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.