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