The Market Risk Project Capital Requirements Solvency Rules for banks

1
The Market Risk ProjectCapital Requirements /
Solvency Rules for banks

• Jacob Hostrup Andersen
• Financial Inspector,
• The Danish Financial Supervisory Authority
• CARTAC Project
• April 2008
• The presentation represents views of the speaker
  and not necessarily views of the Danish FSA.

2

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The Market Risk Project

• Objectives
• Understanding the market risk capital charge for
  a portfolio of
• Interest rate related instruments
• Equity positions
• Foreign exchange and
• Commodity positions
• Review capital regulation, any guidance notes and
  reporting forms

4
Rules for Capital Adequacy

• Basel Committee on Banking Supervision (BCBS)
• global standards for international active banks
• EU Solvency Directives
• common EU rules for all credit institutions and
  investment firms
• Denmark
• acts, executive orders and guidelines

5
The most important rules for Capital Adequacy
till now

• Basel Committee on Banking Supervision
• 1988 The Capital Accord (risk weighted assets)
• 1998 Updated
• 1996 Market Risk Amendment (market risk items,
  incl. VaR models)
• 1998 Updated
• 2004 Basel II (rating models for credit risk,
  rules for operational risk, rules on active
  supervision and market discipline)
• EU
• 1989 Solvency Directive (risk weighted assets),
• now part of the Banking Consolidated Directive
• 1993 CAD (standardized rules to measure market
  risk)
• 1998 CAD2 (Value at Risk models to measure market
  risk and commodities risk)
• 2006 CRD Capital Requirement Directives
• (correspond to Basel II)

6
EU Solvency Directives

• The following EU directives contain the main
  solvency rules and are implemented in Denmark
• Directives 2006/48/ and 2006/49/EC
• recast 2000/12/EC and recast 93/6/EEC
• (from 1 January 2007)
• Directive 2000/12/EC
• relating to the taking up and pursuit of the
  business of credit institutions
• Directive 93/6/EEC
• on the capital adequacy of investment firms and
  credit institutions (CAD).
• Directive 98/31/EC
• amending Directive 93/6/EEC (CAD II).

7
Basel Accord (1988)

• An agreement reached by G10 countries concerning
  capital adequacy standards for banks
• Banks should have specific liabilities to cover a
  minimum of 8 of their capital at risk
• Capital at risk was defined in terms of a set of
  multipliers to be attached to a number of
  different asset classes and multiplied by the
  balance sheet values
• Government 0 weight
• OECD banks 20 weight
• Private sector 100 weight

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The 1996 Market Risk Amendment

• The Amendment set capital standards for treatment
  of market risk items
• The objective was to provide an explicit capital
  cushion for the price risk to which banks are
  exposed
• Those arising from their trading activities

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What are market risks ?

• The risk inherent in dealing on a market where
  prices may change.
• The obvious market risks are
• buying on a market that subsequently falls and
• selling on market that rises.
• Basel definition
• Risk of losses in on- and off-balance sheet
  positions arising from movements in market prices

10
What are market risks ?

• The risk covered by the framework
• For instruments in the trading book
• Interest rate position risk
• Equity position risk
• Throughout the institution
• Foreign exchange risk
• Commodities risk

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Standardized Measurement Method
12
Market risks - measurement

• The measurement of capital charges will follow a
  building-block approach in which specific and
  general market risk are calculated.
• Banks is required to measure and apply capital
  charges in respect of their market risk in their
  trading book in addition to their credit risks in
  their banking book.

13
Purpose with Solvency Rules / Capital
Requirements

• The banks must maintain adequate capital against
  their risks
• The solvency rules are used to determine whether
  a banks capital is sufficient to support its
  activities
• The board of directors, the management and the
  public get a prudential measure of the relation
  between the banks capital and risks
• The banks get methods to calculate the various
  risks by calculating the capital needed using a
  weighting framework to quantify various kinds of
  risks
• The banks have to organize its data in a way that
  allows it to calculate the risks
• The banks get incentives to a better risk
  management systems because this reduces the
  solvency requirements.
• Capital standards are improving the safety of the
  banking industry

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Problems with capital requirements

• Solvency ratios judged in isolation may provide a
  misleading guide
• Some risks are difficult to quantify
• Regulation tend to strike a compromise between
  moving towards economic measures while being
  practical enough to be applicable by all players
• The rules cover wide spectrum of banks
• with very different sizes and activities.
• Capital is only a safety net
• important that banks have adequate controls and
  management
• Not all risks are included in the ratio
• operational risk, concentration risk
• The earnings are the first buffer to absorb
  losses
• earnings provide liquidity and confidence

15
Various market risk

• Banks take various market risk on their book
• (only some of these risk should be classified in
  the trading book)
• Loans and receivables
• fixed priced loans and mortgage deeds generate
  interest rate risk
• Investment/securities portfolio
• Trading portfolio,
• part of the investment portfolio (market maker,
  client driven)
• Own / proprietary portfolio,
• Strategic proprietary portfolio
• Long-term investment and part ownership of the
  banking-infrastructure

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What is the trading book?

