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					           The Market Risk Project
Capital 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.



                                                                                                1
2
            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




                                                                    3
           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

                                                                  4
           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)



                                                                           5
             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).


                                                                                        6
                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

                                                                    7
    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



                                                  8
            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

                                                             9
            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

                                          10
Standardized Measurement Method




                                  11
        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.


                                                      12
                        Purpose with
       Solvency Rules / Capital Requirements

• The banks must maintain adequate capital against their risks

   – The solvency rules are used to determine whether a bank‟s 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 bank‟s 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


                                                                           13
                                  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



                                                                             14
                     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




                                                                                 15
        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.




                                                          16
                              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.



                                                                                                                  17
                                             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




                                                                                                                18
                                              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




                                                                                                           19
      How is the trading book defined
       under the Market Risk Amendment?
• BCBS (1996)

  – (2) The trading book means the bank‟s 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

                                                                         20
                                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:




                                                                                               21
      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.


                                                               22
             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


                                                                                  23
          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.

                                                                24
             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 (repo‟s)
   – 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

                                                                             25
            Trading Book and Banking Book
                                 Danish approach
•   Until End 2006 - the Danish definition of the books implies that a large part of a
    bank‟s 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 bank‟s 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.




                                                                                                        26
              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




                                                                  27
                    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


                                                                      28
                    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


                                                                                   29
                 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

                                                                      30
           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
  – 12.5*Capital Charge for Trading Book items]

  – Tier 3 capital considerations
      • Short term subordinated debt
      • Limited to meet a proportion of capital requirements for market
        risk


                                                                      31
              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

                                                32
               How to set a capital ratio ?
               Solvency Ratio vs. Hair-cut (2)

•   Example 1:                         Example 2:
     – Own Funds = 100                 •   Own Funds = 100
     – Market Risk Hair-cut = 20       •   Market Risk Hair-cut = 80

     – Credit Risk Weighted Assets =   •   Credit Risk Weighted Assets = 50
       1000

     – Market Risk Weighted Items =    •   Market Risk Weighted Assets = 12.5
       12.5*20 = 250                       x 80 = 1000

•   Directives‟ Calculation:           •   Directives‟ Calculation:
     – (100–20)/1000 = 8 %                  –   (100-80)/50 = 40 %


•   Danish Calculation:                •   Danish Calculation:
                                            –   100/(50+1000)= 9.5 %
     – 100/(1000+250)= 8 %



                                                                                33
                 The Danish Solvency Rules
•   The Financial Business Act, section 124:

•   The base capital of banks shall constitute no less than

     1. 8 per cent of the risk-weighted items (the solvency requirement), and
     2. 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

     1. calculation of the risk-weighted items,
     2. 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.



                                                                                              34
           The Danish Solvency Rules

Tier 1 Capital                   • The Financial Business
+ tier 2 Capital:                  Act,
   – (the base capital and the   • sections 129-142
     additional capital)




Risk weighted items:             •   The Executive Order on
                                     Solvency Ratio Rules for
                                     Banks

                                                                35
               On-site Supervision
                The Danish approach

• On site supervision of solvency rules
  – We would look at 3 main areas during on site
    supervision

  – 1. The solvency ratio‟s level and changes
    /developments in the ratio
     • How is the bank‟s ratio and risk profile compared to
       similar banks?
     • Are the bank‟s 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%
                                                               36
                   On-site Supervision
                     The Danish approach

• On site supervision of solvency rules

   – 2. The bank‟s 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 bank‟s
         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 bank‟s internal risk reporting?
       • What does the auditors‟ work with the solvency calculations show?


                                                                                37
              On-site Supervision
               The Danish approach


• On site supervision of solvency rules

  – 3. Errors in the bank‟s 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 ?




                                                              38
          Market Risks Measurement
             in 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
   o   Unsettled contracts with Counterparties
   o   Settlement
   o   Delivery

o 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

                                                                  39
                  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.



