FRTB. The Canadian perspective. Part 2: Standardized approach. kpmg.ca

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1 FRTB The Canadian perspective Part 2: Standardized approach kpmg.ca

2 A comparison between FRTB and CAR In Part 2 of our series on FRTB: the Canadian Perspective, we highlight key differences and similarities between FRTB and the Capital Adequacy Requirements (CAR) guidelines that have been adopted by Canadian banks. The new capital requirements under FRTB are a marked change from those in the Basel 2.5 and CAR guidelines; however, both regulatory documents offer banks a choice between a standardized approach (SA) and an internal models approach (IMA). The FRTB standardized approach is generally more sophisticated than its predeceor, and is based on three components: s under the sensitivities-based method, default, and residual risk add-on. Capital adequacy requirements The standardized approach capital requirement under CAR considers five risk categories: 1 Interest rate position risk 4 Commodities risk 2 Equities risk 5 Options risk. 3 Foreign exchange position risk The capital charges for market risk are predefined by OSFI based on historical loes for each product type, and typically based on a weighted sum, where the weights are prescribed for each risk category and instrument type in Chapter 9 of the CAR guidelines. Current market risk rule Capital adequacy requirements (CAR) Approach Standardized approach (SA) Internal models approach (IMA) Key features Specific risk General market risk VaR & streed VaR Incremental Risk categories IR EQ IR FX EQ CM CR The total capital requirement is the aggregated specific and general market for the applicable risk categories. FRTB 2

3 Fundamental review of the trading book FRTB s standardized approach aligns more closely to the current internal models approach under CAR, incorporating concepts such as sensitivities that were previously mainly used by banks using IMA approach. The standardized approach capital requirement under FRTB is the aggregation of three components: the s under the sensitivities-based method, the default, and the residual risk add-on. The sensitivities based is further divided among seven risk claes defined in the FRTB: General Interest Rate Risk (GIRR) Credit Spread Risk (CSR): non-securitization CSR: securitization Correlation Trading Portfolio (CTP) CSR: securitization non-ctp Foreign Exchange (FX) Risk 6 7 Equity Risk Commodity Risk. The hierarchy of this approach is visualized below. New market risk rule Fundamental review of the trading book (FRTB) Approach Standardized approach (SA) Internal models approach (IMA) Sensitivities based Default risk charge Global expected shortfall Default Key features Residual risk add-on Streed capital add-on Risk claes IR, FX, EQ, CM, CSR (non-sec), CSR (sec-ctp), CSR (sec non-ctp) non-sec, sec CTP, sec non-ctp Sensitivites Delta Vega Curvature It is important to note that under FRTB, the standardized approach calculation will need to be computed, regardle if the desk in question is subject to IMA or not. For IMA banks, the capital charge under the standardized approach will be used to construct a floor on the IMA capital charge. While the details of how this floor is calculated remains to be seen, it will be used to set the binding constraint for the minimum amount of capital that needs to be held. The Canadian Perspective 3

4 Key changes from current CAR to FRTB Sensitivities Based Measures (new): Different from the specific and general risk calculation in CAR, the FRTB guidelines introduce three sensitivities-based measures: Delta, Vega and Curvature. These sensitivities must be calculated for each of the seven risk claes under FRTB, but were not included for use in this way in the CAR framework. Both Vega and Curvature are new concepts from CAR, and Delta was only previously used as a multiplier for specific of options. The capital calculations are specific to each measure and the capital requirement under the sensitivities based measures is obtained by aggregating all three measures. To calculate sensitivities the bank must have a price for each kind of derivative in its portfolio. Default Risk Charge: Default Risk Charge was introduced to capture the jump-to-default (JTD) risk based on the credit risk treatment in the banking book. The motivation behind this new addition is to reduce the poible discrepancy in capital requirements for similar risk exposures acro the banking book and the trading book. Gro JTD is the eential part in the default risk capital charge calculation. It is calculated as a function of the Lo Given Default (LGD), notional amount and the cumulative profit and/or lo already realized on the position. The formulas for calculating gro JTD are subject to specific risk claes. Residual Risk Add-On: The Residual Risk Add-On is introduced by FRTB to capture any other risks beyond the main risk factors already captured in the sensitivities-based method and the Default Risk Charge. The Residual Risk Add-On is to be calculated for all instruments individually and in addition to the other components of the capital requirements under the standardized approach. The calculation is done by summing the gro notional amounts of the individual instruments. This sum is then multiplied by a residual risk weight to determine the residual risk add-on. The magnitude of residual risk weight is dependent on the type of underlying aets. Instruments with exotic underlying aets are given a much higher (100 x higher) residual risk weight. Consideration of Correlations: In order to capture the risk from correlation in periods of financial stre, which previously had not been considered as part of the standardized approach, the Basel committee has set up three different scenarios, representing low, medium and high correlation environments. Under each scenario, different correlation parameters are set and three risk charge figures are calculated using these correlation inputs. The ultimate portfolio level risk capital charge under FRTB is chosen as the maximum of the three scenariorelated portfolio level capital charges. Standardized Approach for the Correlation Trading Portfolio: Under the CAR framework, banks can choose to model the Correlation Trading Portfolio (CTP) risk using the standardized approach or the internal models approach. However, under FRTB, the CTP risk must be captured using the standardized approach. This is due to regulatory concerns around the ability of internal models to adequately capture the CTP s risks. This claification is expected to lead to much larger capital requirements. Based on a sample of 44 bank portfolios, the BCBS has estimated that weighted-mean capital charges of securitizations (excluding CTP instruments) would increase by 22 percent relative to Basel 2.5, whereas CTP securitizations would lead to an increase of 70 percent. 1 1 Banking Tech, (2016), Fundamental Review of the Trading Book: impact on capital requirements and risk architecture FRTB 4

