Stressed VaR
Pascal Gibart
EIFR 7 Feb 2012
Stressed VaR – EIFR Feb 2012
2Contents
03 Regulatory context
08 sVaR in practice
17 sVaR and risk management
28 Conclusion
29 References
Stressed VaR – EIFR Feb 2012
3Regulatory Framework
Stressed VaR – EIFR Feb 2012
4Regulatory Framework
Motivationlosses during the 2008 crisis were higher than the minimum
capital requirement for many banksreduce the procyclicality of the minimum capital requirementexample for EUR/USD FX exposure
Volatility 2*VaR VaR+SVaRV low 8% 16% 28%V neutral 12% 24% 32%V high 20% 40% 40%
Stdev 0,12 0,06
Stressed VaR – EIFR Feb 2012
5Regulatory Framework
Description in BCBS158 article 718 (July 2009)– Current portfolio – Stressed market conditions to be calibrated at least once a year– 99 percentile over a 10 day period– Calculated at least weekly– Same back-testing penalty as the VaR– Added to the capital requirement with a specific multiplier
avgstavgct mmc sVaR,sVaRmaxVaR,VaRmax 11
Stressed VaR – EIFR Feb 2012
6Regulatory Framework
Quantitative Impact (BCBS163 Oct 2009)sVaR is roughtly 2.5 times the VaR in a normal period (2006)there is no specific reduction in the netting effect for the sVar
compared to VaRthese macro results vary greatly across institutions and will
obviously vary as well depending on the present regime– If we move to a low volatility regime the ratio will rise– If we go back to a stressed environment the ratio will decrease
Stressed VaR – EIFR Feb 2012
7Regulatory Framework
Consultation paper on stressed VaR (30 Nov 2011)length of the period is 12 months even if VaR period is longerno scenario weightingdetermination of the stressed period:– Judgment based approach– Formulaic approach
Special care to proxies because they will always staySpecial care to sensitivity based approachesUse test
Stressed VaR – EIFR Feb 2012
8sVar in practice
Stressed VaR – EIFR Feb 2012
9sVaR in practice
Globally a far lower challenge than the other additional market risk measures introduced recently (IRC and CRM)
The natural choice is to build on the existing VaR frameworkthe calibration period is differentfrequency of calculation can be different as well
the main challenge is to reconstruct appropriate historical data over long periods
As a result, it is difficult to go too far back (1987?) particularly for large banks that have positions in complex derivatives for which there was no market at the time
Stressed VaR – EIFR Feb 2012
10sVaR in practice
Going forward it will be more difficult to reconstruct historical data for risk factor that did not exist (or were not liquid) in the past
how do you generate prices for Carbon emission before 2005? what about CDO correlation structure before 2005 ?what proxy do you use for a new stock?
Some data during the 2008 crisis are of poor qualitysome shocks result from very illiquid markets and arbitrage can
be created depending on the initial data structure
Stressed VaR – EIFR Feb 2012
11sVaR in practice
Choosing the stress period is time consumingneed to run VaR on longer and longer periods as time goes byIdeally should be reviewed whenever there is a significant
change in the structure of the portfolio (what is a significant change?)
Do we use the stock of trades for a set of dates or just one?
In the end it seems that most bank will end up with more or less the same period, which will always include September to November 2008
A consultancy, Lepus, organized a survey of 23 banks and all of them included September to November 2008 in their sVaR period
Stressed VaR – EIFR Feb 2012
12sVaR in practice: US Equity Volatility
Stressed VaR – EIFR Feb 2012
13sVaR in practice: European Equity Volatility
Stressed VaR – EIFR Feb 2012
14sVaR in practice: EURUSD 1m ATM volatility
Stressed VaR – EIFR Feb 2012
15sVaR in practice: USDJPY 1m ATM volatility
Stressed VaR – EIFR Feb 2012
16sVaR in practice: USD Swaption 5y5y
Stressed VaR – EIFR Feb 2012
17sVaR as a Risk Management tool
Stressed VaR – EIFR Feb 2012
18sVar for Risk Management
Risk factors can be divided between: the liquid ones that can be hedged easily in all circumstancesthe illiquid ones that can not be hedged at allthe less liquid ones that can not be hedged in stressed period
the liquid risk can be managed by a VaR limitwhen volatility is low the trader can have significant positionswhen volatility is high the trader must reduce exposures
the illiquid risk factors are managed by a global sensitivitya maximum sensitivity is set in order to cap the risk for an
extreme movement
Stressed VaR – EIFR Feb 2012
19sVar for Risk Management
The sVaR has limited appeal for linear portfoliosImagine an Equity Index exposure– When volatility is 15% the 10 day VaR is roughly
2.33*15%*sqrt(25)=7%– When the volatility is 30% the sVaR is simply doubled! There is no
additional information from a risk point of view.