                                                                           40
                      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

                                                                                                      41
                     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.




                                                                                                      42
      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

                                                                43
                              Interest rate risk
                     Positions in debt instruments
•   Only the bank‟s 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



                                                                                                   44
                     Interest rate risk
              Positions in debt instruments

• Options are included, multiplied by the option‟s 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.


                                                                       45
    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




                                                                                    46
                     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).


                                                                            47
                             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



                                                                                                     48
                    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.


                                                                   49
                    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.


                                                                    50
                     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

                                                                                 51
                    Interest rate risk
               Position 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.

                                                                      52
                       Interest rate risk
                 Positions in debt instruments


The specific risk weights of
debt instruments




                                                 53
                          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,


                                                                                                  54
                           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 CAD‟s “recognized third-country investment firm” in the Danish rules is
           defined as an investment firm from a zone A country.


                                                                                               55
         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




                                                                 56
     Overview of the maturity method
           - general interest rate risk

• Calculation

   – 13 time bands (15 for coupon < 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

                                                                 57
Maturity Method: Time Bands & Weights




                                        58
                  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.

                                                                59
                           Interest rate risk
                  Positions in debt instruments
The general risk weights
/Maturity app.




                                                  60
                           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




                                                                                   61
                                    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.


                                                                                                                       62
            Illustration: Maturity approach
                      General interest rate risk
                          Replica of example from BCSC

1) Long position in a Qualifying bond:
    •   Market value USD 13.33m, remaining maturity 8 yrs, coupon 8%.

2) Long position in a Government bond,
    •   Market value USD 75m, remaining maturity 2 months, coupon 7%.

3) 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)


4) 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).



                                                                                                   63
Qualifying bond:
Market value 13.33 million,
remaining maturity 8 years, coupon 8%.




                                         64
Government bond,
Market value 75 million,
remaining maturity 2 months, coupon 7%.




                                          65
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.




                                                                          66
Long position in interest rate future,
50 million, delivery date after 6 months,
life of underlying government security is 3.5 years




                                                      67
Total trading book




                     68
Total trading book (2)




                         69
     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.

                                                                      70
                    Interest rate risk
             Positions 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/(1+r)


                                                                           71
              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



                                                                                                                     72
                      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.

                                                                                       73
                    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




                                                                            74
                    Interest rate risk
              Positions in debt instruments

• The general risk weights/
  Mod. duration approach

• Modified duration =
  V/(1+r)

   – where

   – V = duration
   – r = effective interest rate
     (implicit discount rate)
   – C = repayment of principle
     and interest

                                              75
                              Interest rate risk
                    Positions 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/(1+r) ) * (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


                                                                                                76
                           Interest rate risk
                         Positions 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




                                                                                                  77
          Duration Method:
Time Bands & Assumed Changes in Yield




                                        78
               Duration Method:

• This methods maps each position according to its
  duration to a duration ladder.
• Duration is a measure of average maturity of a bond‟s
  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

                                                              79
                      Interest rate risk
                 Positions in debt instruments

•   The general risk weights /Mod. Duration approach

     – A weight that depends on the modified duration into 3 durations zones




                                                                               80
                   Interest rate risk
              Positions 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.



                                                                          81
                      Interest rate risk
                    Positions 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

                                                                           82
               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




                                                                                                83
                     Interest rate risk
                    Positions in debt instruments


•   The general risk weights /
•   Mod. Duration approach




                                                    84
                     Interest rate risk
                   Positions in debt instruments
•   The general risk weights
    /Mod. Duration app.




                                                   85
Interest rate risk
Positions in debt instruments
 •   The general risk weights
     /Mod. Duration app.




                                86
       Interest rate risk
    Positions in debt instruments

The general risk weights /Mod. Duration app.

 Some examples on weights to general risk




                                               87
                                Interest rate risk
                              Positions 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.


