bp

Value at RiskAn Introduction To Its Use In An Energy Trading Company

Krishan Sabharwal

Manager, Risk & Analytics

BP Energy Company

November 7th, 2003

4

Who We Are

BP. Amoco, ARCO, and Castrol have come together to create one of the largest energy companies on the planet.

Global Presence

8

• we’re the largest gas and oil producer in North America

• we’re fuel for travelers at 1400 airports in 87 countries

• we are among the most profitable petrochemical producers in the world

• we’re the largest marketer of raw materials used to make CD boxes, insulation and other everyday products

• we are the leading solar producer in the world

Performance

Upstream 59% Downstream

23%

Other 2%Chemicals

16%

Capital Employed*$63 Billion

* Excludes liabilities

for current and deferred taxation of

$4 billion for total capital employed of $59 billion

Rank Company 1Q03 1Q02

1 BP 20.1 14.9

2 Mirant 12.6 21.4

3 Coral 9.9 9.2

4 Sempra 9.5 9.5

5 ConocoPhillips 8.8 4.6

6 Cinergy 4.2 3.8

7 Reliant 4.0 10.5

8 Nexen 3.5 2.2

9 Oneok 3.5 2.8

10 Williams 3.5 5.4

Top North American Marketers by Volume (Bcf/d)

Source: Gas Daily

Note: Duke, AEP and Dynegy are no longer reporting volumes; El Paso did not respond to queries

Value at Risk

“Value at risk (VaR) is an attempt to provide a single number for senior management summarizing the total risk in a portfolio of financial assets.” – Hull

JP Morgan’s 4:15 report to senior management

Usually takes the form of “We are X percent certain that we will not lose more than V dollars in the next N days.”• X typically 95 – 99%• N typically 1 day• V typically very large, depending on X and N!

Typical Energy Trading Risk Factors

Natural gas futures prices Natural gas basis (Delivery location price – Futures

Price) Electricity forward market prices Crude oil futures prices Crude products (gasoline, diesel, etc.) prices Coal prices Emission credit prices Interest rates Etc.

Green = Typical BP Energy (Houston) exposures

Definitions of Volatility

1t

tseries

P

PLNStdDevVolatilityDaily

VolatilityDailyVolatilityAnnualized 252

VaRdayNVaRNday 1

VaR Methodologies

Analytic (Variance-Covariance)• RiskMetrics

Monte Carlo Simulation Historical Simulation Stress Testing Principal Components Analysis (w/ MC

Simulation)

Analytic VaR

Benefits:1. Fast

2. Relatively easy to understand

3. Allows for VaR “Greeks” (VaRdelta, Component VaR)

Weaknesses1. Doesn’t handle non-linear (option) portfolios well

2. Highly correlated market exposures can lead to dysfunctional statistics

3. Exposure “bucketing” typical to keep dataset manageable

4. Assumes returns are normally distributed

The Analytic VaR “Bible”

Analytic VaR Example

Analytic VaR Example Cont.

Analytic VaR Example Cont.

Analytic VaR Matrix Math

Monte Carlo VaR

Benefits:1. Handles non-linear (option) portfolios well via full portfolio

valuation

2. Highly correlated market exposures not a problem

3. Relatively easy to understand

Weaknesses1. Doesn’t allow for VaR “Greeks” (VaRdelta, Component VaR)

2. Generally slower than closed-form techniques

3. May require high number of iterations to achieve confidence in results

4. May still require “bucketing”

5. Normal return distribution assumption (typically)

6. The “Monte Carlo” effect!

Monte Carlo VaR Technique

Methodology:1. Estimate volatility of each underlying risk factor in BP

Energy’s portfolio:– Nymex natural gas futures contracts– Basis (physical delivery location – Nymex)– Electricity forward contracts

2. Estimate the correlation of the risk factors:– Intracommodity (June ’02 Nymex gas to July ’02 Nymex

gas)– Cross Commodity (June ’02 Nymex gas to June ’02

Cinergy electricity)– Hybrid (June ’02 Nymex gas to June ’02 Chicago Citygate

gas)

3. Simulate all risk factors & revalue the portfolio for each iteration

Monte Carlo based VaR

Historical Simulation

Benefits:1. No volatility or correlation data required

2. Intuitive – “grounded in reality”

3. Fast

4. Handles non-linear (option) portfolios well via full portfolio valuation

5. Actual return distribution used vs. Normal assumption

Weaknesses:1. “Past returns are not indicative of future results”

2. VaR is a function of historical time period selection – subjective!

3. May be limited historical data for certain commodities

Historical Simulation Cont.

Which Time period would you select?Historic Henry Hub Gas Volatility & Price Levels

(1/1/95 - 12/31/01)

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

01/0

3/95

07/2

2/95

02/0

7/96

08/2

5/96

03/1

3/97

09/2

9/97

04/1

7/98

11/0

3/98

05/2

2/99

12/0

8/99

06/2

5/00

01/1

1/01

07/3

0/01

20-d

ay M

ovin

g A

nn

ualize

d V

ola

tility

$-

$1

$2

$3

$4

$5

$6

$7

$8

$9

$10

Pri

ce (

$/M

Mb

tu)

Prompt NYMEX VolatilityPrompt NYMEX Price

Historical Simulation Cont.

