modeling and hedging the risk in retail load contracts
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1Hess Energy · 2010 All Rights Reserved
Modeling and Hedging the Risk in Retail Load Contracts
Eric Meerdink, Director of Structuring & Analytics
May 3, 2011
2Hess Energy · 2010 All Rights Reserved
Background on Hess Corporation
3Hess Energy · 2010 All Rights Reserved
Hess: Who We are Today
EXPLORATION Discovering oil and gas
PRODUCTION & DEVELOPMENT Getting crude oil out of the ground
SUPPLY, TRADING &TRANSPORTATIONBuying, selling and transporting crude oil and finished products
REFINING Processing the crude oil into finished products
ENERGY TRADINGHess Energy Trading Company, a joint venture buying and selling energy financial instruments
TERMINALSStoring products and distributing fuels to our customers
RETAIL MARKETINGSelling motor fuels and convenience products at retail stores
ENERGY MARKETINGMarketing petroleum products, natural gas and electricity to commercial, industrial and utility customers
A Totally Integrated Energy Company
4Hess Energy · 2010 All Rights Reserved
One of the Largest Energy Suppliers on the East Coast
5Hess Energy · 2010 All Rights Reserved
Hess Energy: Robust Product Suite
Fuel Oil
Delivery to Commercial & Industrial customers
Distributor sales from Hess terminals
110K BPD
Natural Gas
Marketing to Commercial & Industrial customers
Wholesale to LDCs
1.5 BCF/day
Electricity
Marketing to Commercial & Industrial customers
4,500 MWs/hr (RTC ) (enough electricity to power 4 million average homes)
#2 electric marketer on the east coast
Green Suite
Reducing electric usage during times of peak demand
Support renewable energy sources, such as wind, solar, biomass and hydropower
Balance your carbon impact from oil and natural gas with carbon offsets
6Hess Energy · 2010 All Rights Reserved
Volumetric Risk in Retail Load Contracts
7Hess Energy · 2010 All Rights Reserved
What is a Full Requirements Load Following Contract
• Full Requirements Load Following: A fixed price agreement to serve all the electricity load of a customer, and provide all products required to supply the electric load, for a pre-determined interval of time, without restrictions on volume. Typically served at a fixed rate per MWH.
• Also called Full Plant Requirements Contract.
• Typical key products to be supplied:○ Load Following Energy○ Capacity○ Transmission○ Ancillaries○ RECs
8Hess Energy · 2010 All Rights Reserved
Volumetric or Swing Risk
• Volumetric or swing risk is defined as a cash flow risk caused by deviations in delivered volumes compared to expected volumes. The primary cause of these volumetric deviations is weather and economic conditions.
• Not enough that delivered volumes deviate from expected volumes.
○ These deviations in delivered volumes must be positively correlated with market prices.
○ The full requirements load following contract is delta hedged at some expected volume.
• Under these conditions the resulting expected cash flow position is negative and non-linear with respect to changes in market prices.
• Swing risk is similar to the gamma position of an option, as it is a second order price risk.
