onorato (2006a,2006b)
• Milne (2006) Three lessons
• theory informed by extensive interaction with
  practitioners

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Agenda for today

• The rise of bank risk management
• bank economic capital current practice
• A critique of this thinking
• Practical issues
• Cost of regulatory capital requirements
• Skewness
• Two proposed performance measures
• Implications for insurance industry

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Rise of bank risk-management
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Greater competition

• Core business (retail deposits, lending to
  households and smaller
  business) remains profitable but
• Narrower margins in many markets
• Especially corporate sovereign
• New products creating exposure to
  market risks

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Governance centre stage

• Larger, more complex, institutions
• Less state ownership or support more answerable
  to shareholders
• Pressure to increase shareholder returns
• Greater regulatory freedom in choice of
  activities
• Regulatory oversight of risk-management

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Databases and modelling

• Cost of collecting, storing, and manipulating
  data fallen dramatically
• New tools
• Market risk VaR
• Portfolio models of corporate and sovereign
  credit risks
• Search for enterprise wide measures of risk/
  return e.g. pricing tools

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Bank economic capitalcurrent practice
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A new language

• Capital
• Capital as a measures of worst case exposure
• Eg value at risk
• Efficient allocation of this capital, to
  activities earning the highest return
• Two birds with one stone
• Solvency (enough capital) and
• risk-reward tradeoffs (efficient allocation of
  capital)

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RAROC

• Standard formulation
• Economic Capital value at risk type measure
  to cover all risks (market, credit, operational)
• Accept when RAROC exceeds hurdle
• Widely used, especially in trading floors and
  corporate lending

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RAROC Logic

• Equity capital to maintain AA rating, commonly
  99.97 on one year horizon
• average AA default frequency
• By assumption economic prudential
• Equity capital is in limited supply
• ration according to rate of return
• Hurdle rate sometimes related to return on
  equity

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Regulatory dimension

• approved internal models for setting regulatory
  requirements on trading book, since 1996
• Basel II aims to align regulatory and economic
  capital
• Concerns about regulatory arbitrage
• EU implementation 2007, delayed in US
• IRB model based calculations of credit risk
• not based on portfolio models, but asks banks to
  compute PD, LGD as inputs, and these could be
  derived from same databases as a portfolio model

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A critique
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A critique

• Practical problems
• Cost of regulatory capital?
• Skewness
• Conclusions use alternative performance measures,
  distinguish tail risks and risk-return tradeoffs

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Competitive advantage?

• Proposition 1 lower regulatory capital provides
  me with a competitive advantage
• Proposition 2 estimating tail risks and
  allocating economic capital provides me with a
  competitive advantage
• Both must be qualified
• Competitive advantage of regulatory capital is
  small
• Tail risks relatively unimportant to pricing
• focus on value creation
• Requires different metrics than RAROC

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1. Some practical issues
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Data problems credit risk

• Larger corporates/ sovereigns fairly OK
• CreditMetrics/MKMV
• US ratings history back to 1950s or earlier
• Difficulties with LGD
• Retail (including smaller corporates)
• a variety of scoring models, good for PD
• a little work on CVaR
• best UK institutions around 10-12 years data
• UK FSA transitional arrangements accept 5 years
  of data for Basel computations! 2 years for LGD
• Other low default portfolios,
• even more severe data problems
• Correlations?

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Data problems op risk

• Even greater than for credit risk
• High frequency/ low impact
• Most firms have databases, for a few years
• Little comparability between firms
• Mostly EL (minor contribution to EC)
• Low frequency/ high impact
• By their nature no data
• Low correlation with market/ credit risks?

