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The Market Risk Project Capital Requirements Solvency Rules for banks

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Title: 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

3
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

8
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

9
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

11
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

14
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

16
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.

17
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.

18
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

19
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

20
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

21
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

22
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.

23
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

24
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.

25
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

26
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.

27
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

28
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

29
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

30
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

31
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

32
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

33
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

34
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.

35
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

36
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

37
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?

38
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

40
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
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