Basel III Minimum Capital Requirements
FinanceDecember 04, 2018

Basel III minimum capital requirements for market risk (FRTB): a practical example for implementing the default risk charge of non-securitizations (part II)

Financial institutions must devote a series of methods for implementing the standardized approach (SA) to calculate the minimum capital requirements for Market Risk (FRTB) including a) the sensitivities-based method (SbM), b) the default risk charge (DRC), and c) the residual risks add-on (RRAO) methods. Part one of this commentary series covered the SbM while this article will focus on the principles for implementing the DRC following the BCBS frameworks (BCBS, 20131 , 20162, 20183).

Standardized default Risk Charge

Banks holding long credit positions must analyze Mark-to-market (MTM) as well as jump to default (JTD) risks, with the latter stating the default event that may arise over time and the former denoting the daily fluctuations of the credit spreads. Held-to-maturity exposures are more sensitive to JTD risk given the extended time duration and thus the prospect for a default event to occur. The resulting JTD risk losses strikes as a sudden default credit event. The credit spread sensitivities expressed using MTM risk analysis where deterministic shocks applied to credit spreads, may be unable to capture the losses arising from a JTD event.

This is why the final Basel III framework proposes approaches for capturing sudden credit events and resulting losses that are not encapsulated by applying shocks in credit spread when using the MTM method but instead appear in the tail of the default distribution. Moreover, measuring the impact of the sudden credit event to exposure and resulting losses bank can hedge JTD risks. Recoveries may also reduce the degree of credit losses and is therefore considered in calculating JTD risk using the analysis parameters of the expected recovery as it relates to the seniority of the specific credit instrument.

Based on the new BCBS framework (2016, 2017) banks must follow four-steps for calculating the standardized DRC of the trading portfolios which containing both securitization and non-securitization instruments (Figure 1):

  1. For each instrument exposed to counterparty calculating the JTD loss amounts;
  2. For the long and short exposures belonging to the same obligor calculating the netting of the JTD risk amounts that refer which resulting in the net long or net short JTD amount;
  3. Calculating the discounted hedge benefit ratio applied to net short exposures;
  4. Applying the default RWs for calculating DRC assuming no correlation to market risk.

FRTB Commentary 1

Figure 1: Steps for calculating the standardized DRC of the trading portfolios

Let us now explore the steps mentioned above and understand how to calculate the DRC for non-securitizations. We are initially going through the definitions, rules and formulae provided by the framework and then applying them using an example case on trading book portfolio.

Default Risk Charge of non-securitizations

Step 1: Calculating the gross JTD loss amounts

The bank should calculate the gross JTD loss amounts of non-securitization default risk as the higher of (a) the product of LGD and long notional amount of the exposure plus the P&L amount and (b) zero, or the lower of the (c) product of LGD and short notional amount of the exposures plus the P&L amount, and (d) zero.



  • The term notional is the security’s nominal (or face) value of the position
  • The P&L is the cumulative mark-to-market loss (or gain) already taken on the exposure, defined as the delta of the current market value of the position and the security’s notional amount

    P&L=market value – notional

  • The degree of LGD depends on the type of instrument and its level of seniority i.e., LGD = 100% to non-senior debt instruments, LGD = 75% to senior debt instruments, and LGD = 25% to covered bond.

Scaling of JTD Maturity

Banks should also assume a time horizon of one year for the exposures under JTD analysis. However, in case the maturities are between three-month to one year, banks must scale up the exposure to one year. Also, maturities that have a time horizon of less than three months should be scaled up to maturity of three months. Finally, the securities related to cash equity positions are supposed to have a maturity of either three months or more than one year.

Step 2: Net Jump-To-Default risk positions (Net JTD)

Banks should also net the JTD exposures belong to the same obligor based on rules driven by the maturity of the positions:

  • By holding both short and long positions, the offsetting applies only in the case that short exposures have equal or lower seniority to the long exposures;
  • Subject to the abovementioned restrictions, in case that the maturities of the long or short exposures have less than the one-year horizon, banks must weigh the capital horizon by the ratio of the exposure’s maturity relative to time horizon.

The net JTD risk exposures are weighted according to their credit quality4 and allocated to buckets of corporates, sovereigns, and local governments/municipalities.

Step 3: Hedge benefit ratio to net short exposures

Any possible hedging benefit between long and short positions belong to the same bucket should also be calculated by the bank defined as hedge benefit ratio, henceforth, weighted-to-short (WtS) ratio:

FRTB Commentary 2


∑netJTDlong and ∑netJTDshort are the sums of unweighted net long JTD and net short JTD amounts across the credit quality categories.

