Regulatory reporting of market risk under the basel iv framework

Appendix A
Regulatory Reporting of
Market Risk under
the Basel IV Framework
The Presentation Slides for Teaching
Financial Regulations and Compliance Practices
Website : https://sites.google.com/site/quanrisk
E-mail : quanrisk@gmail.com
Copyright © 2016 CapitaLogic Limited

Declaration
Copyright © 2016 CapitaLogic Limited.
All rights reserved. No part of this presentation file may be
reproduced, in any form or by any means, without written
permission from CapitaLogic Limited.
Authored by Dr. LAM Yat-fai (林日辉林日辉林日辉林日辉),
Principal, Structured Products Analytics, CapitaLogic Limited,
Adjunct Professor of Finance, City University of Hong Kong,
Doctor of Business Administration,
CFA, CAIA, CAMS, FRM, PRM.
Copyright © 2016 CapitaLogic Limited 2

Outline
Expected shortfall
Regulatory market risk
Internal model approach
Standardized approach

Expected shortfall
Specification
At the end of a T-day holding period (10-day)
At the qth percentile confidence level (97.5th percentile)
Worst case value
The minimum potential portfolio value at the end of the holding period with the
lowest (1 - q%) situations excluded
Tail value
The average of potential portfolio values when the potential portfolio values
are below the worst case value
Expected value
The average of all potential portfolio values at the end of the holding period
Expected shortfall (“ES”)
The average of unexpected loss relative to the expected value during the worst
(1 - q%) situations
Expected value - Tail value

Expected shortfall at T-day
qth percentile confidence level
Value0
0
Worst case value
Expected value
Expected shortfall
1 - q%
q%
T days
ValueT
Tail value

Expected shortfall at 10-day
97.5th percentile confidence level
Value0
0
Worst case value
Expected value
Expected shortfall
2.5%
97.5%
10 days
ValueT
Tail value

Expected shortfall vs Value-at-risk
Expected shortfall Value-at-risk
Confidence level 97.5th percentile 99th percentile
Extremity Tail value Worst case value
Monte Carlo /
historical simulation
Expected value
- Tail value
Expected value
- Worst case value
Variance-covariance
method factor
NormDist[- Critical value,
0, 1, False] /(1 - q%)
Critical value

Variance-covariance method
Critical value
Expected shortfall
Value-at-risk
( )
[ ]
0
0
NormSInv q%
NormDist - CV,0,1,False
1 - q%
CV =
ES = V σ T ×
VaR = V σ T × CV

Pros and cons of expected shortfall
Theoretical advantage
Sub-additivity
ES(A + B) < ES(A) + ES(B)
Practical disadvantage
Central tenancy at extremity
Statistic drawn from 6 to 7 day end samples
Lack robustness

Outline
Expected shortfall

The potential losses of financial investments arising
from the changes within a short holding period in:
Currency rates
Interest rates
Equity prices
Commodity prices
Credit spreads
Default events
Calculated in accordance with the Basel IV rules

Trading book vs banking book
Trading book exposures
A bank’s investments
Short-term resale
Profiting from short-term price movements
Locking in arbitrage profits
Hedging risks that arise from instruments meeting criteria above
Subject to capital charge for market risk
Banking book exposures
Any exposures not on the trading book
Primarily subject to capital charge for credit risk
Currency rate and commodity price exposures also subject
to capital charge for market risk

Regulatory market risk components
Exposure Trading book Banking book
Currency rate √ √
Interest rate √
Equity price √
Commodity price √ √
Credit spreads √
Default events √

MRCC calculation methods
Internal model approach (“IMA”)
Subject to regulatory approval
For internationally active banks
Expected shortfall approach
Standardized approach (“STA”)
Generic method
For small and medium size banks
Expected shortfall approach
Regulatory variance-covariance method

Bank of China (Hong Kong)
annual report 2015

Outline
Expected shortfall

Capital charges calculated by
ES model at 10-day 97.5th percentile confidence level
Advantages
ES as one the several major approaches for market risk
measurement
Market risk sensitive
Disadvantages
Highly quantitative and complicated
Subject to regulatory approval at a high standard

Qualitative standards
Adequate board and senior management oversight
Effective market risk management system
Independent market risk control unit
Material factors captured and accurately reflected
Use of internal models for daily risk management
purposes
Proper documentation
Internal validation
Comprehensive stress-testing
Independent review or audit

Quantitative standards
ES computed on a daily basis
97.5th percentile confidence interval
10 days base holding period
During a stress period
Data updated at least once a month
Including options risks
Non-linear value effect
Volatility effect
Subject to internal, external and regulatory model
validations

