The Nuances of Hedging Electric Portfolio Risks
Eric MeerdinkDirector, Structuring and AnalyticsElectric Operations
July 13, 2011
2
Demand and Supply Characteristics
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
4
Average Daily THI in Newark, NJ
0
10
20
30
40
50
60
70
80
90
100
1 26 51 76 101 126 151 176 201 226 251 276 301 326 351
Day of the Year
TH
I (T
em
p-H
um
idit
y In
de
x)
Seasonal, Stochastic and Mean Reverting
5
Demand is a Function of WeatherAverage Daily Demand in PSE&G vs. THI
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
0 10 20 30 40 50 60 70 80 90 100
THI (Temp-Humidity Index)
MW
Strong causal relationship between weather and load
6
Intra-Day SeasonalityTypical Hourly Demand in PSE&G
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
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
MW
Winter
Spring
Summer
Fall
7
Intra-Day SeasonalityBy Customer Type in PSE&G
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
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
Ra
tio
of
Ho
url
y L
oa
d t
o A
ve
rag
e L
oa
d
Residential
Commercial
Industrial
Average Customer on 7-15-10
8
SeasonalityAverage Daily Demand in PSE&G
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
6/1
/05
9/1
/05
12
/1/0
5
3/1
/06
6/1
/06
9/1
/06
12
/1/0
6
3/1
/07
6/1
/07
9/1
/07
12
/1/0
7
3/1
/08
6/1
/08
9/1
/08
12
/1/0
8
3/1
/09
6/1
/09
9/1
/09
12
/1/0
9
3/1
/10
6/1
/10
9/1
/10
12
/1/1
0
Date
MW
CoolSummer
Summer
Winter
HotSummer
Recession
June 2005 to December 2010
9
Supply: Converting Fuel to Electricity
YELECTRICITFUEL
MWHMMBTU
MWHMMBTU
MWHMMBTU
Efficiency or Rate HeatMWH
MMBTU
MMBTU
$
MWH
MMBTU
MWH
$
10
Typical Generator Cost
Costs Start Emissions M&O VariableMMBTU
$HR
MWH
$
Combined Cycle Example
Price of natural gas = $6.00/mmbtuHeat rate = 8.0 mmbtu/mwhVOM = $2.00/MWHEmissions = $1.50/MWHStart 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 makea contribution to fixed costs.
11
Generation Bid StackSupply Curve
MW
$/M
WH
Nuclear/Wind/Hydro
CombinedCycle
Simple CycleNat Gas
Represents the variable cost to produce electricityHeavy Oil
Light Oil
Coal
12
Empirical Generation Bid Stack
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
$140.00
$160.00
0 2,000 4,000 6,000 8,000 10,000
MW
$/M
WH
July 15, 2010
13
Price Determination
MW
Hour
Hour
$/MWH
Load curve
Supply Curve
Price Curve
14
Intra-Day Price Shape
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
$140.00
$160.00
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
$/M
WH
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
MW
$/MWH
MW
15
Hourly Energy Prices in PSE&G
$0.00
$50.00
$100.00
$150.00
$200.00
$250.00
$300.00
$350.00
$400.00
$450.00
$/M
WH
July 1, 2005 to December 31, 2010
234% tility Daily Vola
1,2875 atility Hourly Vol
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
17
Forward Curve
$0.00
$10.00
$20.00
$30.00
$40.00
$50.00
$60.00
$70.00
$80.00
Aug-11
Sep-1
1
Oct-1
1
Nov-11
Dec-11
Jan-
12
Feb-1
2
Mar
-12
Apr-12
May
-12
Jun-1
2
Jul-1
2
Aug-12
Sep-1
2
Oct-1
2
Nov-12
Dec-12
Jan-
13
Feb-1
3
Mar
-13
Apr-13
May
-13
Jun-1
3
Jul-1
3
Aug-13
Sep-1
3
Oct-1
3
Nov-13
Dec-13
Date
$/M
WH
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
Vo
lati
lity
%
PJM West Hub Forward Curve and Monthly Option Volatilities
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.
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.
20
Zonal Price in New York ISO
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
$140.00
$160.00
$180.00
$200.00
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
$/M
WH
Capital
Central
Dunwood
Genesee
Hudson Valley
Long Island
Mohawk Valley
Millwood
NYC
North
West
Day-Ahead Zonal Prices on July 11, 2011
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
22
Day-Ahead vs. Real-Time LMPs in PSE&G
$0.00
$50.00
$100.00
$150.00
$200.00
$250.00
1 3 5 7 9 11 13 15 17 19 21 23
Hour
$/M
WH
DA_LMP
RT_LMP
July 15, 2010
23
Pricing and Hedging Retail Load ContractsVolumetric and Swing Risk
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
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.
26
Short-Run Correlation Between Price and Load
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
$140.00
$160.00
$180.00
$200.00
07/12/10 07/13/10 07/14/10 07/15/10 07/16/10 07/17/10
$/M
WH
0
2,000
4,000
6,000
8,000
10,000
12,000
MW
Hourly Load and Price in PSE&G Zone 7/12/10 to 7/17/20
27
Long-Run 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
28
Long Hedge
Short Sale
$/MWH
Net
+
-
P&L
Typical Short Sale and Long Hedge
29
Sources of Swing Risk in Load Following
Pow
er P
rice
$/M
WH
Demand (MW)
DispatchCurveEconomic Impact (A to B)
Weather Impactbetween a and b.
AB
a
b
Weather – Principal source of swing risk.
General Economic Conditions
30
Retail Sale and Long Hedge
Long Hedge
Short Sale
$/MWH
Short Retail Sale
-
$
Net: Swing Risk “Gamma”
+
31
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
32
3020100-10-20-30-40-50-60
0.04
0.03
0.02
0.01
0.00
Cash Flow
De
nsi
ty
Cash Flow @ Risk (CF@R)
32
The positive covariance between prices and load gives the cash flow distributiona negative skew. CF@R is a probabilistic measure of the deviation betweenthe expected cash flow and a loss that can occur with a certain probability. Cash flowis a good measure of risk since we have obligations through delivery.
Mean
%
$50 CV@R% 1
33
P
Cha
nge
in P
&L
+
-
gamma
HedgeHow do we create this hedge?
Monthly Average
Price $/mwh
P
Short Gamma Hedge
34
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
35
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
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, , 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
Initial P&L(Bonds)
DeltaPosition Gamma Hedge: “Swing Risk”
37
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.
• The existence of a second derivative implies a gamma or non-linear contract.
0
0,,
0000
F
FrT dKTKCKfdKTKPKfeFfFV
38
-$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.
Example of a Gamma Function Estimate
39
Mitigating Swing Risk in Practice
“In theory there is no difference between theory and practice.
In practice there is” Yogi Berra
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%.
41
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
This example uses NJ BGS CIEP Load for July.
Approximately 80 MWs average load on-peak.
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.
43
Cash Flow Distribution
Swing Risk
NJ BGS CIEP Load for July
44
Cash Flow Distribution with Swing Hedge
Swing Risk Removed
NJ BGS CIEP Load for July.
Objective was to reduce CF@R by 50%.
45
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 to
achieve a particular level of the 5th percentile.