Top Down and Bottom Up Capital Allocation

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Top Down and Bottom Up Capital Allocation
Colin Burke, Credit Modelling
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Contents

• Treasurys Portfolio
• Risk Platform Project
• Bottom up economic capital calculation
• Bottom-up economic capital allocation
• Relationship with ICAAP
• Challenges and obstacles
• This talk focuses on Treasurys plan for a
  bottom-up capital allocation and how this
  interacts with a top down allocation.

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Treasurys Portfolio

• HBOS Treasury Services (HBOTS) is the Treasury
  Services arm of the HBOS Group
• It provides funding for the Group and hedges for
  the Group and its clients
• The HBOSTS portfolio consists of
• Bonds (bank and government), CDs, CP etc
• Money Market (loans, deposits)
• Derivatives (interest rate, FX, equity, commodity
  and credit)
• Securities Financing Transactions (repos etc)
• ABS investments

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Risk Platform Project (i)
Scope

• Market Risk deliver a platform for CAD 2
• Credit Risk deliver a platform for credit
  exposures, economic capital and stress testing.
• An economic capital model is only as good as its
  inputs PD, LGD, exposures, correlations
• gt stress testing functionality for credit risk
• gt credit exposure in IMM (derivatives and SFT)
• gt back testing of IMM exposures
• gt credit economic capital for derivative and
  non-derivative trades

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Risk Platform Project (ii)

• System selection process
• Request for Proposals (RFPs) were issued on
  February 23rd 2005 with a requested reply date of
  March 24th 2005
• Following preliminary choice of the risk engine
  and market data solutions, a seven week proof of
  concept started on the 24th of August 2005.
  Included comparison to HBOSTS own calculations,
  theoretical review, technology review etc

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Risk Platform Project (iii)

• Project Definition Report produced in early 2006
  defining key required enhancements for credit
  risk under the following headings
• Credit Exposure (IMM)
• Stress and Back Testing
• Economic Capital (see later)
• Project has begun. For Credit Risk initial work
  was the testing of credit exposure
• MTM unit and bulk tests (comparison with front
  office system)
• PFE/EPE unit and bulk tests (comparison with our
  own models)

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Risk Platform Project (iiia)
Example PFE tests
Unit Test (CDS)
Bulk test (portfolio of 20 swaps)
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Risk Platform Project (iv)

• Vendor Components
• Data Consolidation Module
• receives, cleans and stores market data
• Market Risk Engine
• Bootstraps yield curves
• Market Risk Calcs CAD 2 calculation (VaR) etc
• Stress Testing for Credit and Market Risk
• Calibrates stochastic models for PFE / EPE
  Calculator
• Calculates and allocates EC (including use of EPE
  profiles)
• PFE / EPE Calculator
• Calculates PFE, Expected Exposure, EPE etc
• Incorporates correlation, netting and collateral
  effects

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Risk Platform Project (v)
Front Office Systems
Bloomberg
etc
Reuters
Trade data
Data Consolidator
Market Risk Engine/ Parameter Generator
Cleaned market data
Trade data Market data Stochastic Parameters
PFE / EPE Analytics
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Risk Platform Project (vi)
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Economic Capital Enhancements (i)

• Key enhancements for economic capital include
• Using vendor application to implement internally
  defined credit worthiness factor models (no
  reliance on vendors proprietary approaches). This
  gives default correlation.
• Vendor-based Economic Capital Engine will give
  time of default. A multi-period model.
• Economic Capital allocated on basis of Expected
  Shortfall. Total Capital calculated as CVaR. Can
  allocate in different parts of loss distribution

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Economic Capital Enhancements (ii)

• Building our own factor model
• Leverages from market VaR model statistics set
• For Credit this is normally used to calibrate the
  stochastic process for derivative exposure e.g.
  mean reversions and instantaneous volatilities
  for Hull-White interest model, drift and
  volatility in GBM and correlations between risk
  factors

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Economic Capital Enhancements (iii)
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Economic Capital Enhancements (iv)