• In simple terms, position are assigned to the
  trading book because the is a trading intent.
• Trading book positions are more vulnerable to
  short-term changes in their value and therefore
  warrant a capital charge against market risk.

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Bank Accounting

• The accounting rules differentiate between
  financial instruments
• held for trading purposes (in the trading book)
• Transactions such as the buying and selling of
  marketable securities and related instruments
  with the objective of making a profit from
  short-term price variations are part of a bank's
  trading book.
• The use of fair value for these transactions is
  consistent with the availability of market prices
  and the short-term horizon. It is separate from
  the banking book.
• Instruments held in the trading book are valued
  at market prices.
• profit and/or loss arising from the revaluation
  of trading book instruments are recognized in the
  income statement.
• intended to be held to maturity (in the banking
  book)
• Banking book instruments, by contrast, are
  carried in the balance sheet at historical cost.
• where there is a reduction in value of banking
  book assets, banks adjust the carrying value of
  such assets, typically by establishing allowances
  for losses.
• a reduction in value of a banking book asset is
  transferred to the profit and loss account
  (through provisions),
• unrealized gains are not recognized and can
  therefore become undisclosed reserves
• The accounting rules for the banking book do not
  take market risks into account
• except for the FX risk, where the end-period
  value is usually applied to almost all balance
  sheet items.

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GAAP

• Generally Accepted Accounting Principles
• each country has its own GAAP, and
• interpretations vary from country to country
• Example
• Canadian-US GAAP Royal Bank of Canada reports
• Canadian GAAP consolidated assets are slightly
  more than 6 higher than US GAAP consolidated
  assets
• Trade Date Accounting
• US GAAP - For securities transactions, trade date
  basis of accounting is used
• Canadian GAAP For securities transactions,
  settlement date basis of accounting is used for
  the consolidated balance sheet whereas trade date
  basis of accounting is used for the consolidated
  statement of income
• Non-cash Collateral
• US GAAP Non-cash collateral received in
  securities lending transactions is recorded
• Canadian GAAP Non-cash collateral received in
  securities lending transactions is not recognized
  

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IASB International Financial Reporting
Standards

• 1 January 2005,
• publicly-traded companies established in the
  European Union are required to prepare their
  consolidated accounts in conformity with the
  IFRS
• "IFRS as adopted by the EU".
• Whose standards are used ? and does it make a
  difference ?
• What is the prevalence of the IASB, FASB and
  other standards?
• At the end of 2005,
• Market capitalization totaling over USD 36
  trillion
• USD 17 trillion (47) corresponded to markets
  where US GAAP is the rule
• USD 11 trillion (31) corresponded to markets
  where IFRS are either required or permitted
• USD 4 trillion (11) corresponded to Japanese
  GAAP
• link http//www.iasb.org/
• What are the effects of using different
  standards?
• For one large international banking group, the
  reconciliation between US GAAP and IFRS, at
  year-end 2005, shows
• US GAAP net income was 2.6 lower than IFRS
• US GAAP shareholders' equity was 1.2 higher than
  IFRS

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How is the trading book defined under the Market
Risk Amendment?

• BCBS (1996)
• (2) The trading book means the banks proprietary
  positions in financial instruments
• Which are intentionally held for short-term
  resale and/or
• Which are taken on by the bank with the intention
  of benefiting in the short-term from actual
  and/or expected differences between their buying
  and selling prices
• Or positions taken in order to hedge other
  elements of the trading book
• (5) In many countries, marking to market will be
  synonymous with the trading book in these
  countries, therefore the trading book may be
  defined as comprising all securities and
  associated derivatives that are marked to market

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Market risk

• How is trading book defined under Basel II?
• A trading book consist of positions in financial
  instruments or commodities held either with
  trading intent or in order to hedge other
  elements of the trading book
• Positions with trading intent are those held
• for short-term sale
• with the intent of benefiting from actual or
  expected short-term price movements
• to lock arbitrage profits
• Positions in the trading book should be valued
  frequently and accurately, and the portfolio
  should be actively managed.
• Frequent value means daily marked-to-market or in
  limited cases, marked-to-model subject to certain
  operational requirement
• What positions are covered by the Market Risk
  Amendment?
• TB
• General MR Interest Rate Risk, Equity Risk, FX
  Risk, Commodities Risk
• Specific MR Interest Rate Risk, Equity Risk
• BB
• General MR FX Risk, Commodities Risk
• Specific MR

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How is the trading book defined under the Market
Risk Amendment?

• BCBS (2006)
• (footnote 3) the additional guidance does not
  modify the definition of the trading book.
• It focuses on policies and procedures that bank
  must have to book exposures in their trading
  book.
• It is view of the Committee that open equity
  stakes in hedge funds, private equity investment
  and real estate holdings do not meet the
  definition of trading book, owing to significant
  constraints on
• the ability of banks to liquidate these positions
  and
• value them reliably on a daily basis.