Methodology:1. Select historic dataset as a proxy for the future

2. Subject existing portfolio to historic data return distribution, revaluing the portfolio at each step

3. As with MC simulation – find the loss at your confidence level from the resultant P/L distribution

Stress Testing

Benefits:1. Same as historical simulation, generally

2. Allows management to specify a price environment to stress the portfolio

Weaknesses:1. Allows management to specify a price

environment to stress the portfolio

2. “Grounded in reality” is a matter of perception

Principal Components Analysis w/ MC Simulation

Benefits:1. Handles highly correlated datasets very well

2. Reduces the number of simulated underlying risk factors

3. Full portfolio valuation – handles non-linear (options) instruments well

Weaknesses:1. Not as fast as analytic approach

2. Can’t develop VaR “Greeks”

3. “Black Box” effect

Principal Components Analysis w/ MC Simulation Cont.

Good fit for BP Energy’s natural gas position• 63 natural gas delivery locations in North

America• Majority of trading activity in first 13 months or so.

• Analytic or MC Correlation matrix = 819 x 819 = 670,761 elements – very highly correlated – a statistical nightmare!

• Embedded optionality in many positions• Requires a full portfolio valuation approach to

capture the “Greeks”

Principal Components Analysis w/ MC Simulation Cont.

Methodology:1. Extract principal components, or independent normally

distributed return factors, from historic dataset

2. Simulate the the principal components to generate forward curve changes

3. Revalue the portfolio under each iteration of forward curve change

4. As with MC simulation – find the loss at your confidence level from the resultant P/L distribution

Principal Components Analysis w/ MC Simulation Cont.Natural Gas PCA underlying dataset:

Dates NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - Close NG - CloseNatural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)Natural Gas Futures (USD/MMBTU)

4/18/1996 2.331 2.337 2.332 2.302 2.262 2.257 2.287 2.365 2.37 2.27 2.085 1.917 1.912 1.907 1.907 1.907 1.9084/19/1996 2.361 2.366 2.357 2.326 2.28 2.272 2.3 2.38 2.385 2.28 2.095 1.926 1.92 1.915 1.915 1.915 1.9164/22/1996 2.359 2.364 2.364 2.339 2.296 2.29 2.318 2.403 2.41 2.295 2.103 1.928 1.922 1.917 1.917 1.917 1.9184/23/1996 2.28 2.293 2.3 2.294 2.267 2.264 2.292 2.375 2.385 2.27 2.078 1.903 1.897 1.892 1.892 1.892 1.8934/24/1996 2.214 2.258 2.26 2.26 2.235 2.235 2.27 2.355 2.368 2.25 2.06 1.887 1.883 1.882 1.882 1.882 1.8834/25/1996 2.258 2.242 2.238 2.212 2.212 2.252 2.332 2.345 2.225 2.035 1.862 1.858 1.857 1.857 1.857 1.858 1.8884/26/1996 2.207 2.213 2.205 2.183 2.183 2.229 2.305 2.318 2.213 2.025 1.858 1.857 1.857 1.857 1.857 1.857 1.8854/29/1996 2.223 2.204 2.198 2.177 2.177 2.22 2.3 2.313 2.213 2.03 1.873 1.872 1.872 1.872 1.872 1.872 1.8994/30/1996 2.224 2.198 2.191 2.173 2.175 2.225 2.305 2.318 2.223 2.04 1.885 1.884 1.884 1.884 1.884 1.884 1.9115/1/1996 2.229 2.214 2.209 2.192 2.192 2.242 2.322 2.332 2.245 2.07 1.92 1.921 1.923 1.923 1.923 1.923 1.9485/2/1996 2.19 2.191 2.185 2.163 2.168 2.218 2.301 2.312 2.237 2.081 1.951 1.951 1.951 1.951 1.951 1.951 1.9715/3/1996 2.131 2.139 2.14 2.123 2.13 2.183 2.268 2.28 2.22 2.08 1.96 1.96 1.96 1.96 1.96 1.96 1.985/6/1996 2.148 2.164 2.155 2.13 2.135 2.188 2.275 2.287 2.23 2.092 1.98 1.98 1.98 1.98 1.98 1.982 2.0055/7/1996 2.187 2.223 2.205 2.17 2.172 2.218 2.3 2.31 2.245 2.102 1.987 1.987 1.987 1.987 1.987 1.987 2.01