9Hess Energy · 2010 All Rights Reserved
Figure 1. Correlation Between Price and Load
4,800
4,900
5,000
5,100
5,200
5,300
5,400
5,500
May-06 Sep-06 Jan-07 May-07 Sep-07 Jan-08 May-08 Sep-08 Jan-09 May-09 Sep-09 Jan-10 May-10 Sep-10
Month/Yr
MW
$0.00
$10.00
$20.00
$30.00
$40.00
$50.00
$60.00
$70.00
$80.00
$90.00
$/M
WH
MW
$/MWH
12-Month Rolling Average of Load and Price in PSE&G Zone
10Hess Energy · 2010 All Rights Reserved
Figure 2: Retail Sale and Long Hedge
Long Hedge
Short Sale
$/MWH
Short Retail Sale
-
$
Net: Swing Risk “Gamma”
+
11Hess Energy · 2010 All Rights Reserved
Figure 3. Change in Cash Flow when Power is Delta Hedged
Load less than expected load
Load equals expected load
Load greater than expected
load
Price less than expected price - 0 +
Price equals expected price 0 0 0
Price greater than expected
price+ 0 - Swing Risk
- - - - - -
LongPosition
Hedged ShortPosition
1
2
3
A B C
12Hess Energy · 2010 All Rights Reserved
Expected Cost to Serve Load
and Swing Risk
13Hess Energy · 2010 All Rights Reserved
Expected Cost to Serve Load
• Model assumptions:○ Pi = Actual price in hour i (random variable)○ Li = Actual load in hour i (random variable)○ Covi = Covariance between P and L in hour i Cov(Pi,Li).○ i = hours in the month i = 1,…,N○ Averages will be denoted with a bar over the variable○ Expectations will be taken at time t given information available up to and
including time t. Referenced by a subscript t.
N
i
itt PowerofValueForwardP
NP
1
1
N
i
itt LoadExpectedofValueForwardL
NL
1
1
14Hess Energy · 2010 All Rights Reserved
Expected Cost to Serve Load
• Cost to serve load:
• Expected cost to serve load :
• Taking expectations and solving we get:
N
i
iiLP1
Cost
N
i
iitt LPECostE
1
N
i
N
iii
itt
itttt LPCovPLLLPNCostE
1 1
,)1(
Expected blockcost of power.
Expected loadshaping cost.
Expected covariancebetween price and load.
tttt LNPSFE 1Cost2SF = Shaping Factor. Ratio of the sum of the
expected load shaping cost and expected covariance
cost to the expected block cost.
15Hess Energy · 2010 All Rights Reserved
Hedging the Expected Cost
• Start with the expected cost function, equation (1) and take a Taylor series expansion with respect to prices and loads.
• Where refers to higher order terms. Neglecting these terms we can write the change in expected cost as:
iti
t
iti
tit
iti
tit
N
i
it
itt L
LC
PPC
PLPLCost1
)3(
)3(11
tt
it
N
iit
iti
tt
N
i t
it
it
it
t
it
titt L
L
L
L
CPP
P
P
P
C
P
PLLLN
Price Hedge Load Hedge
The delta on a load followingcontract does not equal 1.0
After delta hedging the price riskwe are left with the first order load riskor Gamma risk.
16Hess Energy · 2010 All Rights Reserved
Fair Value of a Load Following Contract
• A fair price or fair value contract has an expected value of zero.
• Fair value contracts require the inclusion of the expected value of the covariance between price and load, not just the expected hourly shaping cost. Excluding this cost component biases the distribution to the left.
• But inclusion of the expected covariance in the contract price does not guarantee that the swing risk has been minimized or removed. It only guarantees that the contract is priced fairly.
• We are still left with the negative tail risk from large positively correlated price and load movements – Cash Flow at Risk.
17Hess Energy · 2010 All Rights Reserved
3020100-10-20-30-40-50-60
0.04
0.03
0.02
0.01
0.00
Cash Flow
De
nsi
ty
Figure 4. P&L Distribution: Swing Risk vs. Swing Cost
17
Negative Skew:
Swing Risk
Swing Cost
Excluding the expected covariance produces a distributionwith a negative expected value.
Mean
18Hess Energy · 2010 All Rights Reserved
Option Hedge Development
19Hess Energy · 2010 All Rights Reserved
P
Cha
nge
in P
&L
+
-
gamma
HedgeHow do we create this hedge?
Monthly Average
Price $/mwh
P
Figure 5. Short Gamma Hedge
20Hess Energy · 2010 All Rights Reserved
Figure 6. Creating a Gamma Position from Options
P
Use vanilla calls and puts to construct the gamma position.