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Definition of trading book

• EU (1993)
• (6a) The trading book of a bank shall consist of
• proprietary positions in financial instruments
• Which are held for short-term resale and/or
• Which are taken on by the bank with the intention
  of benefiting in the short-term from actual
  and/or expected differences between their buying
  and selling prices
• Or positions taken in order to hedge other
  elements of the trading book
• (preamble) the concept of a trading book
  comprising positions in securities and other
  financial instruments
• which are held for trading purposes and are
  subject to mainly market risks and exposures
  relating to certain financial services provided
  to customers

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Definition of trading book

• EU (1993)
• (6b-c) The trading book of a bank shall consist
  of
• The exposures due to the unsettled transactions,
  free deliveries and OTC derivates instruments
  (settlement and counter-party risk), the
  exposures due to repurchase agreements and
  securities lending which are based on securities
  included in the trading book (and similar for
  reverse repurchase agreements)
• Those exposures in form of fees, commission,
  interest, dividends and margin on exchange-traded
  derivatives
• Particular items shall be included in or excluded
  from the trading book in accordance with
  objective procedures including, where
  appropriate, accounting standards.

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Definition of trading book

• Typical definition of trading book
• Positions must be held for trading intent
• (usually for short term gains)
• Positions hedging an exposure in the trading book
  (repos)
• Exposures from unsettled transactions, free
  deliveries.
• The Trading Book consists of securities /
  financial instruments, contracts/ derivatives and
  commodities
• Preconditions
• Free of any restrictive covenants on their
  tradability or able to be hedged completely
• Positions must be marked-to-market daily
• Positions should be actively managed

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Trading Book and Banking BookDanish approach

• Until End 2006 - the Danish definition of the
  books implies that a large part of a banks
  securities and derivatives is covered by the
  definition of the trading book.
• Importance was attached to the actual risk which
  is measurable in the Danish rules .
• Little or less importance was attached to the
  banks intention with the transaction since it is
  not possible to measure the intention.
• Trading Book (1996-2006)
• All quoted and transferable securities and
  derivatives, except
• Securities and derivatives which are used to
  hedge against other assets or liabilities
  interest rate risk. Therefore, these securities
  and derivatives are not marked to market,
• Indexed bonds, and premium bonds,
• Hold-to-expiry assets,
• Financial fixed assets holdings in affiliated
  and associated enterprises, other significant
  holdings, holdings in enterprises jointly owned
  by banks, and holdings acquired in connection
  with formalized agreements of cooperation with
  other financial institutions.

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De minimis clauses / applying the trading book
concept

• BCBS (1996)
• (7) Does not believe that it is necessary to
  allow any de minimis exemptions for the capital
  requirements for market risk,
• because the Capital Accord applies only to
  international active banks

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De minimis clauses

• EU directives
• Banks may calculate the capital requirements for
  their trading book business in accordance with
  credit risk standards provides that
• The trading book business does not normally
  exceed 5 of their total business (never exceed
  6 )
• The total trading book positions do not normally
  exceed EUR 15 million (never exceed EUR 20
  million
• Authorities may refer to either to
• The size of on and off balance sheet business
• The profit and loss account or
• The own funds
• or the combinations

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De minimis clauses

• Danish regulation
• Banks may use the banking book weighs for both
  banking and trading book items provided that
• The gross trading book normally represents a
  maximum of 5 of the total balance sheet and
  off-balance sheet items and normally represents
  the equivalent of EUR 15 million as a maximum (at
  no time exceed 6 or EUR 20 million)
• or where the total of deposits, bond issued,
  subordinated capital and own funds do not exceed
  an amount equivalent to EUR 40 million USD 50
  mio (small banks).
• DFSA will retain the right to apply the framework
  to other banks

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De minimis clauses

• Canada
• Where the greater of the value of trading book
  assets or the value of trading book liabilities
• Is at least 10 of total assets and
• Exceeds CAD 1 billion EUR 650 mill/ USD 850
  mill
• OSFI will retain the right to apply the framework
  to other institutions
• Hong Kong
• Some similarities with EU criteria
• The total trading book positions do not normally
  exceed HKD 50 million EUR 5 mill/ USD 6,5 mill
  (never exceed HKD 60 million)
• The capital adequacy ratio exceed 10
• The adjusted solvency ratio is not more that 1
  -point below the unadjusted, after incorporating
  the market risk requirement

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How to set a capital ratio ?Cooke ratio

• BCBS (1996)
• An explicit numerical link will be created by
  multiplying the measure of market risk by 12.5
  and adding the resulting figure to the sum of
  risk-weighted assets.
• Capital (divided by) /
• Risk Weighted Assets in the banking book plus
• 12.5Capital Charge for Trading Book items
• Tier 3 capital considerations
• Short term subordinated debt
• Limited to meet a proportion of capital
  requirements for market risk

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How to set a capital ratio ? Solvency Ratio vs.
Hair-cut

• Directives
• Own Funds minus Market Risk Hair-cut
• / (divided by)
• Credit Risk Weighted Assets
• Denmark
• Own Funds
• / (divided by)
• Credit and Markets Risk Weighted Items

