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rrao

Calculate residual risk add-on (RRAO) charge results for each portfolio

Since R2024b

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Syntax

RRAOResults = rrao(frtbsaObject)

Description

RRAOResults = rrao(frtbsaObject) computes the residual risk add-on (RRAO) charge results for each portfolio using the frtbsa object. For more information, see Residual Risk Add-on Capital.

example

Examples

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Open Live Script

Use a frtbsa object and the rrao function to calculate the residual risk add-on (RRAO) charge results for each portfolio. FRTB-SA (Standardized Approach for Fundamental Review of Trading Book) is a Basel Committee on Banking Supervision framework for calculating market capital risk requirements that is based on a set of standardized risk factors.

Create frtbsa Object

Use bank format for numeric data to use two decimal places.

format bank

Define the ISDA® FRTB-SA CRIF file.

FRTBSACRIF = "FRTBSA_CRIF.csv";

Define the DRC reference date.

DrcRefCOBDate = datetime(2023,9,21);

Use frtbsa to create the FRTB-SA object.

myFRTBSA = frtbsa(FRTBSACRIF,DRCValuationDate=DrcRefCOBDate)
myFRTBSA = 
  frtbsa with properties:

                CRIF: [159×18 table]
       NumPortfolios: 2.00
        PortfolioIDs: [2×1 string]
          Portfolios: [2×1 frtbsa.Portfolio]
          Regulation: "Basel_d491"
    DomesticCurrency: "USD"
    DRCValuationDate: 21-Sep-2023
         NumDaysYear: 365.00

Examine Output

Display the contents of the ISDA FRTB-SA CRIF file.

myFRTBSA.CRIF
ans=159×18 table
    PortfolioID    TradeID       Variant       SensitivityID      RiskType      Qualifier     Bucket     Label1        Label2        Amount      AmountCurrency    AmountUSD    Label3    EndDate    CreditQuality    LongShortInd    CoveredBondInd    TrancheThickness
    ___________    ________    ____________    _____________    ____________    __________    ______    _________    ___________    _________    ______________    _________    ______    _______    _____________    ____________    ______________    ________________

       "P1"        "EQD_a1"    <missing>        "P1_EQD_a1"     "EQ_DELTA"      "ISSUER A"     "1"      <missing>    "SPOT"           8250.00        "USD"           8250.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQD_a2"    <missing>        "P1_EQD_a2"     "EQ_DELTA"      "ISSUER A"     "1"      <missing>    "REPO"           8333.33        "USD"           8333.33     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQD_b1"    <missing>        "P1_EQD_b1"     "EQ_DELTA"      "ISSUER B"     "2"      <missing>    "SPOT"          22000.00        "USD"          22000.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQV_a1"    "Variant 1"      "P1_EQV_a1"     "EQ_VEGA"       "ISSUER A"     "1"      "0.5"        <missing>         -50.00        "USD"            -50.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQV_a2"    "Variant 1"      "P1_EQV_a2"     "EQ_VEGA"       "ISSUER A"     "1"      "1"          <missing>         200.00        "USD"            200.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQV_b1"    "Variant 1"      "P1_EQV_b1"     "EQ_VEGA"       "ISSUER B"     "2"      "0.5"        <missing>        -166.67        "USD"           -166.67     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQC_a1"    "Variant 1a"     "P1_EQC_a1"     "EQ_CURV"       "ISSUER A"     "1"      "0.5"        <missing>      -18910.00        "USD"         -18910.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQC_a1"    "Variant 1a"     "P1_EQC_a1"     "EQ_CURV"       "ISSUER A"     "1"      "-0.5"       <missing>        6526.25        "USD"           6526.25     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQC_b1"    "Variant 1a"     "P1_EQC_b1"     "EQ_CURV"       "ISSUER B"     "2"      "0.5"        <missing>       -6288.00        "USD"          -6288.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQC_b1"    "Variant 1a"     "P1_EQC_b1"     "EQ_CURV"       "ISSUER B"     "2"      "-0.5"       <missing>        6120.00        "USD"           6120.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMD_a1"    <missing>        "P1_CMD_a1"     "COMM_DELTA"    "COAL"         "1"      "0"          "NEWCASTLE"      2000.00        "USD"           2000.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMD_a2"    <missing>        "P1_CMD_a2"     "COMM_DELTA"    "COAL"         "1"      "0"          "LONDON"         -500.00        "USD"           -500.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMD_b1"    <missing>        "P1_CMD_b1"     "COMM_DELTA"    "BRENT"        "2"      "0"          "LE HAVRE"        666.67        "USD"            666.67     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMD_c1"    <missing>        "P1_CMD_c1"     "COMM_DELTA"    "WTI"          "2"      "2"          "OKLAHOMA"       -875.00        "USD"           -875.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMV_a1"    "Variant 1"      "P1_CMV_a1"     "COMM_VEGA"     "COAL"         "1"      "0.5"        <missing>         333.33        "USD"            333.33     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMV_a2"    "Variant 1"      "P1_CMV_a2"     "COMM_VEGA"     "COAL"         "1"      "1"          <missing>        -100.00        "USD"           -100.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
      ⋮