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Outcome

• lacking data we extrapolate
• standard deviations, using arbitrary multipliers
• PD as in Basel risk curves (Vasicek single factor
  model plus arbitrary correlation loading)
• OP risk low frequency high impact, no
  statistical basis at all
• We are confusing
• Risk/return tradeoff (does not need extreme tail)
• prudential safety (cannot be based on statistical
  models)

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RAROC difficulty (1)

• Liquidity facilities
• eg Lines of credit to a AAA/AA corporates
• eg commercial paper underwriting
• Must back with capital
• to maintain liquidity over (say) 24 months
• Loss v. unlikely 99.97 appropriate
• So VERY safe lending
• 15 required return on this committed capital
  leads to unreasonably high pricing
• Cannot compete with market prices

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RAROC difficulty (2)

• Capital in trading operations
• Liquidity is lifeblood, need to survive
  temporary market fluctuations without being
  forced to close positions
• Well known examples LTCM, Metallgesellschaft
• Investors (shareholders) need to distinguish
  extreme tails and normal range of market
  fluctuations, only latter is priced risk

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Back to basics

• Ultimate objective shareholder value
• Appropriate trade-offs between risk and reward
• Protecting solvency of the institution
• Incentives for employees and line management
• Well developed tools for these tasks for
  non-financial companies
• Net Present Value (NPV)
• Economic Value Added
• So lets apply these tools to banks

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Some findings

• Regulatory capital is NOT expensive
• RAROC can be a misleading measure of returns to
  shareholders
• In order to create shareholder value..
• Distinguish capital management (liquidity,
  solvency) and risk-return tradeoffs
• Modelling should take a back seat, to business
  application and organisational credibility

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2. The cost of regulatory capital
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Basic argument

• WACC weighted average cost of capital
• Sum of debt and equity components
• Changing reg cap only small change WACC
• linked to Modigliani-Miller (1958)
• Detail (Milne and Giles (2004))
• Equity capital small proportion of total funding
• regulatory capital lt 11 impact on equity capital
• e.g. if following rating agency target
• Leverage adjustment
• Higher equity capital makes equity capital less
  risky, lowers cost of equity

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Cost of regulatory capital?

• Even without leverage adjustment, regulatory
  capital not very expensive
• WACC then yields an upper bound
• Financial Services Authority calculations
• eg Basel II, reduces reg cap by 10, worth at
  most 3 basis points on cost of funding your loan
  portfolio
• Some implications
• regulatory capital driven securitisation destroys
  shareholder value
• Basel Pillar 1 calculations not of great business
  importance

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Dimou, Lawrence, Milne (2005)

• Increases tax exposure
• higher equity capital reduces tax shield
• a transfer a private but NOT a social cost
• Reduces access to bank safety net
• Higher equity capital forces bank owners to
  accept more risk
• a transfer a private but NOT a social cost
• Lowers expected costs of bankruptcy
• Higher capital reduces probability of bankruptcy/
  financial distress
• a benefit Social benefits likely to exceed
  private benefits.
• Agency costs
• Bank managers look after themselves, not
  shareholders
• Equity capital gives managers freedom to pursue
  their own ends
• Reg cap is different, it is a discipline on
  managers just like debt
• neutral No private cost of reg cap, if not used
  as risk measure

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3. Skewness
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Theory

• Proposition 1 (Onorato-Milne (2006))
• Economic capital prudential capital
• iff insurance cost of hedging risk w is
  proportional to prudential tail H-1(w)
• Corollary
• RAROC hurdle delivers shareholder value if all
  risk distributions have the same skew
• Turnbull-Crouhy-Wakeman (1999) special case
• Log normal asset returns so (right) skew
  increasing with s
• As s rises, prudential tail rises less than
  insurance cost
• So RAROC threshold rises with s

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Illustrations

• Taken from Milne and Onorato (2006a)
• Apples and Pears? The comparison of bank
  economic and prudential capital.
• Assume market price of risk proportional to
  standard deviation
• Compare symmetric and right-tailed returns
• What then is NPV0 hurdle rate for RAROC?

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A credit risk distribution

• Credit risk left skew
• Vasicek asymptotic single factor model
• Model used for Basel IRB risk curves
• Left skew , so smaller NPV 0 RAROC
• More detail on parameters
• PD probability of default
• ? correlation of credit risk driver with market
• R2 correlation with aggregate (systematic) risk
• How do these parameters affect RAROC hurdle?