                                                                                               88
Horizontal Disallowance Table




                                89
                    What is Convexity?
•   Duration produces a first order approximation to the change in the
    value of a bond or obligation with respect to a change in the interest
    rate.
•   The extent to which the future value of the bond (or bond portfolio)
    changes depends on its convexity.
•   Bonds with the same duration can have different convexities as shown
    in the graph.
     – In the graph, Bond 1 is more convex than Bond 2 and hence its price falls at
       a slower rate as the yield increases.

•




                                                                                      90
             Market Risks Measurement
                in 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
   o   Unsettled contracts with Counterparties
   o   Settlement
   o   Delivery

o 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

                                                                  91
                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.

                                                                      92
                          What is Equity Risk?
•   Equity risk is the risk that a bank's positions
     –   may be adversely affected by movements in equity prices.

•   The Market Risk Amendment sets out a minimum capital standard
     –   to cover the risk of equity positions held in the trading book.
           • It applies to long and short positions in all instruments that exhibit behavior similar
              to equities, with the exception of non-convertible preference shares, which fall under
              interest rate requirements.

•   To calculate the minimum capital charge for equity risk, you must
    calculate two separate charges:

     – A general market risk charge of 8% is applied to the net overall position.
     – A specific market risk charge is applied to the gross equity position:
           • The basic specific risk charge is 8%.
           • For a well-diversified and liquid portfolio, the specific risk charge is reduced to 4%.
     – It is at the discretion of the national supervisory authority to define what
       constitutes a sufficiently well-diversified and liquid portfolio.




                                                                                                       93
                        Equity position risk
                Positions in equity instruments

•   Only the bank‟s positions in equity instruments in the trading book shall
    be included in the statement, except if these are deducted from the
    capital base; e.g.:
     – Securities and derivatives which are used to hedge against other assets‟ or
       liabilities‟ risk. Therefore, these securities and derivatives are not marked to
       market,
     – 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 and holdings in other banks/financial
       institutions,
     – securities and derivatives in pool arrangements where the bank‟s customers
       get the entire profit or loss.

•   Positions must be subject to daily valuation (marked-to-market)

•   Long and short positions in same issue may be reported on net basis


                                                                                          94
                   Equity position risk
            Positions in equity instruments
• Capital requirements
       • per national market and not per currency:

   – Specific risk (gross positions):
       • The sum of long positions plus the sum of short positions
       • Capital charge is 4% (8 % if not a highly liquid portfolio)
       • 2% EU capital charge, if
           – The issuers debts instruments are qualifying items
           – Highly liquid equities
           – No concentration


   – General risk (net positions)
       • The diff. between the sum of long positions and sum of short
         positions
       • Capital charge is 8 %.


                                                                        95
                     Equity position risk
             Positions in equity instruments

• Danish approach
   – Has decided to impose more stringent rules than mentioned in the
     EU directives.

   – This includes the following areas:
       • Annex I of the EU CAD gives an opportunity under certain conditions to
         lower the capital requirement for the specific risk of equities from 4 % to
         2 %. This opportunity is not included in the Danish rules.
       • The EU CAD (1993) does not include rules concerning UCITS (mutual
         funds). In the Danish rules they are treated as equities.

• Austrian approach
   – 2 % capital charge for specific equity risk if following criteria are
     met:
       • Portfolio must be highly diversified – no individual position shall comprise
         more the 5 % of overall value (10 % for stocks included in ATX)


                                                                                    96
                      Equity position risk
             Positions in equity instruments

• UK approach
   – 2 % capital charge for specific equity risk for qualifying equities if
       • It belongs to a country portfolio that satisfies
            – No individual position exceed 10 % of the gross value of the portfolio
            – The sum of positions which individually represent between 5% and 10% of the
              portfolio‟s gross value does not exceed 50% of the portfolio‟s gross values
            – It is not an issuer that has issued debt instruments that attract and 8% capital
              charge.