Display the number of portfolios and their IDs.

myFRTBSA.NumPortfolios
ans = 
          2.00


myFRTBSA.PortfolioIDs
ans = 2×1 string
    "P1"
    "P2"

Display the properties of the first Portfolio object.

myFRTBSA.Portfolios(1)
ans = 
  Portfolio with properties:

    PortfolioID: "P1"
         Trades: [69×1 frtbsa.Trade]
      RiskTypes: [69×1 string]

Display the risk types of the portfolio.

myFRTBSA.Portfolios(1).RiskTypes
ans = 69×1 string
    "EQ_DELTA"
    "EQ_DELTA"
    "EQ_DELTA"
    "EQ_VEGA"
    "EQ_VEGA"
    "EQ_VEGA"
    "EQ_CURV"
    "EQ_CURV"
    "COMM_DELTA"
    "COMM_DELTA"
    "COMM_DELTA"
    "COMM_DELTA"
    "COMM_VEGA"
    "COMM_VEGA"
    "COMM_VEGA"
    "COMM_VEGA"
    "COMM_CURV"
    "COMM_CURV"
    "COMM_CURV"
    "GIRR_DELTA"
    "GIRR_DELTA"
    "GIRR_DELTA"
    "GIRR_VEGA"
    "GIRR_VEGA"
    "GIRR_VEGA"
    "GIRR_CURV"
    "GIRR_CURV"
    "FX_DELTA"
    "FX_DELTA"
    "FX_VEGA"
      ⋮

Display some of the trades of the portfolio.

myFRTBSA.Portfolios(1).Trades(1)
ans = 
  Trade with properties:

             TradeID: "EQD_a1"
             Variant: <missing>
       SensitivityID: "P1_EQD_a1"
            RiskType: "EQ_DELTA"
           Qualifier: "ISSUER A"
              Bucket: "1"
              Label1: <missing>
              Label2: "SPOT"
              Amount: 8250.00
      AmountCurrency: "USD"
           AmountUSD: 8250.00
              Label3: NaN
             EndDate: NaT
       CreditQuality: <missing>
        LongShortInd: <missing>
      CoveredBondInd: <missing>
    TrancheThickness: NaN


myFRTBSA.Portfolios(1).Trades(30)
ans = 
  Trade with properties:

             TradeID: "FXV_b1"
             Variant: "Variant 1"
       SensitivityID: "P1_FXV_b1"
            RiskType: "FX_VEGA"
           Qualifier: "EURCLP"
              Bucket: <missing>
              Label1: "0.5"
              Label2: <missing>
              Amount: 175.00
      AmountCurrency: "USD"
           AmountUSD: 175.00
              Label3: NaN
             EndDate: NaT
       CreditQuality: <missing>
        LongShortInd: <missing>
      CoveredBondInd: <missing>
    TrancheThickness: NaN


myFRTBSA.Portfolios(1).Trades(60)
ans = 
  Trade with properties:

             TradeID: "RRAO_a2"
             Variant: <missing>
       SensitivityID: "P1_RRAO_a2"
            RiskType: "RRAO_01_PERCENT"
           Qualifier: <missing>
              Bucket: <missing>
              Label1: <missing>
              Label2: <missing>
              Amount: 300000.00
      AmountCurrency: "USD"
           AmountUSD: 300000.00
              Label3: NaN
             EndDate: NaT
       CreditQuality: <missing>
        LongShortInd: <missing>
      CoveredBondInd: <missing>
    TrancheThickness: NaN

Compute RRAO Capital Charge

The RRAO charge covers risks that are not fully captured by the other components of the FRTB capital charges, particularly those arising from positions with exotic or nonlinear payoffs, as well as other risks that are deemed to be residual in nature. Use rrao to compute the RRAO charge results for each portfolio using the frtbsa object.

RRAOResults = rrao(myFRTBSA)
RRAOResults = 
  rraoResults with properties:

       NumPortfolios: 2.00
        PortfolioIDs: [2×1 string]
          Regulation: "Basel_d491"
    DomesticCurrency: "USD"
             Charges: [2×1 double]
    ComponentResults: [2×1 frtbsa.rraoPortfolioResults]
        ResultsTable: [2×4 table]

The Charges output contains the RRAO risk charge of the portfolio.