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Critique summarised

• Two different objectives
• Prudential (avoiding financial distress,
  satisfying regulator)
• Risk-return tradeoffs
• Using one measure of capital for both purposes
  creates conflicts
• If tail risk is uncertain
• If tail risk is skewed
• If regulators take a conservative view of risks
• Again does not matter to the business

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Two proposed performance measures
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Proposed measures

• Milne and Onorato (2006a) discount with market
  based risk-premium f
• Milne and Onorato (2006b) use Wang transform

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More theory

• Inventory models
• Incorporate costs of financial distress, or
  penalty costs of raising capital
• Froot and Stein (1998), Milne (2004)
• Outcome additional internal beta G
• Measures the risk of capital shortage
• Depends upon
• Probability of capital shortage
• Costs of financial distress
• For well capitalised bank, G can be ignored
• Probability of capital shortage is negligible

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Implication

• Longer term equity capital not constrained
• Retain earnings or rights issue
• No need to ration, adjust to minimise WACC
• Measuring NPV (shareholder value)
• right WACC input
• e.g. betas (cost of risk)
• depend on correlation with market NOT with
  balance sheet
• Equivalent to cost of insuring exposure
• Capital constrained?
• Additional cost of risk internal or portfolio
  beta G, for rationing capital

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With market prices for risk

• If risk can be priced on market, proceed as
  follows (Milne and Onorato (2006a))
• Discount future returns with risk-premium taken
  from market prices
• equivalently estimate the cost of hedging
  completely on the market and deduct this cost
  from expected return
• (risk neutral pricing)
• Divide by contribution to prudential capital
• Hurdle rate? Zero if unconstrained. Otherwise
  chosen to ration equity capital

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No market prices for risk

• Use distortion measure (Milne and Onorato
  (2006b )) eg Wang transform
• Portfolio based
• Satisfies axioms of coherence and second order
  stochastic dominance
• Divide by contribution to prudential capital
• Hurdle rate? Zero if unconstrained. Otherwise
  chosen to ration equity capital

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Merits of Wang transform

• Yields an expected value
• Analagous to risk neutral pricing distort
  the probability density of returns
• risk appetive can be parameterized using a
  single parameter p

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In practice very limited data

• Especially for tail risks
• Sophisticated modellign of tail risks not ormally
  appropraite
• Simple stress or scenario analysis
• Aim to achieve credibility, within the
  organisation and also with shareholders.

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Implications for insurance

• Some preliminary thoughts open to discussion
• First general insurance, then life

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When re-insurance markets available

• Logic of Milne and Onorato (2006a) applies.
• Price risk according to what it would cost to
  transfer onto re-insurance market deduct from
  premium income
• Set a hurdle rate cost of equity capital
• Zero if unconstrained, gt zero if rationing

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When reinsurance limited

• Use of the Wang transform can help systematise
  thinking about risk-appetite
• Needs to be supplemented by e.g. stressed
  scenarios, to check capital adequacy

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Data sometimes available

• For some products extensive data available
• Also the products where reinsurance markets are
  most liquidy
• Models can be used for computing capital, but
  pricing best done off the market
• For other products, very limited data and
  illiquid markets for re-insurance.
• Here focus on the simplest possible modelling
  tools

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One difference insurance and banking -
segmentation

• Banks all seek to maintain high credit ratings
• Some insurers may opt for lower capitalisation,
  and lower premium pricing to customers, with the
  understanding that they may fail in the event of
  a large aggregate rise in claims
• Customers carry aggregate tail risks
• Other insurers may choose high capitalisation,
  high pricing

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Life insurance

• Very long term mortality risks
• No possibility of precise quanitification
• Operate with conservative capitalisation
• Should not restrict business, provided need for
  capital is understood by sharholders

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Summary
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I have discussed

• The rise of bank risk management
• bank economic capital current practice
• A critique of this thinking
• Practical issues
• Cost of regulatory capital requirements
• Skewness
• Two proposed performance measures
• Implications for insurance industry

53
Some findings

• Regulatory capital is NOT expensive
• RAROC can be a misleading measure of returns to
  shareholders
• In order to create shareholder value..
• Distinguish capital management (liquidity,
  solvency) and risk-return tradeoffs
• Modelling should take a back seat, to business
  application and credibility in the organisation
• Similar issues in insurance no problem with
  conservative capitalisation

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Priority better risk language

• Simple enough to be understood throughout the
  organisation
• Key concepts
• Balance sheet commitment and liquidity
• Not a pricing issue
• Expected loss
• Cost of carrying risk
• What reward do shareholders require for holding
  risk?
• Use models where appropriate (market risk,
  corporate credit risk, retail insurance)