   – 0 % capital charge for specific equity risk for qualifying indices

       • Contain at least 20 equities
       • No single equity represents more than 20% of the total index
       • No 5 equities represent more than 60% of the total index
            – FTSE 100, S&P 500




                                                                                             97
                             Example

•   First we must determine the overall net open position




                                                            98
                           Example (2)

•   Short USD 220,000 –
•   Capital charge is 8% of USD 220,000 or USD 17,600
•   Capital charge for general risk is USD 17,600
•   Second we must work out the specific risk




                                                        99
                             Example (3)

•   Gross position is USD 1,520,000
•   Capital charge for general risk is USD 17,600
•   Capital charge for specific risk is USD 60,800
•   The overall charge for the portfolio is USD 78,400




                                                         100
           Treatment of Equity Derivatives

•   Equity derivatives, except for options, and other off-balance sheet
    positions that are affected by changes in equity prices, are subject to
    the measurement approach for equities.

     – Positions in these equity derivatives should be converted into notional
       positions in the relevant underlying stock or portfolio of stocks.
     – For example, stock index futures should be reported as the marked-to-
       market value of the notional underlying equity portfolio.

     – Equity swaps should be treated as two notional positions.
     – For example, in an equity swap where a bank is receiving an amount based
       on the change in value of one stock index and paying an amount based on a
       different index, the bank is regarded as having a long position in the former
       index and a short position in the latter index.
     – An equity swap is an agreement between two counterparties to swap the
       returns on a stock or a stock index for a stream of payments based on some
       other form of asset return. Often, one payment leg is determined by a stock
       index with the second leg determined by a fixed or floating rate of interest.
       Alternatively, the second leg may be determined by some other stock index
       (often referred to as a relative performance swap).

                                                                                   101
             Calculating the Capital Charge

•   What is the overall capital charge for market risk for this portfolio assuming that it
    is subject to an 8% capital charge for specific risk?




                                                                                       102
                                   Commodities
•   A commodity is defined as a physical product that can be traded on a secondary
    market, for example,
     –   agricultural products
     –   minerals and
     –   precious metals

•   Price risk in commodities is often more complex and volatile than price risk
    associated with currencies and interest rates.
•   Commodity markets often lack liquidity.

•   Offsetting
     –   When you are measuring risk in commodities, offsetting between positions is restricted.
     –   Offsetting is allowed between long and short positions in each commodity to calculate
         open positions.

•   In general, offsetting is not allowed between positions in different commodities.
     –   However, national supervisory authorities may permit netting between different sub-
         categories
     –   different categories of crude oil, if they are deliverable against each other or they are
         close substitutes to each other,
           •   with a minimum correlation of 0.9 between price movements over a period of at least one year




                                                                                                              103
        Calculating the Capital Charge

• Simplified Approach
   – banks must express each commodity position, spot
     plus forward, in terms of the standard unit of
     measurement (barrels, kilos, grams, and so on).
• The capital charge is the sum of two charges:
   – 15% of the net position in each commodity
   – 3% of the bank's gross commodity positions, that is,
      • the sum of the net long plus net short positions in
        each commodity,
      • calculated using the current spot price

                                                              104
      Treatment of Commodity Derivatives


•   All commodity derivatives and off-balance sheet positions affected by changes in
    commodity prices should be included in the commodities risk measurement
    framework.

•   To calculate the market risk, commodity derivatives should be converted into
    notional commodities positions and assigned to maturities as follows:

     –   Futures and forward contracts relating to individual commodities should be incorporated
         as notional amounts of barrels, kilos and so on, and assigned a maturity with reference to
         expiry date.
     –   Commodity swaps, where one leg is a fixed price and the other the current market price,
         should be incorporated as two positions.
           •   Each position should be equal to the notional amount of the contract, with a position corresponding to
               each payment on the swap and slotted into the maturity ladder accordingly.
           •   The positions are long positions if the bank is paying fixed and receiving floating, and
           •   short positions if the bank is receiving fixed and paying floating.
     –   Commodity swaps where the legs are in different commodities should be incorporated in
         the relevant maturity ladder.
     –   Offsetting is only allowed if the commodities belong to the same sub-category.