The WtS is a discount factor of the function that estimates the DRC.

Step 4: Default Risk Capital Charge for non-securitizations

Banks can calculate the default risk charge DRCb at the level of bucket b as the difference between the sum (across the credit quality categories) of (a) the risk-weighted long net JTD, and (b) the risk-weighted short net JTD weighted by the WtS discounting factor; or zero.

FRTB Commentary 3

Given that the new framework disallows hedging between different buckets, the total capital charge for default risk of non-securitizations is made up of the aggregation capital charges of individual buckets.

Example of calculating Default Risk Capital Charge

Let us examine a case of a banking institution which holds a trading book portfolio with the following exposures:

  • A long senior position, P1, of a pharmaceutical corporate bond which is maturing in six years having a notional of EUR 30 million, hedged by a EUR 35 million short equity position, P2, of pharmaceutical corporate of the same issuer with a maturity of nine months. The rating of the issuer is set to B while the level of LGDs is for P1 set as LGDP(1) =75% and for P2 is set LGDP(2) =100%;
  • A long CDS position, P3, used to sell three-month protection of EUR 15 million against the default of a B-rated Energy corporate, whose expected LGD is 100%;
  • A short position, P4, of EUR 10 million on a C-rated IT company for three months;
  • A long senior auto industrial corporate bond position, P5, with notional of EUR 15 million, with credit quality A, with maturity of two years, and an expected LGD of 75%;
  • A long senior telecom corporate bond position, P6, with notional of EUR 150 million duration of two years, hedged by a EUR 150 million short position, P7, of bought protection against the default of the same issuer for a duration of one year. The credit quality of the issuer is A. The level of LGDs is for P6 set as LGDP(6) =75% and for P7 is set LGDP(7)=100%;

Following the steps described above and illustrated numerically in Table I, the resulting Default Risk Charge is DRCb=EUR 0.302 million.

Table I Calculating Steps to Default Risk Charge

FRTB Commentary 4

Layout of a process for implementing Basel III minimum capital requirements for calculating Default Risk Capital Charge

There are few points to make in conclusion. Firstly, the necessary input data need for calculating Default Risk Capital Charge refer to the Maturity, Notional, Credit Quality of the Issuer, seniority and corresponding LGD of the position. Secondly, the definitions of maturity adjustments and Risk Weights defined by the framework. The P&L resulted mainly based on the Face, MtM and Market Value together with the volatility’s degrees. Gross and Net JTD as well as DRCb for both long and short positions are calculated based on the formulae provided by the framework. Banks must also apply aggregation within the buckets, and report associated capital against risk and losses. The cycle process of implementing Basel III minimum capital requirements for calculating DCC based on the standardized approach is illustrated in Figure 2.

FRTB Commentary 5

Figure 2: Process steps of implementing Basel III minimum capital requirements for DRC of the trading portfolios

Beyond the silos

As discussed in part one, the SbM measures the capital against seven risk classes whereas the RRAO ensures the coverage of the remaining gap, correlation, and behavior risks. Furthermore, separately from the market risks, banks must calculate DRC for the trading book portfolios exposed to counterparty credit risk. This siloed approach to calculation excludes any attention of possible dependences across the different risk classes. While banks can simply aggregate, the capital resulted from the SbM, DRC and RRAO approaches.

However, financial institutions are increasingly integrating siloed ways of thinking to deal with the undeniable shift regarding cultural and technological challenges spurred by external regulatory and internal management pressures. The higher the degree of integration, the more financial institutions are benefit from a holistic and consistent view of their balance sheet, earnings, capital, liquidity and leverage under normal and stress conditions through time - to support more informed and confident decision making. The FRTB regulation is no exception, especially given its ties to the Basel III regulation.


1Basel Committee on Banking Supervision (BCBS). (2013, October). Fundamental review of the trading book: A revised market risk framework. Retrieved October 2013, from

2Basel Committee on Banking Supervision (BCBS). (2016, January). Minimum capital requirements for market risk. Retrieved January 2016, from  

3Basel Committee on Banking Supervision (BCBS). (March 2018). Revisions to the minimum capital requirements for market risk. Retrieved March 2018, from

4The classification of the credit quality set by rating grades of AAA, AA, A, BBB, BB, B, CCC, unrated, and defaulted to the default RWs of 0.5%, 2%, 3%, 6%, 15%, 30%, 50%, 15%, and 100%, respectively.

Dr. Ioannis Akkizidis, Product Manager, Risk and Finance, Wolters Kluwer
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