This document discusses the characteristics of electricity demand and supply, and the implications for electricity prices. Some key points: - Electricity demand is seasonal, stochastic, and varies throughout the day based on factors like weather and customer type. - Generation costs depend on fuel prices and heat rates. Supply stacks generators from lowest to highest variable cost to meet demand. - With supply needing to equal demand instantaneously and limited storage, electricity prices are highly volatile and can spike during periods of high demand or supply constraints. - Prices vary locally based on transmission congestion, resulting in nodal or zonal pricing structures across markets. Day-ahead and real-time prices may differ. - Full requirements

1. The Nuances of Hedging Electric Portfolio Risks
Eric Meerdink
Director, Structuring and Analytics
Electric Operations
July 13, 2011

2. Demand and Supply Characteristics
2

3. Demand for Electricity
•Demand for electricity is seasonal
•Weather
•Appliance/equipment usage
•Lighting
•Demand for electricity is stochastic
•Weather is stochastic
•Demand for electricity varies throughout the day
•Appliance usage
•Lighting
•Demand varies by customer type
•Residential
•Commercial
•Industrial
3

4. Average Daily THI in Newark, NJ
Seasonal, Stochastic and Mean Reverting
100
90
80
THI (Temp-Humidity Index)
70
60
50
40
30
20
10
0
1 26 51 76 101 126 151 176 201 226 251 276 301 326 351
Day of the Year
4

5. Demand is a Function of Weather
Average Daily Demand in PSE&G vs. THI
Strong causal relationship between weather and load
10,000
9,000
8,000
7,000
6,000
MW
5,000
4,000
3,000
2,000
1,000
0
0 10 20 30 40 50 60 70 80 90 100
THI (Temp-Humidity Index)
5

6. Intra-Day Seasonality
Typical Hourly Demand in PSE&G
10,000
9,000
8,000
7,000
6,000
MW
5,000
4,000
Winter
3,000 Spring
Summer
2,000 Fall
1,000
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
6

7. Intra-Day Seasonality
By Customer Type in PSE&G
Average Customer on 7-15-10
1.6
1.4
Ratio of Hourly Load to Average Load
1.2
1
0.8
0.6
Residential
Commercial
0.4 Industrial
0.2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
7

8. Seasonality
Average Daily Demand in PSE&G
8,000
June 2005 to December 2010
Hot
7,000 Summer Summer
Cool
Summer
6,000
Winter
5,000
MW
4,000
Recession
3,000
2,000
1,000
0
12/1/05
12/1/07
6/1/05
9/1/06
12/1/06
6/1/07
3/1/08
9/1/08
12/1/08
6/1/09
12/1/09
3/1/10
9/1/10
12/1/10
9/1/05
3/1/06
6/1/06
3/1/07
9/1/07
6/1/08
3/1/09
9/1/09
6/1/10
Date
8

9. Supply: Converting Fuel to Electricity
FUEL ⇒ ELECTRICIT Y
MMBTU ⇒ MWH
MWH
MMBTU × = MWH
MMBTU
MMBTU
= Heat Rate or Efficiency
MWH
$ MMBTU $
= ×
MWH MWH MMBTU
9

10. Typical Generator Cost
$ $
= HR × + Variable O & M + Emissions + Start Costs
MWH MMBTU
Combined Cycle Example
Price of natural gas = $6.00/mmbtu
Heat rate = 8.0 mmbtu/mwh
VOM = $2.00/MWH
Emissions = $1.50/MWH
Start cost = $1.50/MWH
Variable Cost to Generate = 8.0 x $6.00 + $2 + $1.5 + $1.5= $52.75/MWH
Always produce as long as you can cover your variable costs and make
a contribution to fixed costs.
10

11. Generation Bid Stack
Supply Curve
Heavy Oil
Represents the variable cost to produce electricity
Light Oil
$/MWH
Simple Cycle
Nat Gas
Combined
Cycle
Nuclear/Wind/ Coal
Hydro
MW
11

12. Empirical Generation Bid Stack
July 15, 2010
$160.00
$140.00
$120.00
$100.00
$/MWH
$80.00
$60.00
$40.00
$20.00
$0.00
0 2,000 4,000 6,000 8,000 10,000
MW
12

13. Price Determination
$/MWH
Supply Curve
Price Curve
Hour MW
Load curve
Hour
13

14. Intra-Day Price Shape
$160.00 10,000
9,000
$140.00
MW
8,000
$120.00
7,000
$100.00
6,000
$/MWH
MW
$80.00 5,000
4,000
$60.00
$/MWH
3,000
$40.00
2,000
$20.00
1,000
$0.00 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
14

15. Hourly Energy Prices in PSE&G
July 1, 2005 to December 31, 2010
$450.00
$400.00
Hourly Volatility = 1,2875
$350.00
Daily Volatility = 234%
$300.00
$250.00
$/MWH
$200.00
$150.00
$100.00
$50.00
$0.00
15