                                                                                                                  105
                                        Commodity risk
                      Positions in commodity instruments
•   Definition:
     –   A physical product which is or can be traded on a secondary market,
           •   e.g. oil, electricity or metals


•   Risks are often more volatile and positions less liquid than with currencies or
    interest rates

•   Long and short positions in same issue may be reported on net basis

•   The simplified approach:

     –   Specific risk (gross positions):
           •   The sum of long positions plus the sum of short positions in each commodity
           •   Capital charge is 3%
     –   General risk (net positions)
           •   The diff. between the sum of long positions and sum of short positions
           •   Capital charge is 15 % in each commodity.


•   The maturity ladder approach is not offered in Denmark




                                                                                             106
                      Capital Standards for
                   Foreign Exchange (FX) Risk

•   Foreign exchange risk is the risk that the value of foreign exchange
    positions may be adversely affected by movements in currency
    exchange rates.
     – Foreign exchange risk incurs only general market risk
     – The capital charge for foreign exchange risk may also include a charge for
       positions in gold

•   The capital requirement for positions held in foreign currencies,
    including gold, is calculated at 8% of the overall net open position. Gold
    is included because its volatility is more in line with foreign currencies)


•   Two steps are required to calculate the overall net open position:

•   Step 1: Determine the exposure in each currency
•   Step 2: Determine the overall net open position across FX exposures

                                                                                    107
                 Foreign Exchange Risk
       Positions in foreign currencies and gold

• The risk is related to the whole book and not only trading book.

• Net positions in each currency is measured on all outstanding
  accounts (spot, forward, irrevocable guarantees, delta adjusted
  options).
   – Closely correlated currencies could be merged.

• The ‘shorthand’ methods:

   – Capital charge is
       • 8 % of the sum of the net short positions or the sum of the net long
         positions whichever is higher, plus position in gold (regardless of sign)
       • Minus a deduction of 2 % of the capital base.




                                                                                     108
                          FX Exceptions
•   In certain cases the national supervisory authority may allow banks to
    exclude FX positions from the capital charges calculation.

•   Banks with positions taken deliberately to hedge against an adverse
    exchange rate movement on its capital ratio may exclude these
    positions provided:

     – the position is of a structural nature
     – the excluded position protects only the bank's capital adequacy ratio
     – the exclusion of the position is applied consistently

•   Banks with negligible business in foreign currencies and with no FX
    positions taken for their own account may exclude their FX positions if
    they meet both of the following requirements:

     – their FX business (the greater of the sum of their gross long positions and the
       sum of their gross short positions) does not exceed 100% of eligible capital
     – its overall net open position does not exceed 2% of its eligible capital


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                Step 1:
Determine the Exposure in Each Currency

• The open position in each currency is the sum of:

   – the net spot FX position
   – the net forward FX position
   – guarantees and similar instruments that are certain to be
     called and are likely to be irrecoverable.
   – net future income and expenses not yet accrued but already
     fully hedged
   – any other item representing a profit or loss in foreign
     currencies
   – the net delta-based equivalent of the total book of foreign
     currency options

                                                              110
                   Step 2:
    Determine the Overall Net Open Position
             Across FX Exposures


• You can determine the overall net open position
  of the portfolio by
  – first converting the exposure in each foreign currency into the
    reporting currency at the spot rates.
  – Then, calculate the overall net position by summing the following:
       • the greater of
           – the sum of the net short positions or
           – the sum of the net long positions
               » (excluding positions in gold)
          – the net position in gold,
               » regardless of whether it is long or short


                                                                         111
    Example of calculating the capital
           charge for FX risk
•   A bank has the following positions that have been converted at spot
    rates into its reporting currency, Swiss francs (CHF).
     – The higher of the sum of the net long and net short currency positions is CHF
       300m.
     – The capital charge is therefore calculated as 8% of CHF 300m, plus the net
       position in gold (CHF 35m):
•   Capital charge = 8% of CHF 335m = CHF 26.8m




                                                                                  112
                             Counterparty Risk

•   In general, counterparty risk is only present in the trading book on contracts that
    are not finally settled.