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How to set a capital ratio ? Solvency Ratio vs.
Hair-cut (2)

• Example 1
• Own Funds 100
• Market Risk Hair-cut 20
• Credit Risk Weighted Assets 1000
• Market Risk Weighted Items 12.520 250
• Directives Calculation
• (10020)/1000 8
• Danish Calculation
• 100/(1000250) 8

• Example 2
• Own Funds 100
• Market Risk Hair-cut 80
• Credit Risk Weighted Assets 50
• Market Risk Weighted Assets 12.5 x 80 1000
• Directives Calculation
• (100-80)/50 40
• Danish Calculation
• 100/(501000) 9.5

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The Danish Solvency Rules

• The Financial Business Act, section 124
• The base capital of banks shall constitute no
  less than
• 8 per cent of the risk-weighted items (the
  solvency requirement), and
• EUR 5 million (minimum capital requirement)
• The absolute minimum capital is therefore at
  least 8 of the risks
• The Financial Business Act, section 143
• The Danish FSA shall lay down more detailed
  regulations for
• calculation of the risk-weighted items,
• reporting of the risk-weighted items, the capital
  requirement and the base capital,
• The DFSA can allow a bank to use internal models
  for calculation of the market risk weighted
  assets.
• There are similar rules for mortgage credit banks
  and investment firms.

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The Danish Solvency Rules

• Tier 1 Capital
• tier 2 Capital
• (the base capital and the additional capital)
• Risk weighted items

• The Financial Business Act,
• sections 129-142
• The Executive Order on Solvency Ratio Rules for
  Banks

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On-site SupervisionThe Danish approach

• On site supervision of solvency rules
• We would look at 3 main areas during on site
  supervision
• 1. The solvency ratios level and changes
  /developments in the ratio
• How is the banks ratio and risk profile compared
  to similar banks?
• Are the banks board of directors and senior
  management aware of a low ratio or a high risk
  profile?
• We can allocate individually applied capital
  requirements above 8

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On-site SupervisionThe Danish approach

• On site supervision of solvency rules
• 2. The banks procedure and IT systems in
  connection with the solvency calculations
• Do the bank have the necessary manuals and IT
  systems?
• Do the employees understand the calculations ?
• Is the bank dependent on a few key persons ?
• To what extent does a computer center do the work
  with the banks report to the DFSA?
• To what extent does the bank control the work of
  the computer center and other external suppliers?
• What similarities and differences are there
  between the solvency calculations and the banks
  internal risk reporting?
• What does the auditors work with the solvency
  calculations show?

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On-site SupervisionThe Danish approach

• On site supervision of solvency rules
• 3. Errors in the banks solvency calculations
• Are there often errors in the regular reports to
  the DFSA?
• Are there errors in the items the DFSA looks at
  during the inspection ?

39
Market Risks Measurementin the trading book

• Measurement of various risks arising from
• Positions related to interest rates
• Positions related to equities
• Positions in commodities
• Positions in Foreign Exchange
• Unsettled contracts with Counterparties
• Settlement
• Delivery
• Are non market risk in the trading book
• All market risk charges are transformed to risk
  weights items
• Exposures in the Trading Book are named positions

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Definition of position

• A "long position"
• shall mean a position that yields a premium in
  the event of a rise in prices/fall in interest
  rates for the relevant security/instrument.
• Bought call options and sold put options shall be
  covered by the definition of a long position.
• A "short position"
• shall mean a position that yields a loss in the
  event of a rise in prices/fall in interest rates
  for the relevant security/instrument.
• Sold call options and bought put options shall be
  covered by the definition of a short position.
• A "net position"
• shall mean the difference between the long and
  the short position in identical securities and
  financial derivative instruments.

41
Various risk definitions

• Position risk
• which is the risk that the institution will
  suffer a loss as a result of changes in the
  market value of a position in debt instruments
  etc., or equities etc.
• The position risk is broken down into
• Specific risk
• which is the risk that the institution will
  suffer a loss because the market value of a
  position changes as a result of factors related
  to the individual issuer of the debt instrument
  or equity or the individual debt instrument or
  equity itself.
• Is unrelated to underlying market parameters
• General risk
• which is the risk that the institution will
  suffer a loss because the position's market
  value changes due to factors related to the
  market as a whole.
• Refers to co-movements of prices
• Commodity risk
• which is the risk that the institution will
  suffer a loss due to changes in commodities prices

42
Various risk definitions

• Counterparty risk
• which is the risk that the institution will
  suffer a loss because a counterparty in a
  contract for a derivative or a spot transaction
  fails to fulfil his obligations towards the
  institution. Counterparty risk is relevant
  throughout the maturity of the transaction.
  Counterparty risk is a credit risk, but the
  designation only covers the cases mentioned.
• Settlement risk
• which is the risk that the institution will
  suffer a loss because a securities transaction
  cannot be completed. Settlement risk is relevant
  in connection with the performance and completion
  of transactions.
• Delivery risk
• which is the risk that the institution will
  suffer a loss because a counterparty is unable to
  pay for a debt instrument or equity delivered by
  the institution, or because a counterparty fails
  to deliver a debt instrument or equity which the
  institution has paid for. Delivery risk is
  relevant when the institution has met its
  obligations. Delivery risk is a credit risk, but
  the designation only covers the cases mentioned.
• Foreign-exchange risk
• which is the risk that the institution will
  suffer a loss due to changes in the exchange
  rates.