Model validation standards
Assumptions
% change distributions
Valuation models
Replicating portfolios
Back-testing
Sufficient long testing period
At least three years

Liquidity adjusted ES
( ) ( ) ( )
( ) ( )
2 2 2
10 20 40
2 2
60 120
ES + ES + 2 ES
ES =
+ 2 ES + 6 ES

Market risk factors
Market
risk factor
Category Holding
period
Currency rate USD as domestic currency or foreign currency 10
Other currency pairs 20
Volatility 40
Interest rate USD, EUR, JPY, GBP, AUD, SEK, CAD and a bank’s
domestic currency
10
Other currencies 20
Volatility 60
Equity index Large capitalization 10
Small capitalization 20
Large capitalization volatility 20
Small capitalization volatility 60

MRCC components under the IMA
For currency rate risk, interest rate risk and
equity price risk, the larger of
Last trading day’s
Liquidity adjusted expected shortfall
Average of the last 60 trading days’
Liquidity adjusted expected shortfall
× Back testing multiplier

ES approaches
Historical simulation
Simple and model independent
Outdated historical information incorporated
Monte Carlo simulation
Simple to incorporate any model assumptions
Computationally intensive
Variance-covariance method
Fast
Material linear model error

Why and why not the IMA?
Why?
Unify market risk management and regulatory
reporting
An exhibition of advanced market risk
management expertise
Why not?
Expensive investments in experts and systems
Extensive regulatory model validation

Regulatory back testing
Compare 1-day static portfolio value with the
1-day 99% worst case value
1 violation if
1-day static portfolio value
< 1-day 99% worst case value
Count the number of violations in 250
consecutive trading days

Back testing multiplier
No. of violations Back testing multiplier
0 to 4 1.5
5 1.7
6 1.76
7 1.83
8 1.88
9 1.92
10 or more 2

Outline
Expected shortfall

Standardized mathematical method
Regulatory variance-covariance method
Standardized standard deviations
Standardized deviations provided in Basel IV rules
Standardized correlation coefficients
Standardized correlation coefficients provided in
Basel IV rules

Regulatory
variance-covariance method
Bank estimates
Quantities
Currency rates
Interest rates
Equity prices
Regulatory estimates
Standard deviations
Correlation matrix

Pros and cons of
standardized approach
Advantages
Simple regulatory rules
Less market risk measurement expertise
Disadvantages
Less risk sensitive
Capital arbitrage
Encourage higher market risk trading activities

Linear market risk exposures
Currency rate risk
Foreign currencies
FX forwards
Interest rate risk
Government bonds
Certificate of deposits
Equity price risk
Equities
Equity futures

Capital charge for
individual foreign currency
For each foreign currency
Value
Quantity × FX rate
Capital charge ratio (“CCR”)
30% / √2 for USD as domestic or foreign currency
30% for other domestic currencies
Capital charge
CC = Value × CCR

Total currency rate risk
[ ]
[ ]
[ ]( )
1 2
1
2
3
M
C
3 MQ = CC CC CC ... CC
CC1 0.6 0.6 ... 0.6
CC0.6 1 . ... .
CorrelMatrix = Transpose Q = CC0.6 . 1 ... .
:: : : ... :
CC0.6 . . ... 1
Λ = Sum Q × CorrelMatrix × Transpos [Ctrl]-[Shift]e Q -[Enter]
CC
  
  
  
  
  
  
     
R = Λ

Capital charge for
individual treasury rate curve
For treasury rate curve for each currency
For each tenor
Value
Cash flow × Currency rate / Discount factor
Exposure
PV01 of value × 10,000
Capital charge
cc = Exposure × CCR

Capital charge ratios
Tenor (years) CCR (%) Tenor (years) CCR (%)
0.25 2.4 5
1.5
0.5 2.4 10
1 2.25 15
2 1.88 20
3 1.73 30

Inter-tenor correlation coefficient
[ ]AB
| Tenor A - Tenor B |
ρ = Max exp - , 40%
Min Tenor A, Tenor B
  
   
   

Inter-tenor correlation coefficient
0.25 0.5 1 2 3 5 10 15 20 30
0.25 1 0.9704 0.9139 0.8106 0.7189 0.5655 0.4000 0.4000 0.4000 0.4000
0.5 0.9704 1 0.9704 0.9139 0.8607 0.7634 0.5655 0.4190 0.4000 0.4000
1 0.9139 0.9704 1 0.9704 0.9418 0.8869 0.7634 0.6570 0.5655 0.4190
2 0.8106 0.9139 0.9704 1 0.9851 0.9560 0.8869 0.8228 0.7634 0.6570
3 0.7189 0.8607 0.9418 0.9851 1 0.9802 0.9324 0.8869 0.8437 0.7634
5 0.5655 0.7634 0.8869 0.9560 0.9802 1 0.9704 0.9418 0.9139 0.8607
10 0.4000 0.5655 0.7634 0.8869 0.9324 0.9704 1 0.9851 0.9704 0.9418
15 0.4000 0.4190 0.6570 0.8228 0.8869 0.9418 0.9851 1 0.9900 0.9704
20 0.4000 0.4000 0.5655 0.7634 0.8437 0.9139 0.9704 0.9900 1 0.9851
30 0.4000 0.4000 0.4190 0.6570 0.7634 0.8607 0.9418 0.9704 0.9851 1