5 Example of capital requirements calculation Example: Cro-Currency Swap capital requirement calculation 1 year cro currency swap To illustrate the difference between the capital requirements under CAR vs. FRTB, here below is an example of a cro-currency swap calculation under both regimes. Risk weights Risk weighted positions Risk factors Basis risk charge Yield curve Net position charge Total general market risk Total specific market risk Total capital requirement For this example, it is aumed that the maturity T is 1yr: at time CC T we buy C 1 of currency 1 and sell C 2 in currency 2. Also aume the counterparty has a BBB rating. General risk IRR (Basis Risk Charge) The IRR charge for basis risk is given by the maximum of long and short positions at each maturity band (measured in the reporting currency) multiplied by that bands risk weight and the basis charge (10%). Since there is only 1 maturity period in our example this is given by. IIIIII IIIIII!"#$# = MMMMMM MMMMMM CC CC! FFFF FFFF!, CC CC! FFFF FFFF! RRRR RRRR!!!" 10% 10% Where RW 6 12 is the risk weight for a position with maturity between 6 and RR12 months. RW 6 12 is given in the CAR guidelines as 0.70%. IRR (Yield Curve Charge) The yield curve charge is given by the net offsetting position multiplied by the zone yield charge: MMMMMM CC CC! FFFF FFFF!, CC CC! FFFF FFFF! RRRR RRRR!!!"!!!" ZZZZZZZZ ZZZZZZZZ 1 yyyyyyyyyy yyyyyyyyyy cccccccccc cccccccccc cchaa cchaaaaaaaa The Zone 1 (maturities 12 months or le) yield charge is given by 40% in the CAR guidelines. The Canadian Perspective 5

6 IRR (Net Position Charge) Net position charge is applied to unmatched positions. However, since the timing of the swap payments is the same, there is no unmatched positions, resulting in no net position charge. Foreign exchange position risk Foreign Exchange risk is given by 8% of the larger of the total long and total short positions of each currency. In the case of a single cro-currency swap this is given by: FFFF cchaaaaaaaa = max CC FFFF, CC FFFF 8% FFFF cchaaaaaaaa = max CC! FFFF!, CC! FFFF! 8% Specific risk Since cro-currency swaps are not based on an underlying instrument, no specific risk capital charge is required. Total The total capital charge is the simple sum of these charges: CCCCCCCCCCCCCC CChaaaaaaaa = IIIIII!"#$# + IIIIII!"#$%! CCCCCCCCCCCCCC CChaaaaaaaa = IIIIII CChaaaaaaaa!"#$# + IIIIII = IIIIII!"#$% +!"#$% + FFFF cchaaaaaaaa CCCCCCCCCCCCCC + FFFF!"#$% + CChaaaaaaaa FFFF cchaaaaaaaa = IIIIII!"#$# + IIIIII!"#$%!"#$% + FFFF cchaaaaaaaa = MMMMMM CC! FFFF!, CC! FFFF! 0.7% 10% + MMMMMM CC! FFFF!, CC! FFFF!! 0.7% 10% + MMMMMM CC 10%! FFFF + MMMMMM!, CC! FFFF CC! 0.7% 40% +max FFFF! FFFF, CC FFFF 0.7% % 0.7% 40% 10% +max + MMMMMM CC CC! = MMMMMM! FFFF FFFF! CC! FFFF!, CC, CC!! FFFF FFFF!!, CC! FFFF! 8% 0.7% 40% +max CC!! 8.07% + MMMMMM CC! FF = MMMMMM CC! FFFF!, CC! FFFF! 8.07% + MMMMMM CC! FFFF!, CC! FFFF! 0.28% = MMMMMM FFFF CC!, CC! FFFF! FFFF!, CC!! FFFF 0.28%! 8.07% + MMMMMM CC! FFFF!, CC! FFFF! 0.28% Example: Cro-Currency Swap capital requirement calculation 1 year cro-currency swap Delta GIRR Delta FX Risk weights Weighted Delta GIRR Weighted Delta FX Correlation within buckets Default Delta GIRR risk position Delta FX risk position Correlation betweem buckets Delta GIRR Delta FX Total capital requirement FRTB 6