43
Underlying economics principles

• Tradable assets have random variations
• Long and short exposures/positions to the same
  instrument are offset
• Offsetting reduce the base for calculating the
  capital charges
• Long and short exposures/positions in similar
  instruments are also partially offset
• the price movement of a 4-year bond and a 5-year
  bond correlate because the 4-year and 5 year
  interest rate do

44
Interest rate risk Positions in debt instruments

• Only the banks positions in debt instruments
  /-securities in the trading book shall be
  included in the statement.
• A bank must
• Identify which positions must be included
• Derive the net positions
• Include these net positions for general market
  risk and specific risk
• Add the general market risk and specific risk
• Separated calculations for each currency.
• Thus, net positions may not be calculated and
  positions may not be matched in different
  currencies
• Derivatives based on debt instruments/securities
  are divided in a position in the underlying
  instrument and a position corresponding to the
  financing.
• Futures
• Forwards
• Swaps
• Options

45
Interest rate risk Positions in debt instruments

• Options are included, multiplied by the options
  delta.
• Banks may apply own models to calculate the
  deltas or
• use others sources like the deltas published by
  the stock exchange.
• Delta mean the expected change in a option price
  as a proportion of a small change in the price of
  the underlying instrument
• Net positions between long and short positions
  may only be calculated for identical debt
  instruments.

46
Treatment of Interest Rate Derivatives

• The interest rate risk measurement system should
  include all interest rate derivatives and
  off-balance sheet instruments assigned to the
  trading book that are sensitive to changes in
  interest rates.
• The derivatives are converted into positions in
  the relevant underlying.
• These positions are subject to the general market
  risk charges and, where applicable, the specific
  market risk charges for interest rate risk.
• The amounts reported should be the market value
  of the principal amount of the underlying or
  notional underlying.
• Interest rate derivatives include
• forward rate agreements (FRAs)
• other forward contracts
• bond futures
• interest rate swaps
• cross currency swaps
• forward foreign exchange positions
• interest rate options

47
Interest rate risk Positions in debt instruments

• Interest-rate futures
• This means agreements to exchange agreed interest
  rates at a given future date.
• The buyer of an interest rate future hedges
  against sinking interest rates.
• The transaction must be recorded as a long
  position of the underlying credit transaction and
  short up to the settlement in the future.
• Example a future on the 3-month LIBOR valued at
  50 million, which was bought in January and
  becomes due in Marts is dived into
• a 5-month long position (3-6 month long band) and
  
• a 2 month short position (1-3 month short band).
  

48
Interest rate risk Positions in debt instruments

• Forward contract
• Dealing in commodities, securities, currencies
  etc., for delivery at some future date at a price
  agreed at the time of the contract is made.
• Similar to futures (however some forwards cannot
  be closed out by matching).
• FRA (forward rate agreement)
• An agreement which one party agrees to pay a
  fixed interest rate and the other and variable
  interest rate on contracts. The net payment is
  the difference between these two rates.
• Buyers of FRAs hedge against the rising interest
  rates
• If interest rate increase, they will receive a
  cash settlement payment to equal to the diff.
  between the agreed FRA rate and the actual market
  rate at settlement.
• The purchased FRA shall be broken down into
• Short position (liability) up to maturity of the
  underlying credit transaction
• Long position (claim) up to the settlement of the
  FRA

49
Interest rate risk Positions in debt instruments

• Swap
• The essence of a swap is that the parties
  exchange the net cash flows of different types of
  borrowing instruments
• Interest rate swap
• under which a bank is receiving floating rate
  interest and paying fixed will be treated as
• a long position (receiving leg) in a floating
  rate instrument of maturity equivalent to the
  period until next interest fixing and
• a short position (paying leg) in a fixed rate
  instrument of maturity equivalent to the residual
  life of the swap.

50
Interest rate risk Positions in debt instruments

• Option
• The right to buy or sell a fixed quantity of a
  commodity, currency or security at a particular
  date at a particular price. Unlike futures the
  purchaser of an option is not obliged to buy or
  sell at the exercise price and will only do so if
  it is profitable.
• An option on a debt security must be treated as a
  position in the debt security
• Options on interest rates, debt instruments,
  equities, equities indices, financial futures,
  swaps and foreign currencies shall be treated as
  if the where positions equal in value to the
  amount of the underlying instrument multiplied by
  its delta.