Adding limits depending on the sVaR has limited appealIf risk factors are not very liquid, in a stressed period it will be
even worse.– A 10 day VaR or sVaR will be a bad predictor of future losses
anyway!
Stressed VaR – EIFR Feb 2012
20sVar for Risk Management
The sVaR is more interesting for non-linear portfoliossVaR produces large moves in risk factors and hence exhibits
non linear behavior of the P&L of complex portfoliosIn that respect, it is very similar to historical stress scenarios
which are already part of the Internal Model framework
Example of a Long Term FX portfoliomajor risk factors are– FX spot– FX volatility– Interest rate spread
in the following graphs the 3 factors are moved together
Stressed VaR – EIFR Feb 2012
21sVar for Risk Management
Long Term FX PortfolioFX up- FX Vol up- Spread up
0
50 000
100 000
150 000
200 000
250 000
300 000
350 000
400 000
450 000
500 000
0 0,2 0,4 0,6 0,8 1
1st derivative MtM
Stressed VaR – EIFR Feb 2012
22sVar for Risk Management
Long Term FX PortfolioFX up- FX Vol down-Spread down
-200 000
-150 000
-100 000
-50 000
0
50 000
100 000
150 000
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
1st derivative MtM
Stressed VaR – EIFR Feb 2012
23sVar for Risk Management
Even when each underlying risk factor is liquid, hedging the multi factor dynamic is not easy and gaps appear
– Correlation risk or cross gamma risk– High order derivative risk
As a result, complex portfolios will generate high stress scenarios (or sVaR) values
Stressed VaR – EIFR Feb 2012
24sVar for Risk Management
Stylized example Consider a simple OTM option in a Black Scholes frameworkIt is hedged with an ATM option
European Call European Call Vega Ratio C1 - ratio C2Value 0,3889 Value 5,6449 0,323 (1,436) Delta 0,066 Delta 0,535 (0,107)
Gamma 0,0091 Gamma 0,022 0,002 Vega 9,099 Vega 28,138 - Vanna 1,058 Vanna 0,141 1,013 Volga 112,580 Volga (0,882) 112,866
Strike 125,00 Strike 100,00Maturity 03-août-12 Maturity 03-août-12Today 02-févr-12 Today 02-févr-12Spot 100 Spot 100
Volatility 20% Volatility 20%Rate 0,00% Rate 0,00%
Dividends 0,00% Dividends 0,00%
Stressed VaR – EIFR Feb 2012
25sVar for Risk Management
Stylized example We generate 5000 simulations with low volatility:– Index volatility=20%– Volatility of volatility=30%– Correlation=-50%– 10 day shocks
and then high volatility– Index volatility=40%– Volatility of volatility=60%
Stressed VaR – EIFR Feb 2012
26sVar for Risk Management
sVaR=12*VaR
Distribution of P&L for each VaR scenario
-6
-5
-4
-3
-2
-1
0
1
2
Low Vol High Vol
P&L Low Vol High VolAverage 0,008 (0,070)
Stdev 0,053 0,389 0,01 0,175 0,568 0,99 (0,147) (1,770)
Stressed VaR – EIFR Feb 2012
27sVar for Risk Management
Exotic portfolio tend to be accumulated during low volatility periods
– In low volatility environment, the VaR coming from the unhedged risk is small
– When volatility rises in stressed periods, the VaR rises and even if traders hedge tightly the major risks, cross risks will become an issue
Monitor sVaR at inception in order to make sure that the VaR in future stress periods can still be managed efficiently by the traders
Stressed VaR – EIFR Feb 2012
28Conclusion
sVaR is a natural extension of the current VaR framework
Managing proxies in the long run may prove difficult
For most banks, the sVaR period includes the 3 months periodstarting with the Lehman collapse (15 Sep 2008) ending the Citigroup bail out (23 Nov 2008)
In terms of risk management, sVaR is useless for linear portfoliosMonitoring sVaR for non linear portfolios will limit sizes to
manageable levels
Stressed VaR – EIFR Feb 2012
29References
Revisions to the Basel II market risk framework, Jul 2009, www.bis.org/publ/bcbs158.pdf
Analysis of the trading book quantitative impact study, Oct 2009, www.bis.org/publ/bcbs163.pdf
EBA Consultation Paper on the Draft Guidelines on Stressed Value At Risk (CP48) Nov 2011, http://www.eba.europa.eu/cebs/media/Publications/ConsultationPapers/2011/CP48/EB A-BS-2011-166r-(CP48-on-GL-Stressed-VaR)-FINAL.pdf
Lepus. Stressed VaR December 2011