7 Aume our portfolio consists of the same cro-currency swap as in the previous example. The capital charge is the sum of the Delta charge, DRC and Residual risk charge. This example will focus on the first 2 charges. Delta FF! exp rr The price exp of a rr! CC Cro-Currency! CC! FFFF Swap! FFFF! exp is! given expby: VV = CC! FFFF! exp rr rr! rr! rr!! CC! FFFF! exp rr! The first step is to identify the risk factors: General rr interest! rate: rr! r 1 (T) and r 2 (T) and foreign exchange: rates FX 1 and FX 2. Then we calculate the sensitivities to each risk factor: = CC FFFF exp rr!"! = CC!"! CC! exp rr! exp rr! = dd! dd!! rr =!"! = CC!"! CC! exp! exp!"! rr rr! =! CC! exp!! = FFFF CC = dd rr dd! ddffff! exp!! = dd!!!!! = CC CC!! rr FFFF FFFF!!! exp exp!"! = rr rr! CC!! exp = rr FFFF!! dd =! = FFFF FFFF! dd! dd dd!!!!!!! = CC CC!! FFFF FFFF!! exp exp rr rr!! = FFFF FFFF!! dd dd!! Weighted sensitivities = RRRR!! are obtained!!! WWWW as the!"! = RRRR product!"! of risk!" weight and sensitivity: WWWW!! = RRRR!!!! ; WWWW!! = RRRR!!!! ; WW WWWW!"! = RRRR!"!!"! ; WWWW!"! = RRRR!"!!"! The risk weights for FX and Interest rates are provided in the FRTB standard:!!! WWWW WWWW!!! = RRRR RRRR!!! RRRR!!! WWWW = WWWW RRRR!"!!" = = RRRR RRRR!"!!" = 2.25%!"!!" WWWW WWWW!"!!" = RRRR!"! = RRRR!"! = RRRR!" = 30% RRRR!! = RRRR!! = RRRR! = 2.25% RRRR!"! = RRRR Next we calculate the total delta using bucket correlations. There are 4 buckets: each currencies interest RR rate!"! and = RRRR FX.!" All risk = 30% factors belong RRRR to each! = own RRRR! bucket; so no inside-bucket aggregation and inside-bucket correlation is irrelevant. Cro bucket correlation is calculated RR RRRR! = using RRRR =! cro RRRR = 2.25% bucket = RRRR correlations: = 30% g. Full Delta acro IR and FX risk claes is computed via: DDDDDDDDDD = DDDDDDDDDD!" + DDDDDDDDDD!" = WWWW!!! + WWWW!!!!! + 2 γγ!" WWWW!! WWWW!! + WWWW!"! + WWWW!"! + 2 γγ!" WWWW!"! WWWW!"! The standard identifies cro bucket correlations for each aet cla: γγ!" = g50% IR = 50%; γγ!" = 60% g FX = 60%. DDDDDDDDDD = DDDDDDDDDD + DDDDDDDDDD WWWW WWWW + WWWW + WWWW The Canadian Perspective 7

8 JJJJJJ long = max LLLLLL Notional + PP&LL, 0 Default JJJJJJ short = min LLLLLL Notional + PP&LL, 0 Jump-to-Default (JTD) charge in general is: JJJJJJ long = max LLLLLL Notional + PP&LL, 0 JJJJJJ short = min LLLLLL Notional + PP&LL, 0 = max VV, 0 JJJJJJ short = and when the price of the instrument is not linked to the recovery rate of defaulter, there should be no multiplication of the notional by the LGD. This case is exactly related to IR/FX derivative, so the above equations reduce to: JJJJJJ JJJJJJ long = max VV, 0 ; JJJJJJ short = min VV, 0 For maturity of 1 year there is no exposure offset for JTD. Hedging relationship with respect to short: JJJJJJ = VV JJJJJJ = 0 WWWWWW = 1 JJJJJJ long = max VV, 0 JJJJJJ JJJJJJ!"#$ short = min VV 0 JJJJ JJJJJJ!"#$ = 0WWWWWW JJJJJJ JJJJJJ!!!"# = = VV WWWWWW WWWWWW = 0 JJJJJJ!"#$ + JJJJJJ!!!"# When V > 0 it gives: JTD long = V, JTD short = 0, WtS = 1. JJJJJJ JJJJJJ For V < 0 it will be: JTD!"#$ long = VVWWWWWW 0, JTD JJJJJJ = short = V, WtS!!!"# 0 WWWWWW = 0. = 1 JJJJJJ!"#$ + JJJJJJ!!!"# Default for a bucket: 0 JJJJJJ!!!"# = VV WWWWWW = 0 DDDDDD!! = RRRR!"# max JJJJJJ!"#$ WWWWWW JJJJJJ!!!"#, 0, 0 JJJJJJ = VV JJJJJJ = 0 WWWWWW = 1 or DDDDDD!"# VV, VV! = RRRR!"# VV, VV > 0 = max RRRR 0, 0, VVVV 0!"#!"# VV, VV, 0 = RRRR RRRR!"# max!"# VV, 0 It is only one bucket here, so DRC = DRC RR max JJJJJJ b. WWWWWW JJJJ Residual risk add-on DDDDDD = DDDDDD DDDDDD DDDDDD!! This trade is not a subject of Vega or Curvature risk and is not a Correlated Trade Portfolio. There is no residual risk connected to it. FRTB 8