51
Interest rate risk Positions in debt instruments

• Capital requirements are calculated to
• Specific risk (credit risk by issuer)
• Capital charge on each security whether it is a
  short or long position
• Only offsetting matched positions in identical
  issue
• General risk (real interest rate risk)
• Maturity approach
• Mod. Duration approach
• Capital charge on the net short or net long
  positions,
• where matching/ offsetting risk is taken place
  between time bands and zones

52
Interest rate riskPosition in debt instruments

• Why calculate a specific market risk capital
  charge?
• The charge for specific market risk protects
  against price movements in a security owing to
  factors related to the individual issuer, that
  is, price moves that are not initiated by the
  general market.
• Offsetting
• Offsetting between positions is restricted
• Offsetting is only permitted for matched
  positions in an identical issue.
• Offsetting is not allowed between different
  issues, even if the issuer is the same. This is
  because differences in coupon rates, liquidity,
  call features, and so on, mean that prices may
  diverge in the short run.

53
Interest rate risk Positions in debt instruments
The specific risk weights of debt instruments
54
Specific Market Risk

• The Market Risk Amendment and Basel II address
  the specific market risk capital charge
  differently.
• The main difference is that Basel II focuses more
  on relating the capital charge for specific
  market risk to the individual creditworthiness of
  the issuer.
• Market Risk Amendment - 5 broad categories
• 0 - government
• Qualifying
• 0.25 residual term less 6 months
• 1.00 residual term between 6 - 24 months
• 1.60 residual term exceeding 24 months
• 8 - other
• Basel II 5 broad categories
• 0 - AAA to AA- in credit rating
• Qualifying (A to BBB)
• 0.25 residual term less 6 months
• 1.00 residual term between 6 - 24 months
• 1.60 residual term exceeding 24 months
• 8 - all other
• Subject to national discretion, a lower specific
  risk charge may be applied when a government
  security is denominated in the domestic currency
  and funded by the bank in the same currency.
  Banks can include debt securities not externally
  rated under the A to BBB- category where the
  issuer has other securities listed on a
  recognized stock exchange,

55
Interest rate risk Positions in debt instruments

• More stringent rule in Denmark
• When defining qualifying issuers the options in
  section 2(12) of the EU CAD rules about external
  and internal rating are not used
• Only claims on issuers who fulfill the conditions
  of the Solvency Ratio Directive for a weighting
  of 10 or 20 are in the Danish rules
  considered as claims on qualifying issuers
• Banks, mortgage banks, ship finance
• Exposures on Investment firms,
• Exchange and Clearing Houses
• The EU CAD rules on weighting of banks exposures
  on investment firms, exchanges and clearing
  houses are not entirely clear.
• In the Danish rules these entities have the same
  weight as banks.
• The weight depends on whether it is a zone A
  (OECD approach) or a zone B entity.
• Thus, the CADs recognized third-country
  investment firm in the Danish rules is defined
  as an investment firm from a zone A country.

56
What is interest rate risk?

• Why calculate a general market risk capital
  charge?
• The capital charge for general market risk is
  designed to capture the risk of loss arising from
  adverse changes in market interest rates.
• Two methods for mapping interest rate positions
• maturity method
• duration method

57
Overview of the maturity method- general
interest rate risk

• Calculation
• 13 time bands (15 for coupon lt 3) for assigning
  instruments
• Offsetting long and short position within time
  bands is possible
• Partial offsets across time bands possible
• The procedure uses zones of maturity buckets
  grouping the narrower time band, where offsets
  decrease with distance between the time bands

58
Maturity Method Time Bands Weights
59
Maturity Method Time Bands Weights

• Time Bands for the Maturity Method
• Fixed income instruments with low coupons have
  higher sensitivity to changes in the yield curve
  than fixed income instruments with high coupons,
  all other things being equal.
• Fixed income instruments with long maturities
  have higher sensitivity to changes in the yield
  curve than fixed income instruments with short
  maturities, all other things being equal.
• This is why the maturity method uses a finer grid
  of time bands for low coupon instruments (less
  than 3) with long maturities.
• Fixed and Floating Rate Instruments
• Fixed rate instruments are mapped according to
  the residual term to maturity.
• Floating rate instruments are allocated according
  to the residual term to the next repricing date.

60
Interest rate risk Positions in debt instruments
The general risk weights /Maturity app.
61
Interest rate risk Positions in debt instruments

• The general risk weights /Maturity app.
• 1. step
• Each positions (the market value) is multiplied
  with
• a weight that depends on the maturity
• 2. step
• Allowance shall be made
• when a weighted positions is held alongside an
  opposite weighted position
• within the same maturity band or
• same zone and finally between zones
• 3.
• The principal rule is that matched positions
• is assigned a smaller capital charge than
  unmatched positions

62
Interest rate risk Positions in debt instruments

• The general risk weights /Maturity app.
• Calculation principles of matched and unmatched
  positions that are short and long in the final
  determination of the general risk weight
• The EU-rules explains capital charge for
• Maturity-weighted matched positions in a band
  (weight 0,10)
• Maturity-weighted matched positions in a zone
  1(weight 0,40)
• Maturity-weighted matched positions in a zone 2
  or 3 (weight 0,30)
• Maturity-weighted matched positions between zone
  1 and 2 and also between zone 2 and 3 (weight
  0,4)
• Maturity-weighted matched positions zone 1 and 3
  (weight 1,5)
• Maturity-weighted unmatched positions (weight
  1,0)
• The capital charge reflects the estimated
  interest rate structure.
• As an example, the interest rate risk in a
  maturity weighted position in zone 1 that is
  hedged by a proportionate maturity weighted
  position in zone 2 is assume to make 40 of the
  risk compared with an unmatched position.
• The allowance is less than in duration approach.