Cha
nge
in P
&L
+
-
Monthly Average
Price $/mwh
P ˆ
21Hess Energy · 2010 All Rights Reserved
Solving for the Estimated Gamma Function
• Select a series of strikes, Ki , and quantities, , to create a portfolio of puts and calls.
• To estimate the gamma function we need to choose the amount of options for each strike, , so as to minimize the distance between the estimated gamma function and the true gamma function.
• Estimated gamma function equals:
• Choose the optimal quantities by minimizing the sum of the squared errors between the true and estimated gamma function over a set of Q prices.
i
i
i
M
iii
N
ii PKMaxKPMaxP
11
0,0,ˆ
2
1
ˆmin
Q
jjj PP
22Hess Energy · 2010 All Rights Reserved
Theoretical Model
• It has been shown that a static hedge of plain vanilla options and forwards can be used to replicate any European derivative (Carr and Chou 2002, Carr and Madan 2001).
• Any twice continuously differentiable payoff function, , of the terminal price S can be written as:
• Our payoff function is the terminal profit. It can be decomposed into a static position in the day 1 P&L, initially costless forward contracts, and a continuum of out-of-the-money options. F0 is the initial forward price.
)(Sf
0
0
0000
F
FdKKSKfdKSKKfFSFfFfSf
InitialP&L
DeltaPosition Gamma Hedge: “Swing Risk”
23Hess Energy · 2010 All Rights Reserved
Theoretical Model, Cont.
• The initial value of the payoff must be the cost of the replicating portfolio.
• Where P(K,T) and C(K,T) are the initial values of out-of-the-money puts and calls respectively.
• Interpretation of term within the integral: Second derivative of the payoff function representing the quantity of options bought or sold.
○ R = Fixed revenue rate○ SF = Shaping Factor○ L(S) = MWH, function of S (spot price of power)
0
0,,
0000
F
FrT dKTKCKfdKTKPKfeFfFV
SLSSFRSf 1
SLSFKf
12
24Hess Energy · 2010 All Rights Reserved
Estimating the Gamma Function
• Need to estimate the relationship between load and price.
• Use historic data to estimate the following regression equation.
• The data for this equation is average load (peak, off-peak) and average price (peak, off-peak). LMP is the price, D is a monthly dummy variable, and DXLMP is an interactive dummy variable with price.
• Next set up a portfolio of a short load sale and a long hedge using monthly forwards. The fixed rate on the load sale equals the RTC cost of serving the load ($/MWH).
• Use the relationship estimated in the regression equation to vary the average monthly load with respect to a change in average monthly price. Use this to estimate the gamma function.
11
1
11
1i itiiiitt lmpDDlmpLoad
25Hess Energy · 2010 All Rights Reserved
Example Regression Output On-Peak PSE&G FP
Regression StatisticsMultiple R 87.27%R Square 76.16%Adjusted R Square 75.61%Standard Error 417.5841127Observations 445
ANOVAdf SS MS F Significance F
Regression 10 241771008.8 24177100.88 138.6488552 2.4513E-128Residual 434 75679397.18 174376.4912Total 444 317450406
Coefficients Standard Error t Stat P-valueIntercept 3,698.5486 64.27 57.55 0.00%LMP 7.1820 0.83 8.64 0.00%Mar_P -4.9284 1.02 -4.81 0.00%Apr_P -6.7488 1.01 -6.68 0.00%May_P -5.8316 0.96 -6.08 0.00%Jun_P 6.4907 0.73 8.94 0.00%Jul_P 11.8957 0.73 16.30 0.00%Aug_P 10.2282 0.77 13.28 0.00%Sep_P 4.6888 0.84 5.61 0.00%Oct_P -2.2002 0.92 -2.38 1.77%Nov_P -3.5755 0.99 -3.62 0.03%
Adjusted R2 = 75 %.
Interactive dummy variables
StatisticallySignificant
A $1 change is prices equals a 7 MW change in average daily peak load.For July the change equals 19 = 7 + 12.