•   The risk that at some future date some party fails to complete a contract,
    resulting in a loss to the bank.
     –   The market risk is covered by the relevant positions risk - e.g. interest rates.

•   Types of contracts
     –   Interest rate related contracts
     –   Equity related contracts
     –   FX related contracts
     –   Commodity contracts

•   Risk calculation:
•   Contracts with positive market value are included (price has moved in favour of
    the bank) and the underlying principal amount of contracts are included.
     –   Longer maturity demands more capital.
•   Netting considerations


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                                         Other risks

•   Settlement risk (delivery versus payment)
     –   High capital charge, if settlement fails.
     –   Progressive capital charge the longer timer after due settlement day.
     –   Only the price differences to which a bank is exposed is charged (settlement price minus
         current market value).

•   Delivery Risk (free deliveries)

     –   Capital charge on free deliveries is 8 %.
     –   Free deliveries if the bank has paid for securities before receiving them or has delivered
         securities before receiving the payment.

•   Option risk
     –   Delta-equivalent positions are part of the standardised methodology.
     –   No explicit capital charge for gamma and vega risks (or rho and theta risk).

     –   EU directive:
           •   “The competent authorities shall require that other risk associated with options are safeguarded
               against.” No explicit formula given.



                                                                                                                  114
                                Other risk

•   Option risk (case by case capital
    charge)
     – The simplified approach is not
        offered in Denmark




                                             115
                  Simplified Approach
• Option positions and their associated underlyings (cash or
  forward) are 'carved out' from the standardized methodology.
   – They are subject to separately calculated capital charges that
     incorporate both general market risk and specific risk. These
      charges are then added to the capital charges for the
      relevant risk categories: interest rate risk, equities risk,
      foreign exchange risk or commodities risk.




                                                                      116
             Simplified Approach – Example

•   A bank holds 100 shares currently valued at USD 10, and also holds an equivalent
    number of put options with a strike price of USD 11
     –   (each option entitles the bank to sell one share).
•   Since these are equity options, they are subject to the capital charges for general
    and specific market risk according to the standardized framework for equity risk.
     –   The capital charge is levied at 8% for general market risk and
     –   8% for specific market risk, giving a summed charge of 16%.
•   Market value of 100 shares = USD 1,000
•   First, multiply the market value by the sum of general and specific market risk
    charges.
     –   USD 1,000 x 16% = USD 160
•   Then, calculate the amount the option is in-the-money.
     –   (USD 11 - USD 10) x 100 = USD 100
•   The capital charge is the general and specific market risk charge less the amount
    the option is in-the-money.
     –   USD 160 - USD 100 = USD 60
•   A similar methodology applies for options whose underlying is a foreign currency,
    an interest rate related instrument or a commodity.




                                                                                      117
             Intermediate Approaches




• Delta-plus methods:
  – use the sensitivities parameters or Greek letters
    associated with options to measure their market risk
    and capital requirements.
  – the delta-equivalent position of each option becomes
    part of the standardizes methodology, with the delta-
    equivalent amount, subject to the general market risk
    charges. Separate capital charges are then applied to
    gamma and vega risk of the option positions.
  –

                                                        118
                               Greek Letters
•   Five coefficients are used to help explain how option values behave in
    relation to changes in market parameters
     –   price of the underlying asset,
     –   the strike price,
     –   the volatility of the underlying,
     –   the time to maturity and
     –   the risk-free interest rate
     –
•   These are represented by the Greek letters delta, gamma, vega, theta
    and rho, and are referred to as the 'option Greeks'.
     – Delta (Δ) measures the rate of change in the value of an option with respect
       to a change in the price of the underlying asset.
     – Gamma (Γ) measures the rate of change in the delta of an option with
       respect to a change in the price of the underlying asset.
     – Vega (Λ) measures the rate of change in an option price with respect to a
       change in market volatility for the underlying asset price.
     – Theta (Θ) measures the rate of change in an option value with respect to a
       change in the remaining maturity (time) of the option.
     – Rho (Ρ) measures the rate of change in the value of an option with respect
       to a change in the risk-free interest rate.