63
Illustration Maturity approachGeneral interest
rate riskReplica of example from BCSC

• Long position in a Qualifying bond
• Market value USD 13.33m, remaining maturity 8
  yrs, coupon 8.
• Long position in a Government bond,
• Market value USD 75m, remaining maturity 2
  months, coupon 7.
• Interest rate swap,
• Notional value USD 150m, bank receive floating
  rate interest and pays fixed, next interest reset
  after 9 months, remaining life of swap is 8
  years.
• (assumes the current interest rate is identical
  to the one the swap is based on)
• Long position in interest rate government bond
  future,
• Contract size is USD 50 m, delivery date after 6
  months, life of underlying government security is
  3.5 years
• (assumes the current interest rate is identical
  to the one on which the swap is based on).

64
Qualifying bondMarket value 13.33 million,
remaining maturity 8 years, coupon 8.
65
Government bond, Market value 75 million,
remaining maturity 2 months, coupon 7.
66
Interest rate swap, 150 million, bank receive
floating rate interest and pays fixed, next
interest reset after 12 months, remaining life of
swap is 8 years.
67
Long position in interest rate future, 50
million, delivery date after 6 months, life of
underlying government security is 3.5 years
68
Total trading book
69
Total trading book (2)
70
Overview of the duration method- General
interest rate risk

• Calculation
• Allows direct measurement of the sensitivities,
  skipping the time bands complexity, by using a
  spectrum of durations
• 3 in EU version 15 in the Basel Committee
  version
• Assign sensitivities to a duration ladder
• Sensitivities values should refer to changes of
  interest rates, whose values are within the 0.6
  to 1.0 range
• Offsetting is subject to a floor for residual
  risk, because of duration mismatched.

71
Interest rate riskPositions in debt instruments

• The general risk weights/ Mod. Duration approach
• Duration
• The sensitivity of market values to changes in
  interest rates is the modified duration
• The duration is the ratio of present values of
  future cash flow, weighed by dates, to the market
  value of an asset
• Unlikely maturity, duration considers all cash
  flows and gives some weights to their timing
• For a zero-coupon, the duration is identical to
  maturity
• The modified duration is duration multiplied by
  1/(1r)

72
What is Duration? Why is Modified Duration
Important?

• Duration is a measure of the average
  cash-weighted term-to-maturity of a bond.
• There are two types of duration
• Macaulay duration this measures the weighted
  average of the time to each payment
• Modified duration this measures the sensitivity
  of a bond price to yield changes by detailing the
  bond price change, given a certain change in the
  bond's yield
• While all bond prices are sensitive to changes in
  yields (that is, interest rates), this
  sensitivity tends to be greater for longer-term
  bonds. However, duration is a better measure of
  sensitivity to yields than maturity.
• For example, a 30-year coupon-paying bond and a
  30-year zero-coupon bond have the same maturity
  but 30-year zero-coupon is more sensitive to
  yield changes than the 30-year coupon-paying
  bond.
• Duration measures sensitivity of bond prices to
  interest rate changes, that is, it is a measure
  of
• bond price volatility
• interest rate risk
• Duration is useful in the management of risk,
  where
• you can hedge the interest rate sensitivity of an
  investment
• you can match the duration of assets and
  liabilities immunization against changes in
  yields

73
Macaulay Duration

• The formula clarifies that the duration of a bond
  is the weighted average of the time to each
  payment, with weights proportional to the present
  value of each payment.
• The duration can therefore be thought of as a
  measure of the 'average' maturity of the bond,
  taking into account the fact that the holder of
  the bond doesn't have to wait until the
  redemption date to receive all of the bond's cash
  flows.
• The duration of a bond can be shown to measure
  the sensitivity of the bond price to changes in
  interest rates. Duration is shorter than maturity
  for all bonds except zero-coupon bonds.
• The duration of a zero-coupon bond is equal to
  its maturity.