RRAOResults.Charges
ans = 2×1

       3310.00
       2800.00

The ResultsTable output contains the high-level risk RRAO charge calculations of the portfolios.

RRAOResults.ResultsTable
ans=2×4 table
    PortfolioIDs     Total     Exotic      ORR  
    ____________    _______    _______    ______

        "P1"        3310.00    3000.00    310.00
        "P2"        2800.00    2500.00    300.00

The ComponentResults output contains detailed RRAO risk charge information for a given portfolio. Examine the RRAO risk charge for the first portfolio.

RRAOResults.ComponentResults(1)
ans = 
  rraoPortfolioResults with properties:

               PortfolioID: "P1"
                    Charge: 3310.00
     ChargeBySensitivityID: [4×5 table]
    ChargeByInstrumentType: [2×2 table]

Display charges by instrument type. Portfolio P1 has both exotic underlying instruments and other residual risk instruments.

RRAOResults.ComponentResults(1).ChargeByInstrumentType
ans=2×2 table
    InstrumentType    Charge 
    ______________    _______

       "Exotic"       3000.00
       "ORR"           310.00

Input Arguments

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FRTB-SA object, specified as a frtbsa object. You create a frtbsa object using frtbsa.

Data Types: object

Output Arguments

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Residual risk add-on capital charge results , returned as a RRAOResults object. The RRAOResults object has the following properties:

  • NumPortfolios — Number of portfolios whose residual risk add-on capital charges are contained in the RRAOResults object.

  • Regulation — Jurisdiction. The default is "Basel".

  • DomesticCurrency — Domestic currency. The default is "USD".

  • Charges — NumPortfolios-by-1 array of residual risk add-on capital charges.

  • PortfolioIDs — NumPortfolios-by-1 array of strings containing the portfolio IDs of each portfolio.

  • ComponentResults — NumPortfolios-by-1 array of frtbsa.rraoPortfolioResults objects containing the calculation results for each portfolio. The frtbsa.rraoPortfolioResults object properties are:

    • PortfolioIDs — Scalar string indicating the ID of the portfolio.

    • Charge — Residual risk add-on capital charge of the portfolio.

    • ChargeBySensitivityID — Table displaying the residual risk add-on capital calculations by sensitivity ID.

    • ChargeByInstrumentType — Table displaying the residual risk add-on capital calculations by instrument type.

  • ResultsTable — Table displaying the high-level risk add-on capital calculation results for all portfolios.

More About

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Residual Risk Add-on Capital

Under the FRTB-SA framework, the residual risk add-on capital (RRAO) covers risks that are not fully captured by the other components of the FRTB capital charges, particularly those arising from positions with exotic or nonlinear payoffs, as well as other risks that are deemed to be residual in nature.

Residual risks are those risks that arise from:

  • Gap risk — A risk of a significant change in vega parameters in options due to small movements in the underlying, which results in hedge slippage. Relevant instruments subject to gap risk include all path dependent options, such as barrier options, and Asian options as well as all digital options.

  • Correlation risk — A risk of a change in a correlation parameter necessary for determining the value of an instrument with multiple underlyings. Relevant instruments subject to correlation risk include all basket options, best-of-options, spread options, basis options, Bermudan options, and quanto options.

  • Behavioral risk — A risk of a change in exercise and prepayment outcomes such as those that arise in fixed rate mortgage products where retail clients might make decisions motivated by factors other than pure financial gain (such as demographical features or other social factors). A callable bond can be seen as possibly behavioral risk only if the right to call lies with a retail client.

RRAO is calculated by applying risk weights to notional amounts of instruments with nonlinear payoffs, where the risk weight is determined based on the portfolio's asset class.

References

[1] Bank for International Settlements. "MAR21 — Standardised Approach: Sensitivities-Based Method." March 2020. https://www.bis.org/basel_framework/chapter/MAR/21.htm.

[2] Bank for International Settlements. "MAR22 — Standardised Approach: Default Risk Capital Requirement." March 2020. https://www.bis.org/basel_framework/chapter/MAR/22.htm.

[3] Bank for International Settlements. "MAR23 — Standardised Approach: Residual Risk Add-On." March 2020. https://www.bis.org/basel_framework/chapter/MAR/23.htm.

[4] Bank for International Settlements. "CRE42 — Securitisation: External-Ratings-Based Approach (SEC-ERBA)." January 2023. https://www.bis.org/basel_framework/chapter/CRE/42.htm.

[5] Bank for International Settlements. "Basel Committee on Banking Supervision: Minimum Capital Requirements for Market Risk." January 2019. https://www.bis.org/bcbs/publ/d457.pdf.

Version History

Introduced in R2024b

See Also

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