• The basic infrastructure to build a CreditMetrics
  style factor model already exists (CreditMetrics
  uses equity values as a proxy for asset values)
  Use linear factor model for credit worthiness or
  ability to pay process

• To use VaR Statistics Sets we need to add
  industry and country breakdowns for each
  counterparty
• We also need to use a longer history of data than
  we would normally use for credit exposure

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Economic Capital Enhancements (v)

• Time of default. Why is it important? Consider
  the following EPE profile

• A default today (01/06/2006) has zero exposure.
  A default around June 2011 has maximum exposure
• If default occurs, we are not indifferent to its
  timing
• Conventional economic capital models do not give
  the time of default or assumes at the single risk
  horizon (usually one year from today)

• See bottom up calculation for illustration

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Bottom Up Capital Calculation (i)

• Inputs
• Non-derivatives trades (bonds, CP etc) input
  into market risk engine at trade level
• Derivatives and SFT input EPE profile from
  analytics engine at the netting pool level into
  the market risk engine.
• Market risk engine forms factor model
  (correlation)
• Combine with Basel II PDs and LGDs. PDs are term
  structure of PDs entered via a transition matrix
• Credit spreads by rating (for effects of MTM
  moves in non-default states)

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Bottom Up Capital Calculation (ii)

• Modelling Approach
• Monte Carlo Simulation
• Time of default due to multi-time step
  simulation. Uses ideas from Hull and Whites
  credit derivative methodology

Asset Value
etc...
Barrier 2

Barrier 3
Defaulted
Time
Today
H2
H1
Barrier 1
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Bottom Up Capital Calculation (iii)

• Output (i) Portfolio Loss distribution and
  portfolio capital i.e. a Treasury estimate of
  Treasurys economic capital

Expected Loss
Probability
Economic Capital
Loss
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Bottom Up Capital Calculation (iv)

• Output (ii)
• Capital to each trade/netting pool
• Sum of allocated capital equals total capital

Risk Appetite
Shortfall
Economic Capital
Probability
Loss
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Using The Economic Capital (i)

• Treasury only context
• Concentration analysis
• EC limits
• RAROC / performance measurement
• Pricing advice
• Own alpha estimation (IMM)
• Plan to run Economic Capital calculations and IMM
  calculations daily
• Typical pricing advice relates to swap
  transactions conducted for customers of Corporate
  Bank. Currently use an EPE/market implied
  approach. Risk Platform will supplement this with
  EPE/RAROC approach

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Using The Economic Capital (ii)
Example Consider an interest rate swap with a
risky-counterpart. The risky counterparty
exposure is given by
Vrisky Vriskless EL where

• The contribution of the credit spread to economic
  capital is reflected in two ways
• A component due to credit migration (via changes
  in the marginal default probabilities above) and,
• Changes due to simulated market rates as the
  counterparty portfolio ages to the risk horizon
  i.e. a forward value of EL(t)

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Relationship with ICAAP

• Current plans are for Group to allocate capital
  to business on Basel II basis
• Plan to use Risk Platform as part of challenge
  process to the Group allocation
• Once the allocation to Treasury is agreed, use
  Risk Platform to allocate agreed capital to trade
  and netting pool level

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Relationship with ICAAP

• Some challenges
• Model Differences Our Treasury model differs
  from the wider model in terms of its modelling
  approach
• Data Our Treasury model differs in terms of its
  default correlation source
• Diversification The Treasury model will show our
  one portfolio in isolation.

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Summary

• HBOS Treasury are implementing a credit and
  market risk Risk Engine
• For Credit Risk, this performs IMM and Economic
  Capital calculations and is the exposure stress
  testing engine
• Key enhancements for economic capital include
• Time of default
• Capital Allocation based on expected shortfall
• Building our own factor model (correlations)
• And others.
• Will use as part of challenge process for Group
  allocation produce and then to allocate agreed
  capital to netting pool/trade level and own alpha
  estimation.