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

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Value at RiskAn Introduction To Its Use In An
Energy Trading Company
November 7th, 2003

• Krishan Sabharwal
• Manager, Risk Analytics
• BP Energy Company

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Who We Are
BP. Amoco, ARCO, and Castrol have come together
to create one of the largest energy companies on
the planet.
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Global Presence
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Performance

• were the largest gas and oil producer in North
  America
• were fuel for travelers at 1400 airports in 87
  countries
• we are among the most profitable petrochemical
  producers in the world
• were 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

Capital Employed 63 Billion
Excludes liabilities for current and
deferred taxation of 4 billion for total
capital employed of 59 billion
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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
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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 Morgans 415 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!

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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

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Definitions of Volatility
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VaR Methodologies

• Analytic (Variance-Covariance)
• RiskMetrics
• Monte Carlo Simulation
• Historical Simulation
• Stress Testing
• Principal Components Analysis (w/ MC Simulation)

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Analytic VaR

• Benefits
• Fast
• Relatively easy to understand
• Allows for VaR Greeks (VaRdelta, Component VaR)
• Weaknesses
• Doesnt handle non-linear (option) portfolios
  well
• Highly correlated market exposures can lead to
  dysfunctional statistics
• Exposure bucketing typical to keep dataset
  manageable
• Assumes returns are normally distributed

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The Analytic VaR Bible
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Analytic VaR Example
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Analytic VaR Example Cont.
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Analytic VaR Example Cont.
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Analytic VaR Matrix Math
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Monte Carlo VaR

• Benefits
• Handles non-linear (option) portfolios well via
  full portfolio valuation
• Highly correlated market exposures not a problem
• Relatively easy to understand
• Weaknesses
• Doesnt allow for VaR Greeks (VaRdelta,
  Component VaR)
• Generally slower than closed-form techniques
• May require high number of iterations to achieve
  confidence in results
• May still require bucketing
• Normal return distribution assumption (typically)
• The Monte Carlo effect!

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Monte Carlo VaR Technique

• Methodology
• Estimate volatility of each underlying risk
  factor in BP Energys portfolio
• Nymex natural gas futures contracts
• Basis (physical delivery location Nymex)
• Electricity forward contracts
• 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)
• Simulate all risk factors revalue the portfolio
  for each iteration

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Monte Carlo based VaR
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Historical Simulation

• Benefits
• No volatility or correlation data required
• Intuitive grounded in reality
• Fast
• Handles non-linear (option) portfolios well via
  full portfolio valuation
• Actual return distribution used vs. Normal
  assumption
• Weaknesses
• Past returns are not indicative of future
  results
• VaR is a function of historical time period
  selection subjective!
• May be limited historical data for certain
  commodities

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Historical Simulation Cont.

• Which Time period would you select?

Historic Henry Hub Gas Volatility Price Levels
(1/1/95 - 12/31/01)
200
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Prompt NYMEX Volatility
Prompt NYMEX Price
180
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160
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140
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120
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20-day Moving Annualized Volatility
Price (/MMbtu)
100
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80
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60
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40
2
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1
0
-
01/03/95
07/22/95
02/07/96
08/25/96
03/13/97
09/29/97
04/17/98
11/03/98
05/22/99
12/08/99
06/25/00
01/11/01
07/30/01
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Historical Simulation Cont.

• Methodology
• Select historic dataset as a proxy for the future
• Subject existing portfolio to historic data
  return distribution, revaluing the portfolio at
  each step
• As with MC simulation find the loss at your
  confidence level from the resultant P/L
  distribution

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Stress Testing

• Benefits
• Same as historical simulation, generally
• Allows management to specify a price environment
  to stress the portfolio
• Weaknesses
• Allows management to specify a price environment
  to stress the portfolio
• Grounded in reality is a matter of perception

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Principal Components Analysis w/ MC Simulation

• Benefits
• Handles highly correlated datasets very well
• Reduces the number of simulated underlying risk
  factors
• Full portfolio valuation handles non-linear
  (options) instruments well
• Weaknesses
• Not as fast as analytic approach
• Cant develop VaR Greeks
• Black Box effect

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Principal Components Analysis w/ MC Simulation
Cont.

• Good fit for BP Energys 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

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Principal Components Analysis w/ MC Simulation
Cont.

• Methodology
• Extract principal components, or independent
  normally distributed return factors, from
  historic dataset
• Simulate the the principal components to generate
  forward curve changes
• Revalue the portfolio under each iteration of
  forward curve change
• As with MC simulation find the loss at your
  confidence level from the resultant P/L
  distribution

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