74
Modified Duration

• Interest Rate Elasticity of a Bond
• modified duration is considered more useful
  because it measures the price sensitivity to
  interest rate changes and is computed as follows

75
Interest rate riskPositions in debt instruments

• The general risk weights/ Mod. duration approach
• Modified duration V/(1r)
• where
• V duration
• r effective interest rate (implicit discount
  rate)
• C repayment of principle and interest

76
Interest rate riskPositions in debt instruments

• Danish banks shall apply the duration method, but
  not the maturity method in the calculation of
  the general risk of debt instruments.
• Danish banks hold approximately 20 of their
  balance in bonds.
• Callable mortgage credit bonds
• In the case of bonds which may be redeemed at par
  before the expiry date on the initiative of the
  issuer, modified duration shall be reduced by the
  discount factors published by the DFSA.
• However, the bank may use its own models when
  calculating duration and modified duration for
  callable debt instruments. The bank shall inform
  the DFSA of the models applied for this purpose.
• The modified duration can be adjusted for
  prepayment risk
• (V/(1r) ) (1-f)
• V Duration (e.g. from the stock exchange list
  or based on zero coupon rates)
• r Yield to maturity/ the implied discount rate
  (e.g. from the stock exchange list)
• f Reduction factor calculated by DFSA or bank
  by themselves

77
Interest rate riskPositions in debt instruments

• The general risk weights /Mod. Duration approach
• 1. step
• Each position (the market value) is multiplied
  with
• The modified duration figure (potentially reduced
  for the prepayment risk on callable bonds), and
• a weight that depends on the modified duration
  placement into the 3 durations zones
• 2. step
• Allowance shall be made
• when a weighted positions is held alongside an
  opposite weighted position within the same
  maturity band or same zone and finally between
  zones
• 3. step
• The principal rule is that matched positions is
  assigned a smaller capital charge than unmatched
  positions

78
Duration Method Time Bands Assumed Changes in
Yield
79
Duration Method

• This methods maps each position according to its
  duration to a duration ladder.
• Duration is a measure of average maturity of a
  bonds cash flows from both coupon and principal
  repayment. It is expressed in years and allows
  bonds with different coupons and maturities to be
  compared.
• The price sensitivity is calculated with respect
  to small changes in the yield curve. The
  amendment assume shifts between 60 and 100 b.p.
  in the yield curve for each time (duration) band.
  
• The price sensitivity is a more accurate measure
  of market risk

80
Interest rate riskPositions in debt instruments

• The general risk weights /Mod. Duration approach
• A weight that depends on the modified duration
  into 3 durations zones

81
Interest rate riskPositions in debt instruments

• The general risk weights /Mod. Duration approach
• The weights result in capital requirements, which
  express the assumed change in interest rate for
  each duration zone
• In duration zone 1, the capital requirement
  corresponds to
• an assumed change in interest of 1 percentage
  point.
• In duration zone 2, the capital requirement
  corresponds to
• an assumed change in interest of 0.85 percentage
  point.
• In duration zone 3, the capital requirement
  corresponds to
• an assumed change in interest of 0.70 percentage
  point.
• The differences take into account the differences
  in interest rate volatilities in the 3 zones.

82
Interest rate riskPositions in debt instruments

• The general risk weights /Mod. Duration app.
• The spreadsheet application Excel can calculate
  the duration.
• Function is called duration
• Type in
• settlement,
• maturity,
• coupon,
• yield,
• frequency,
• Function called XIrr returns the internal yield
  for a schedule of cash flows

83
Calculating Duration in Excel

• Wish to calculate duration for the two following
  bonds
• Bond A maturity 5 yrs, coupon 7
• Bond B maturity 5 yrs, coupon 13
• Assume yield to maturity of 7
• There is an add-in function in Microsoft Excel
  called Duration( ), which requires that we give
  the start and end date of the bond.
• However, these can be chosen arbitrarily to give
  the desired maturity.
• Suppose a bond has a 13 annual coupon and
  matures in 5 years. The yield to maturity is also
  7.
• In this case, the settlement is dated as
  (2007,3,31) and
• the maturity as (2012,3,31), which gives the
  desired maturity of the bond equal to 5 years.
• The duration of bond B is given by
• DURATION(DATE(2007,3,31),DATE(2012,3,31),13,7,
  1)
• 4.086656968

84
Interest rate riskPositions in debt instruments

• The general risk weights /
• Mod. Duration approach

85
Interest rate riskPositions in debt instruments

• The general risk weights /Mod. Duration app.

86
Interest rate riskPositions in debt instruments

• The general risk weights /Mod. Duration app.

87
Interest rate riskPositions in debt
instruments The general risk weights /Mod.
Duration app. Some examples on weights to
general risk
88
Interest rate riskPositions in debt
instruments The general risk weights /Mod.
Duration app.

• Calculation principles of matched and unmatched
  positions that are short and long in the final
  determination of the general risk weight
• The EU-rules explains weight for
• Duration-weighted matched positions in a zone
• (weight 0,02)
• Duration-weighted matched positions between zone
  1 and 2 and also between zone 2 and 3
• (weight 0,4)
• Duration-weighted matched positions zone 1 and 3
• (weight 1,5)
• Duration-weighted unmatched positions
• (weight 1,0)
• The weights reflects the estimated interest rate
  structure.
• As an example, the interest rate risk in a
  duration-weighted position in zone 1 that is
  hedged by a proportionate duration weighted
  position in zone 2 is assume to make 40 of the
  risk compared with an unmatched position.

89