16. What are the Characteristics of Electricity Prices?
•Electricity cannot be stored (economically)
•Supply must equal demand instantaneously
•Demand is seasonal and stochastic (weather)
•Generation cost is a function of stochastic fuel prices
•Generation is subject to random outages
•What does this imply about electricity prices
•Stochastic
•Mean reverting, because load and weather are mean reverting
•Asymmetric price jumps, positive jumps > negative jumps
•Seasonality, price returns have a seasonal pattern
•Extremely volatile
16

17. $/MWH
Au
$10.00
$20.00
$30.00
$40.00
$50.00
$60.00
$70.00
$80.00
$0.00
g
Se - 11
p-
O 11
ct
No -11
v
De -11
c-
Forward Curve
Ja 11
n-
Fe 12
b-
M 12
ar
-
Ap 1 2
r
M - 12
ay
-
Ju 12
n-
1
Ju 2
l-1
Au 2
g
Se - 12
p-
O 12
ct
No -12
v
Date
De -12
c-
Ja 12
n-
Fe 13
b-
M 13
ar
-
Ap 1 3
r
M - 13
ay
-
Ju 13
n-
1
Ju 3
l-1
Au 3
g
Se - 13
p-
O 13
ct
No -13
v
De -13
c-
13
PJM West Hub Forward Curve and Monthly Option Volatilities
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
Volatility %
17

18. Nodal Prices
• Prices in the markets Hess serves (New England, NY and Mid-Atlantic)
are locational or nodal.
• Each node or pricing point has can have a different price. So for
example in the Mid-Atlantic region (PJM) there are 8,000+ nodes.
• The reason for the differences in prices between nodes is the presence
of “congestion” on the transmission lines.
• If there were no congestion then each node would have the same price,
and that price would be the cost to supply the last megawatt of electricity
(marginal generator).
• Congestion is caused by thermal limits on the transmission lines.
• To alleviate this problem the power pool reduces generation supplying
load on that line and turns on a more expensive generator to serve that
load and that will not cause congestion on that line.
• When this happens prices split in the system causing some locations to
be more expensive than other locations.
18

19. Locational Marginal Price
Locational Marginal Price (LMP)
LMP = Marginal Energy + Marginal Congestion + Marginal Losses
The marginal energy price is the same for all nodes and locations.
The only difference is in marginal congestion and marginal losses.
Each power pool has a hub from which basis to the various
locations is quoted. The hubs are the most liquid locations in
which to trade.
Basis is the difference in price between the location and the hub.
For example, the basis to PSE&G zone in PJM is the difference
between the PSE&G LMP and the West Hub LMP.
LMPs can be NEGATIVE.
19

20. Zonal Price in New York ISO
Day-Ahead Zonal Prices on July 11, 2011
$200.00
$180.00 Capital
Central
$160.00 Dunwood
Genesee
$140.00
Hudson Valley
Long Island
$120.00
Mohawk Valley
$/MWH
$100.00 Millwood
NYC
$80.00 North
West
$60.00
$40.00
$20.00
$0.00
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
20

21. Day-Ahead vs. Real-Time
• There are two types of prices in the power pools.
•Day-Ahead and Real-time
• The power pools allow generators and load serving entities (LSEs)
to bid their generation and load into the pool the day prior.
• The power pool schedules the load and generation looking for the
least cost solution to meet demand.
• The power pools then produce a schedule for generators and
LSEs that specifies the LMPs by hour and either the load they are
buying or the generation they are supplying the next day. These
costs and revenues are fixed.
• In the real time market weather, load and generation outages can
be different than those forecasted the day prior. For this reason
LSEs may need to purchase more energy or generators my need
to generate more energy. The power pools calculate real-time
prices for this “imbalance” energy
21

22. Day-Ahead vs. Real-Time LMPs in PSE&G
July 15, 2010
$250.00
$200.00
DA_LMP
RT_LMP
$150.00
$/MWH
$100.00
$50.00
$0.00
1 3 5 7 9 11 13 15 17 19 21 23
Hour
22

23. Pricing and Hedging Retail Load Contracts
Volumetric and Swing Risk
23

24. 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
24

25. 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.
25

26. Short-Run Correlation Between Price and Load
Hourly Load and Price in PSE&G Zone 7/12/10 to 7/17/20
$200.00 12,000
$180.00
10,000
$160.00
$140.00
8,000
$120.00
$/MWH
MW
$100.00 6,000
$80.00
4,000
$60.00
$40.00
2,000
$20.00
$0.00 0
07/12/10 07/13/10 07/14/10 07/15/10 07/16/10 07/17/10
26

27. Long-Run Correlation Between Price and Load
12-Month Rolling Average of Load and Price in PSE&G Zone
5,500 $90.00
$80.00
5,400
$70.00
5,300
$60.00
5,200
$50.00
$/MWH
MW
$40.00
5,100
MW
$30.00
$/MWH
5,000
$20.00
4,900
$10.00
4,800 $0.00
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
27