Single curve (k) interest rate risk
[ ]
k k k k
0.25 0.5 1 30
k
0.25,0.5 0.25,1 0.25,30 0.25
k
0.5,0.25 0.5
k
1,0.25 1
k
30,0.25 30
Q = cc cc cc ... cc
1 ρ ρ ... ρ cc
ρ 1 . ... . cc
ρ . 1 ... .CorrelMatrix = Transpose Q = cc
: : : ... : :
ρ . . ... 1 cc
Λ = Sum
  
  
  
  
  
  
  
  
   
[ ]( )
k
[CQ × trlCorre ]-[ShilMatrix × Tr ft]-[Enter]
C
anspose
C
Q
= Λ

Total interest rate risk
[ ]
[ ]( )
1 2 3 M
1
2
3
M
Q = cc cc cc ... cc
cc0 0.5 0.5 ... 0.5
cc0.5 0 . ... .
CorrelMatrix = Transpose Q = cc0.5 . 0 ... .
:: : : ... :
cc0.5 . . ... 0
Λ = Sum Q × CorrelMatrix × Transp [Ctrlose Q ]-[Shift
  
  
  
  
  
  
  
     
∑ ∑ ∑ ∑
∑
∑
∑
∑
M
2
IR k
k=1
CC = Λ + C
]-[Ente
C
r]
∑

Equity price risk buckets

Equity risk buckets
Capitalization
Large – Market capitalization > USD 2 bn
Small – Market capitalization < USD 2 bn
Economy
Advanced market
United States, Canada, Mexico, Euro zone, United Kingdom,
Norway, Sweden, Denmark, Switzerland, Australia, New Zealand,
Japan, Singapore and Hong Kong
Emerging market
Not advanced market

Capital charge ratios
and correlation coefficients
Bucket CCR (%) Correl Bucket CCR (%) Correl
1 55 0.15 7 40 0.25
2 60 0.15 8 50 0.25
3 45 0.15 9 70 0.075
4 55 0.15 10 50 0.125
5 30 0.25 11 70
6 35 0.25

Individual equity price risk
For each equity in buckets 1 to 10
Value
Quantity × Currency rate × Equity price
Capital charge
cc = Value × CCR
For each equity in buckets 11
Value
Quantity × Currency rate × Equity price
Capital charge
cc = | Value | × CCR

Bucket (k = 1 to 10) equity risk
[ ]
[ ]( )
k k k k
1 2 3 1
k
1
k
2
k
3
k
k
M
Q = cc cc cc ... cc
1 ρ ρ ... ρ cc
ρ 1 . ... . cc
CorrelMatrix = Transpos
[Ctrl]-[Shift]-[
CC
e Q =ρ . 1 ... . cc
: : : ... : :
ρ . . ... 1 cc
Λ = Sum Q × CorrelMatrix × Transpo EnteQ re ]s
  
  
  
  
  
  
  
     
= Λ

Bucket 11 equity risk
CC11
Sum of individual capital charges (cc) in bucket 11

Total equity price risk
[ ]
[ ]( )
1 2 3 10
1
2
3
10
Q = cc cc cc ... cc
cc0 0.15 0.15 ... 0.15
cc0.15 0 . ... .
CorrelMatrix = Transpose Q = cc0.15 . 0 ... .
:: : : ... :
cc0.
[Ctr
15 . . ... 0
Λ = Sum Q × CorrelMatrix × Transpos le Q
  
  
  
  
  
  
  
     
∑ ∑ ∑ ∑
∑
∑
∑
∑
M
2
EQ k 11
k=1
CC = Λ + CC
]-[Shift]-[En
+
t r]
CC
e
∑

Market risk capital charge
Three scenarios of correlation coefficient
Base correlation coefficient × 1
Base correlation coefficient × 1.25
Base correlation coefficient × 0.75
Market risk capital charge
MRCC = Max[CCCR] + Max[CCIR ] + Max[CCEQ ]
Risk weighted amount
RWA = 12.5 × MRCC

Regulatory reporting of market risk under the basel iv framework

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