26Hess Energy · 2010 All Rights Reserved
-$2,000
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
$18,000
$20,000
$0.00 $20.00 $40.00 $60.00 $80.00 $100.00 $120.00 $140.00
Market Price
Ch
an
ge
in P
&L
($
00
0)
-Gamma
Estimate
Cost as of February 9, 2009.
Estimated gamma function for July 2010 PSE&G FP load.The option cost equals $1.89/MWH per MWH served.
Figure 7: Example of a Gamma Function Estimate
27Hess Energy · 2010 All Rights Reserved
Mitigating Swing Risk in Practice
“In theory there is no difference between theory and practice.
In practice there is” Yogi Berra
28Hess Energy · 2010 All Rights Reserved
Minimizing Cash Flow at Risk
• In practice we cannot purchase options in such a way as to create the smooth curves depicted earlier. Instead we need to find discrete strikes so as to minimize the “swing risk”.
• Swing risk is here defined as Cash Flow at Risk (CF@R). CF@R is the expected loss assuming that all contracts are taken to delivery. I am defining CF@R as the difference between the mean of the distribution and the 5th percentile.
• Since we cannot perfectly hedge the swing risk by purchasing a continuum of options we need another objective risk minimization strategy.
• Use as a strategy the minimization of the CF@R or an objective level for the CF@R. An example would be to reduce the CF@R by 50%.
29Hess Energy · 2010 All Rights Reserved
Reduce Cash Flow at Risk
3020100-10-20-30-40-50
0.06
0.05
0.04
0.03
0.02
0.01
0.00
X
Density
Accountnig or Actuarial w ith Options
Accounting Model
Cash Flow
Swing RiskReduced
Delta Hedged
Hedged with
Options
30Hess Energy · 2010 All Rights Reserved
Methodology
• Use Monte Carlo simulation to model the load following contract and all hedges.
• Model takes into account the relationship between price and load, volatilities and correlations.
• Run the model to estimate the expected cost to serve the load and establish the fair price of the contract.
• Layer in delta hedges to estimate the cash flow distribution and estimate the CF@R.
• Determine the amount of risk to be minimized. This is a management decision. Cut the CF@R by 50%.
• Determine the portfolio of available options in the market.• Use an available optimization routine to determine the optimal option
portfolio that meets the required risk criteria.
31Hess Energy · 2010 All Rights Reserved
Simulated Gamma Position
($1,600,000)
($1,400,000)
($1,200,000)
($1,000,000)
($800,000)
($600,000)
($400,000)
($200,000)
$0
$200,000
$400,000
$0 $50 $100 $150 $200 $250 $300 $350
Average On-Peak LMP
To
tal P
&L
Example uses NJ BGS CIEP Load for July.
Approximately 80 MWs average load on-peak.
32Hess Energy · 2010 All Rights Reserved
Cash Flow Distribution
Swing Risk
NJ BGS CIEP Load for July
33Hess Energy · 2010 All Rights Reserved
Cash Flow Distribution with Swing Hedge
Swing Risk Removed
NJ BGS CIEP Load for July.
Objective was to reduce CF@R by 50%.
34Hess Energy · 2010 All Rights Reserved
Efficient Frontier Analysis
($1,200,000)
($1,000,000)
($800,000)
($600,000)
($400,000)
($200,000)
$0
$0 $200,000 $400,000 $600,000 $800,000 $1,000,000 $1,200,000
Option Cost
5th
Pe
rce
nti
le
+/- 10% Strangle
+/- 30% Strangle
The efficient frontier tells what the minimum option cost would be toachieve a particular level of the 5th percentile.
35Hess Energy · 2010 All Rights Reserved
Contact
Eric Meerdink
Director of Structuring & Analytics
Hess Corporation
One Hess Plaza
Woodbridge, NJ 07095
Office: 732-750-6591
Cell: 732-425-4655
Email: emeerdink@hess.com
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