28. Typical Short Sale and Long Hedge
P&L
Long Hedge
+
Net
$/MWH
-
Short Sale
28

29. Sources of Swing Risk in Load Following
Dispatch
Economic Impact (A to B) Curve
Power Price $/MWH
 Weather – Principal source of
swing risk.
General Economic Conditions
a
b Weather Impact
between a and b.
B A
Demand (MW)
29

30. Retail Sale and Long Hedge
$
Long Hedge
+
$/MWH
Net: Swing Risk
“Gamma”
-
Short Sale
Short Retail Sale
30

31. Change in Cash Flow when Power is Delta Hedged
A B C
Load greater
Load less than Load equals than expected
expected load expected load load
Price less than
1 expected price - 0 +
2 Price equals
expected price 0 0 0
3 Price greater
than expected
price
+ 0 - Swing Risk
- - - - - -
Long Hedged Short
Position Position
31

32. Cash Flow @ Risk (CF@R)
The positive covariance between prices and load gives the cash flow distribution
a negative skew. CF@R is a probabilistic measure of the deviation between
the expected cash flow and a loss that can occur with a certain probability. Cash flow
is a good measure of risk since we have obligations through delivery.
0.04
Mean
0.03
Density
0.02
0.01
α%
0.00
-60 -50 -40 -30 -20 -10 0 10 20 30
Cash Flow
(1 − α ) % CV@R = $50
32
32

33. Short Gamma Hedge
− Γ( P )
How do we create this hedge?
+ Hedge
Change in P&L
Monthly
Average
Price $/mwh
gamma
-
Γ ( P)
33

34. Creating a Gamma Position from Options
Use vanilla calls and puts to construct the gamma position.
+ − Γ( P)
− Γ ( P)
ˆ
Change in P&L
Monthly
Average
Price $/mwh
-
34

35. Solving for the Estimated Gamma Function
• Select a series of strikes, Ki , and quantities, θi , to create a portfolio of
puts and calls.
• To estimate the gamma function we need to choose the amount of
options for each strike, θ i , so as to minimize the distance between
the estimated gamma function and the true gamma function.
• Estimated gamma function equals:
N M
− Γ( P ) =
ˆ
∑Max( P − K , 0) ×θ + ∑Max( K
i =1
i i
i =1
i − P,0 ) ×θi
• 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. 2
∑ [Γ( P ) − Γ( P )]
Q
min ˆ j j
θ
j =1
35

36. 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, f (S ) , of the
terminal price S can be written as:
F0 ∞
f ( S ) = f ( F0 ) + f ′( F0 )( S − F0 ) + ∫ f ′′( K )( K − S ) dK +
+
∫ f ′′( K )( S − K ) + dK
0 F0
Initial P&L Delta
(Bonds) Position Gamma Hedge: “Swing Risk”
•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.
36

37. Theoretical Model, Cont.
• The initial value of the payoff must be the cost of the replicating
portfolio.
F0 ∞
V0 ( F0 ) = f ( F0 ) e − rT
+ ∫ f ′′( K ) P ( K , T ) dK + ∫ f ′′( K ) C ( K , T ) dK
0 F0
• 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.
• The existence of a second derivative implies a gamma or non-linear
contract.
37

38. Example of a Gamma Function Estimate
Estimated gamma function for July 2010 PSE&G FP load.
The option cost equals $1.89/MWH per MWH served.
$20,000
$18,000
$16,000
$14,000
Change in P&L ($000)
$12,000
-Gamma
$10,000
Estimate
$8,000
$6,000
$4,000
$2,000
$0
$0.00 $20.00 $40.00 $60.00 $80.00 $100.00 $120.00 $140.00
-$2,000
Market Price
Cost as of February 9, 2009.
38

39. Mitigating Swing Risk in Practice
“In theory there is no difference between theory and practice.
In practice there is” Yogi Berra
39

40. 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%.
40

41. Simulated Gamma Position
This example uses NJ BGS CIEP Load for July.
$400,000
Approximately 80 MWs average load on-peak.
$200,000
$0
($200,000)
($400,000)
Total P&L
($600,000)
($800,000)
($1,000,000)
($1,200,000)
($1,400,000)
($1,600,000)
$0 $50 $100 $150 $200 $250 $300 $350
Average On-Peak LMP
41

42. 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.
42

43. Cash Flow Distribution
NJ BGS CIEP Load for July
Swing Risk
43

44. Cash Flow Distribution with Swing Hedge
NJ BGS CIEP Load for July.
Objective was to reduce CF@R by 50%.
Swing Risk Removed
44

45. Efficient Frontier Analysis
he efficient frontier tells what the minimum option cost would be
to
$0
chieve a particular level of the 5th percentile.
+/- 10% Strangle
($200,000)
($400,000)
5th Percentile
+/- 30% Strangle
($600,000)
($800,000)
($1,000,000)
($1,200,000)
$0 $200,000 $400,000 $600,000 $800,000 $1,000,000 $1,200,000
Option Cost
45