                                                                                 119
                                          To sum up:
•   Interest Rate Risk
     –   The capital requirement for interest rate risk is the sum of two separately calculated
         capital charges for general market risk in the portfolio and specific market risk for each
         security.
•   General market risk
     –   There are two methods which both use time bands to map different positions to reflect the
         price sensitivities of the positions:
           •   the maturity method
           •   the duration method
     –   For both methods, the capital charge is the sum of the following four elements:
           •   the net short or long position in the whole trading book
           •   a 'vertical disallowance' charge for the matched positions in each time band
           •   a 'horizontal disallowance' charge for the matched positions across different time bands
           •   a charge for positions in options (if applicable)
     –   Separate maturity ladders should be used for each currency in order to calculate the
         capital charges per currency; these should then be summed with no offsetting between
         positions of opposite sign.

•   Specific market risk
     –   The capital charge for specific risk is graduated in five broad categories, depending on the
         type of security.
           •   When measuring specific risk, offsetting is restricted to matched positions in the identical issue.




                                                                                                                     120
                           To sum up (2)

•   Equity Risk
     – Long and short positions in the same issue can be reported on a net basis.
       The capital requirement for equity risk in the trading book is the sum of two
       separately calculated charges:
•   general market risk
     – The capital charge is 8% of the overall net position, that is, the difference
       between the sum of the long positions and the sum of the short positions in
       the stock market.
•   specific risk
     – The capital charge is 8% of the bank's gross equity positions, that is, the sum
       of all long equity positions and all short equity positions. For a well-diversified
       and liquid portfolio, as approved by the supervisory authority, the capital
       charge is reduced to 4%.

     – Banks are likely to hold equities in different national markets.
     – A separate calculation for specific and general market risk must be carried
       out for each market.


                                                                                       121
                          To sum up (3)

•   Foreign Exchange Risk

     – The capital charge for foreign exchange risk throughout the bank is 8% of the
       overall net open position.

     – In order to calculate the capital requirement for FX risk, two steps are
       required:

•   Step 1: Calculate the bank's open position in each currency.

•   Step 2: Determine the overall net open position in a portfolio:
     – Convert the open position in each currency into the reporting currency at
       current spot prices. The overall net open position is the sum of:
     – the greater of the sum of the net short positions or the sum of the net long
       positions (excluding positions in gold)
     – the net position in gold, regardless of whether it is long or short


                                                                                      122
                       To sum up (4)

• Commodities Risk

   – Banks first have to express each commodity position (spot plus
     forward) throughout the bank in terms of the standard unit of
     measurement. Positions in each commodity are to be converted at
     current spot rates into the reporting currency.

• The simplified approach

   – The capital charge is the sum of:

       • 15% of the net position in each commodity
       • 3% of the bank's gross position (the sum of all long positions and all
         short positions) in each commodity to capture spread risk



                                                                                  123
                          To sum up (5)
•   Options
     – Banks that only use purchased options may use the simplified approach.
       Banks that also write options are expected to use one of the intermediate
       approaches.

•   The simplified approach
     – The options positions and the associated underlyings are carved out from the
       standardized methodology. These capital charges are then added to the
       capital charges for the relevant category.

•   Intermediate approaches
     – The delta-plus method uses the sensitivity parameters associated with
       options to measure their market risk and capital requirements.
     – The delta-equivalent amount is subject to general market risk charges and
       separate capital charges are applied to the gamma and vega risks of the
       option positions.
     – The specific risk capital charges are determined separately by multiplying the
       delta-equivalents by specific market risk charges.



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