Designing a system to analyze portfolio risks and to determine optimum margin requirements

1“RACR-2011, 22-25 May, 2011, Laredo, TX USA” “S. KABA & M. ACAR”

Designing a system to analyze portfolio risks and to determine optimum margin

requirements

Serkan KABA & Murat ACAR

[email protected] [email protected]

ISE Settlement and Custody Bank Inc.Istanbul/TURKEY

mailto:[email protected]

mailto:[email protected]


Designing a system to analyze portfolio risks and to determine optimum margin

requirements

“RACR-2011, 22-25 May, 2011, Laredo, TX USA” “S. KABA & M. ACAR”

Overview

• Objective

• Problem statement

• Background information

• Description of the system

• Methods

• Results

• Conclusions

3


Objective

• Designing a real-time risk management system to evaluate portfolios

• Developing a responsive system to analyze portfolios and orders in real-time

• Updating the portfolio risks accordingly

• Determining the best method to estimate margin levels for every asset class


Problem Statement

• Uncertainty and risk are everywhere in finance

• Determining the value loss that the derivatives portfolio could hypothetically suffer with some given probability and assumptions

• Defining margins required by brokers from their customers for certain kinds of transactions

• Protecting brokers from losses that may result from adverse price changes affecting the customer's net balance


ISE & ISE Data - 1

• Istanbul Stock Exchange (ISE) is a dynamic and growing emerging market with an increasing number of publicly traded companies, state-of-the-art technology and strong foreign participation

• The derivatives market began operation in 2001. In 2005, Turkish Derivatives Exchange (TURKDEX) started its operation as a successor

• ISE National 100 Index data is used to estimate PSR values for ISE100 derivatives.


ISE & ISE Data - 20

5/0

1/1

99

0

01

/05

/19

90

23

/08

/19

90

12

/12

/19

90

02

/04

/19

91

01

/08

/19

91

21

/11

/19

91

10

/03

/19

92

06

/07

/19

92

21

/10

/19

92

11

/02

/19

93

15

/06

/19

93

01

/10

/19

93

20

/01

/19

94

11

/05

/19

94

02

/09

/19

94

20

/12

/19

94

10

/04

/19

95

04

/08

/19

95

22

/11

/19

95

18

/03

/19

96

09

/07

/19

96

25

/10

/19

96

20

/02

/19

97

17

/06

/19

97

02

/10

/19

97

23

/01

/19

98

26

/05

/19

98

10

/09

/19

98

31

/12

/19

98

05

/05

/19

99

02

/09

/19

99

22

/12

/19

99

24

/04

/20

00

10

/08

/20

00

28

/11

/20

00

30

/03

/20

01

18

/07

/20

01

07

/11

/20

01

06

/03

/20

02

24

/06

/20

02

10

/10

/20

02

04

/02

/20

03

02

/06

/20

03

17

/09

/20

03

16

/01

/20

04

11

/05

/20

04

27

/08

/20

04

21

/12

/20

04

14

/04

/20

05

02

/08

/20

05

24

/11

/20

05

20

/03

/20

06

06

/07

/20

06

27

/10

/20

06

16

/02

/20

07

06

/06

/20

07

24

/09

/20

07

21

/01

/20

08

08

/05

/20

08

26

/08

/20

08

25

/12

/20

08

14

/04

/20

09

04

/08

/20

09

25

/11

/20

09

18

/03

/20

10

07

/07

/20

10

01

/11

/20

10

0

10000

20000

30000

40000

50000

60000

70000

80000


Components of the System

• CME SPAN (http://www.cmegroup.com/clearing/risk-management/span-overview.html)

• SPAN parameters and parameter estimation

• Realtime risk management system using SPAN


CME SPAN

• Developed and implemented in 1988 by Chicago Mercantile Exchange (CME)

• Portfolio based risk and margin calculation.

• Scenario based: 16 scenarios taken into consideration and worst loss is taken into account.

• Currently used by more than 50 exchanges and clearinghouses.


Realtime Risk Management System using SPAN - 1

• Trades are fed to clearing system as soon as they’re matched.

• Trades are processed in clearing system and new positions are calculated.

• New positions are sent to SPAN daemon for margin calculations. For efficiency multiple SPAN calculation engines are used and multiple portfolios are evaluated concurrently.

• Margin requirements are sent back to clearing system and account risk is updated accordingly.

• Notification is sent to exchange if the account becomes risky.



• Similar mechanism is used for processing orders of risky accounts.

• Single order for risky accounts are fed to clearing system as soon as they’re issued.

• Orders are processed in clearing system and hypothetical positions are calculated.

• Hypothetical positions are sent to a separate SPAN daemon for margin calculations.

• Margin requirement (if the order is matched) are sent back to clearing system and the new account risk is determined.

• Notification is sent to exchange if the account becomes non-risky.


SPAN Parameters

• Price scan range (PSR)

• Volatility scan range (VSR)

• Inter-commodity spread credit

• Short option minimum (SOM)

• Intra-commodity spread charge

• Spot month charge


Variables used to judge methods

• All variables used to estimate VaR and judge methods we use. We start by calculating the daily return series and estimating VaR's. Then we judge methods based on characteristics of these VaR estimates.