9 Total = DDDDDDDDDD + DDDDDD Capital = DDDDDDDDDD Charge + = DDDDDD Delta + DRC = WWWW!! + WWWW!! + 2 γγ!" WWWW!! WWWW!! = + WWWW WWWW!!! + WWWW +! WWWW!! + 2 γγ + 2!" WWWW γγ!! WWWW WWWW WWWW!! + RRRR max VV, 0 +!! WWWW!"! + WWWW!"! + 2 γγ!" WWWW!"! WWWW!"! + RRRR!"# max!! + WWWW!"! + WWWW!"! + 2 γγ!" WWWW!"! WWWW!"! + RRRR!"# max VV, 0 = RRRR! dd!! FFFF!! + dd!! FFFF!! + 2 γγ!" dd! dd! FFFF! FFFF! = RRRR! dd!! FFFF!! + dd!! FFFF!! + 2 γγ!" dd! dd! FFFF! FFFF! = RRRR +RRRR!!" dd! dd!! FFFF +! dd! +! + dd! 2! FFFF γγ!"!! + dd 2! dd γγ! +!" dd RRRR!!"# dd! FFFF max! FFFF VV, 0! +RRRR!" dd!! + dd!! + 2 γγ!" dd! dd! + RRRR!"# max VV, 0 +RRRR!" dd!! + dd!! + 2 γγ!" dd! dd! + RRRR!"# max VV, 0 = dd!! FFFF!! + dd!! FFFF!! + dd! dd! FFFF! FFFF! = dd!! FFFF!! + dd!! FFFF!! + dd! dd! FFFF! FFFF! = dd dd! + FFFF dd!! dd dd FFFF! dd! + + dd0.06 max FFFF dd FFFF! FFFF! dd! FFFF!, dd!! + dd!! dd! dd! max dd! FFFF! dd! FF +0.3 dd + dd dd dd max dd FFFF dd FFFF, 0 What can banks leverage from CAR for FRTB? CAR Internal models for FRTB standardized approach Banks currently using internal models may leverage their existing models and systems for the FRTB Standardized Approach (which will be a mandatory calculation). Specifically, banks may adapt their frameworks for calculating the sensitivitiesbased risk measures. Both pricing and risk internal models may have Delta, Vega and Curvature elements, especially in the case of derivative instruments, and these sensitivities may be extended to the FRTB standardized approach. Additionally, the new FRTB JTD risk is a function of notional amount, market value of the instruments and prescribed LGD. Banks modeling incremental (IRC) under IMA have incorporated LGD in the expected lo calculation. The existing models and systems relating to LGD, used in IMA development, can be modified to implement default. The Canadian Perspective 9

10 Conclusion The BCBS, through their Fundamental Review of the Trading Book has proposed an overhaul of the standardized approach for market capital calculation purposes which is, in general, more complex than the existing Canadian standards under CAR. The new standardized approach must be calculated institution wide, and must be used for capitalization for all trading desks that do not gain IMA approval, as well as for all instruments in the correlation trading portfolio. Coming up next.. In our final installment of the series, we will focus on the comparison in the Internal Models approach. FRTB 10

11 The Canadian Perspective 11

12 Contact us John Armstrong National Industry Leader, Financial Services T: E: Jennifer Liu Senior Manager, Financial Risk Management T: E: kpmg.ca The information contained herein is of a general nature and is not intended to addre the circumstances of any particular individual or entity. Although we endeavor to provide accurate and timely information, there can be no guarantee that such information is accurate as of the date it is received or that it will continue to be accurate in the future. No one should act on such information without appropriate profeional advice after a thorough examination of the particular situation. firms affiliated with KPMG International Cooperative ( KPMG International ), a Swi entity. All rights reserved The KPMG name and logo are registered trademarks or trademarks of KPMG International.