1/31/2003 5.605 5.345 5.027 4.899 4.879 4.859 4.804 4.799 4.917 5.022 5.087 4.944 4.724 4.344 4.191 4.149 4.1542/3/2003 5.766 5.485 5.163 4.993 4.963 4.928 4.87 4.855 4.973 5.078 5.14 5 4.78 4.385 4.22 4.175 4.182/4/2003 5.762 5.512 5.212 5.049 5.009 4.969 4.909 4.894 5.019 5.134 5.201 5.057 4.835 4.416 4.236 4.176 4.1762/5/2003 5.644 5.414 5.171 5.061 5.014 4.969 4.909 4.904 5.046 5.166 5.244 5.104 4.889 4.464 4.289 4.239 4.2442/6/2003 5.828 5.578 5.298 5.158 5.093 5.033 4.968 4.958 5.083 5.203 5.273 5.133 4.905 4.455 4.27 4.22 4.222/7/2003 6.043 5.78 5.448 5.283 5.208 5.138 5.068 5.058 5.183 5.298 5.368 5.228 4.988 4.518 4.328 4.278 4.273

2/10/2003 5.852 5.617 5.327 5.197 5.142 5.082 5.022 5.022 5.162 5.287 5.357 5.225 4.995 4.525 4.345 4.295 4.292/11/2003 5.977 5.722 5.417 5.272 5.217 5.157 5.102 5.102 5.242 5.377 5.442 5.302 5.067 4.557 4.367 4.317 4.3122/12/2003 5.785 5.56 5.315 5.205 5.164 5.116 5.069 5.074 5.224 5.377 5.447 5.312 5.082 4.572 4.382 4.332 4.3222/13/2003 5.74 5.55 5.35 5.26 5.23 5.185 5.145 5.155 5.305 5.455 5.53 5.39 5.155 4.625 4.43 4.37 4.3552/14/2003 5.851 5.644 5.439 5.344 5.324 5.284 5.244 5.259 5.409 5.559 5.639 5.497 5.262 4.702 4.502 4.437 4.422

Principal Components Analysis w/ MC Simulation Cont.Natural Gas PCA results:

Eigen ValuesF1 F2 F3

Eigen Value: 0.0103 0.0012 0.0002 Variance (%) 86.7% 9.8% 2.0%Cumulative (%) 86.7% 96.5% 98.5%

Eigen Vectors

FEB 0.455284 -0.485427 0.360784MAR 0.412056 -0.387287 0.181597APR 0.321384 -0.135265 -0.10103MAY 0.260764 -0.037553 -0.27311JUN 0.227856 0.039848 -0.33875JUL 0.213105 0.066264 -0.31856AUG 0.201009 0.082781 -0.28562SEP 0.190895 0.097382 -0.25817OCT 0.181146 0.117005 -0.22419NOV 0.162593 0.127384 -0.14102DEC 0.149436 0.139668 -0.08145JAN 0.141895 0.143573 -0.04404FEB 0.140349 0.154909 -0.02296MAR 0.139832 0.170801 0.01453APR 0.129057 0.19359 0.112487MAY 0.12583 0.207628 0.140506JUN 0.122726 0.214065 0.154115JUL 0.120056 0.217761 0.163537AUG 0.119295 0.217062 0.170479SEP 0.117425 0.219017 0.186745OCT 0.115155 0.215751 0.199751NOV 0.109022 0.215455 0.201155DEC 0.103991 0.211066 0.197997JAN 0.102727 0.206659 0.204305

January

Eigen ValuesF1 F2 F3

Eigen Value: 0.0107 0.0007 0.0000 Variance (%) 93.2% 6.0% 0.3%Cumulative (%) 93.2% 99.2% 99.5%

Eigen Vectors

FEB 0.301791 -0.386739408 -0.30426MAR 0.289281 -0.370925675 -0.18528APR 0.267494 -0.330572504 -0.10229MAY 0.258825 -0.278897924 0.001271JUN 0.235983 -0.17270135 0.116535JUL 0.216933 -0.091371034 0.193058AUG 0.210146 -0.05878705 0.210769SEP 0.207935 -0.012111404 0.231448OCT 0.206124 0.03469249 0.243369NOV 0.19853 0.102297972 0.243661DEC 0.193315 0.135454562 0.24138JAN 0.189531 0.14454585 0.21112FEB 0.186549 0.154298409 0.183328MAR 0.183167 0.162931468 0.143526APR 0.180479 0.164067994 0.104102MAY 0.176693 0.169296441 0.054528JUN 0.166414 0.181342192 -0.03719JUL 0.158443 0.179255835 -0.07044AUG 0.155079 0.18404749 -0.12844SEP 0.156373 0.195013846 -0.17739OCT 0.159401 0.206647744 -0.23453NOV 0.165147 0.220484995 -0.30494DEC 0.1666 0.224652249 -0.32828JAN 0.165753 0.220127913 -0.33803

June

Principal Components Analysis w/ MC Simulation Cont.

Natural Gas PCA results:

J anuary

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 6 12 18 24

F1 F2 F3

June

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 6 12 18 24

F1 F2 F3

Principal Components Analysis w/ MC Simulation Cont.

Natural Gas PCA results:

Implied Forward Volatility Structure

0%

10%

20%

30%

40%

50%

60%

70%

80%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Months to Maturity

January

June