ISE National 100 index series

ISE National 100 index return series

Exceedances

Total Exceedances

Exceedance rate

xt

r t=xt

xt−1

− 1

∑t= 1

T

e t

∑t= 1

T

e t

T

Average Margin


ISE National 100 Index daily return series (rt)0

5/0

1/1

99

0

01

/05

/19

90

23

/08

/19

90

12

/12

/19

90

02

/04

/19

91

01

/08

/19

91

21

/11

/19

91

10

/03

/19

92

06

/07

/19

92

21

/10

/19

92

11

/02

/19

93

15

/06

/19

93

01

/10

/19

93

20

/01

/19

94

11

/05

/19

94

02

/09

/19

94

20

/12

/19

94

10

/04

/19

95

04

/08

/19

95

22

/11

/19

95

18

/03

/19

96

09

/07

/19

96

25

/10

/19

96

20

/02

/19

97

17

/06

/19

97

02

/10

/19

97

23

/01

/19

98

26

/05

/19

98

10

/09

/19

98

31

/12

/19

98

05

/05

/19

99

02

/09

/19

99

22

/12

/19

99

24

/04

/20

00

10

/08

/20

00

28

/11

/20

00

30

/03

/20

01

18

/07

/20

01

07

/11

/20

01

06

/03

/20

02

24

/06

/20

02

10

/10

/20

02

04

/02

/20

03

02

/06

/20

03

17

/09

/20

03

16

/01

/20

04

11

/05

/20

04

27

/08

/20

04

21

/12

/20

04

14

/04

/20

05

02

/08

/20

05

24

/11

/20

05

20

/03

/20

06

06

/07

/20

06

27

/10

/20

06

16

/02

/20

07

06

/06

/20

07

24

/09

/20

07

21

/01

/20

08

08

/05

/20

08

26

/08

/20

08

25

/12

/20

08

14

/04

/20

09

04

/08

/20

09

25

/11

/20

09

18

/03

/20

10

07

/07

/20

10

01

/11

/20

10

-0,2

-0,15

-0,1

-0,05

0

0,05

0,1

0,15

0,2

0,25


Methods discussed

• Extreme Value Theory

• Historical Simulation

• GARCH

• EGARCH

• Asymmetric CaViaR


Extreme Value Theory

• Models possibility of big losses.

• Focuses on tails instead of the entire distribution.

• Our approach uses Peaks Over Threshold method which uses values above a high threshold and Generalized Pareto Distribution (GPD) as limiting distribution of these values.


Historical Simulation

• Non-parametric method

• Directly uses historical data to estimate the current market conditions

• Determines nth worst loss in historical data depending on the window size and confidence level.

• 750 day window is used as opposed to other methods which we used a 500 day window.


GARCH

• Established by Tim Bollerslev in 1986

• Models current volatility by recent volatility values and returns.

• We calculate the VaR using the volatility estimate by assuming that the returns are normally distributed.

• We use GARCH(1,1) since higher lags don't improve the results.


EGARCH

• GARCH model considers positive and negative returns equally.

• In practice, positive and negative returns have asymmetric effect on volatility. For equities, volatility increases more with a negative return shock where as foreign exchange volatilities exhibit an opposite relationship.

• EGARCH model established by Nelson is a form of GARCH which considers these asymmetries.

• We calculate the VaR using the volatility estimate using Student's t distribution.


Asymmetric CAViaR

• Conditional autoregressive value at risk (CAViaR) methods introduced by Engle and Manganelli.

• Focus on behavior of a quantile.

• They model quantiles autoregressively relationship.

• We use the asymmetric variation which takes into account asymmetric effect of returns on volatility.


Results (1990/12-2010/12)


Results (2004/01-2010/12)


Comparing PSR Estimation Methods - 1

• When the methods tested against near term data, none of the methods is able to meet the 5‰ exceedance level.

• Extreme value and EGARCH, come close to this performing below 1% exceedance rate.

• Next best performers are CAViaR asymmetric and historical simulation performing below 1.5% exceedance rate.

• Results obtained from long term data show that exceedance rates for extreme value, EGARCH and historical simulation decreased slightly, whereas that of CAViaR asymmetric decreased drastically for long term.

• We can conclude that CAViaR asymmetric could have performed better for earlier years of ISE and other 4 slightly underperformed in the near term.


Comparing PSR Estimation Methods - 2

• When average margins are taken into account we see that extreme value comes with a price, higher margin rates.

• Long term margin averages of the best perfoming models, extreme value and EGARCH, are 11% and 8.9% respectively, way above the 7.5% maintenance margin rate currently used.

• Near term averages are more acceptable 8.8% and 5.6% respectively.

• Analyzing average margins, since both methods cause exceedances below 1%, approximately 2 exceedances per year, we can say that EGARCH can be more usable since it produces much lower margin rates.


Graph of PSR Estimates vs. Current Margin Rate


Conclusions

• We presented a methodology for estimating PSR parameter for SPAN because it's important for a risk management system to calculate optimum margin rates.

• PSR estimation methods can be further compared by analyzing other characteristics such as margin variance.

• Margins changes can be decreased by smoothing, in other words discarding tolerable changes in margin levels.

• The other parameters of SPAN that we mentioned can be estimated using similar methods.


THANKS ...

Designing a system to analyze portfolio risks and to determine optimum margin requirements

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