Cost Evaluation of Credit Risk ... - RWTH Aachen

FCN Working Paper No. 13/2010

Cost Evaluation of Credit Risk Securitization in the

Electricity Industry: Credit Default Acceptance vs.

Margining Costs

Enno Bellmann, Joachim Lang and Reinhard Madlener

September 2010 Revised May 2011

Institute for Future Energy Consumer Needs and Behavior (FCN)

School of Business and Economics / E.ON ERC

FCN Working Paper No. 13/2010

Cost Evaluation of Credit Risk Securitization in the Electricity Industry: Credit

Default Acceptance vs. Margining Costs

September 2010

Revised May 2011

Authors’ addresses:

Enno Bellmann c/o Institute for Future Energy Consumer Needs and Behavior (FCN) School of Business and Economics / E.ON Energy Research Center

RWTH Aachen University Mathieustrasse 6 52074 Aachen, Germany

E-mail: [email protected] Joachim Lang E.ON AG Controlling / Corporate Planning E.ON Platz 1

40479 Dusseldorf, Germany E-mail: [email protected] Reinhard Madlener Institute for Future Energy Consumer Needs and Behavior (FCN) School of Business and Economics / E.ON Energy Research Center RWTH Aachen University

Mathieustrasse 6

52074 Aachen, Germany E-mail: [email protected]

Publisher: Prof. Dr. Reinhard Madlener Chair of Energy Economics and Management Director, Institute for Future Energy Consumer Needs and Behavior (FCN) E.ON Energy Research Center (E.ON ERC) RWTH Aachen University Mathieustrasse 6, 52074 Aachen, Germany

Phone: +49 (0) 241-80 49820 Fax: +49 (0) 241-80 49829 Web: www.eonerc.rwth-aachen.de/fcn E-mail: [email protected]

1

Cost Evaluation of Credit Risk Securitization in the Electricity

Industry: Credit Default Acceptance vs. Margining Costs

Enno Bellmanna, Joachim Lang

b, and Reinhard Madlener

c,

a RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

b E.ON AG, Controlling / Corporate Planning, E.ON Platz 1, 40479 Düsseldorf, Germany

c Institute for Future Energy Consumer Needs and Behavior (FCN), School of Business and Economics /

E.ON Energy Research Center, RWTH Aachen University, Mathieustrasse 6, Aachen, Germany,

First version September 2010.

Revised version as of 25 May 2011

Abstract Institutions such as the European Commission (EC) are currently seeking to

increase the transparency of the derivatives markets. This course of action includes in

particular the installation of a centralized clearing entity and with this the obligation to clear

all relevant financial derivatives. Besides the expected securitization of the financial system,

these steps would also significantly influence the electricity industry, as most of the

commodity trading in this sector is currently still done in the largely non-cleared OTC

markets. Despite the fact that clearing of the OTC contracts in this sector has significantly

increased over the last years, credit risk mitigation is still largely effected with bilateral

netting agreements, standardized contracts and individual trading limits between partners.

This paper explores the impact of margining on the financial costs in comparison to the direct

management and the intentional acceptance of credit risk. For this purpose, the losses due to

defaulting business partners in the electricity industry are compared with the interest

requirements of the cash reserve for an assumed margining account. The results show that for

an asset-backed utility, depending on the price trajectory, the cost of margining may

significantly outreach the costs stemming from the acceptance of credit risk.

Keywords: Credit risk mitigation, margining collateralization risk capital power plants

JEL Classification G12 G32 L94 O16

R. Madlener ()

Tel. +49 241 80 49 820, fax. +49 241 80 49 829, e-mail: [email protected];

[email protected]; [email protected].

2

1 Introduction

In response to the recent global financial crisis, institutions such as the European Commission

(EC) are aiming to increase the transparency of the derivatives markets. This course of action

includes, in particular, the installation of a centralized clearing party (CCP) and, with this, the

obligation to clear all1 relevant financial derivatives. The EC’s new policy will also markedly

affect the electricity industry, where most of the commodity trading is still done in the non-

cleared over-the-counter (OTC) markets. In this sector, despite the fact that in recent years

clearing of the OTC contracts has significantly increased, credit risk mitigation is still largely

pursued via bilateral netting agreements, standardized contracts, and individual trading limits

between partners (e.g., Pschick 2008, p.286 f).

One of the major advantages of clearing is its applicability to a wide range of financial

products (Hull 2010). Unfortunately, the CCP comes at a price and requires additional

prerequisites that the trading partners must fulfill. These are especially related to the need of

risk capital requirements and standardization issues. This paper, which is based on Bellmann

(2010), compares the impact of margining on the financial costs of power companies to the

direct management and the intentional acceptance of credit risk. For this purpose, the losses

due to defaulting business partners are compared with the interest requirements of the cash

reserve for an exemplary margining account. Furthermore, the robustness of the model is

tested through the use of sensitivities on commodity prices, partner structure of the

sales/purchase portfolios, and the underlying fuel mix.

The remainder of the paper is organized as follows. Section 2 provides a general

overview of related research. Section 3 describes the methodological approach on the

assessment of credit risk and the liquidity risk from margining. Section 4 applies the

developed methodology and shows the results. A sensitivity analysis is also employed to

pinpoint drivers of the developed models. Section 5 concludes.

2 Literature research

2.1 Credit risk and centralized clearing

The hedging of commodities exposes electricity producers to credit risk. This type of risk has

been widely analyzed by the scientific community as well as by companies. Therefore, the

1 Where appropriate. Note that it may not be able to value certain specialized OTC contracts on a daily basis (see

European Commission, 2009a).

3

literature review in this section is not exhaustive and focuses on the main strands only.

Modigliani and Miller (1958) built the foundation of valuation of firms and their shares. They

analyze the cost of capital and the influence of the debt position on the financing costs. Black

and Scholes (1973) developed a framework for pricing options that uses observable variables

only. Merton (1974) utilized the framework to price corporate debt in general. His model uses

an endogenous default methodology that can be used to calculate default probabilities. Hull

and White (1995) designed a model to value derivative securities with a default risk. This

model can be used to incorporate the default risk into the prices of the securities. According to

Jarrow and Turnbull (1995), some of Merton’s assumptions are not feasible. They conclude

that Merton’s approach is not practical enough to be applied to real life companies. They

define a reduced-form model in which default is determined by an exogenous boundary.

Using their methodology, it is possible to price corporate debt and other securities. Jarrow and

Yu (2001) extend the reduced-form models to include the correlation between defaults. Kao

(2000) depicts current credit risk evaluation models. He compares the original Merton model

with current reduced-form models. Crouchy et al. (2000) give a general overview of practical

credit risk methodologies applied by banks and financial institutions. The analysis includes

the credit mitigation approach used by CreditMetrics of JP Morgan, the KMV approach,

initiated by Merton, the Credit Risk+ approach as used by Credit Suisse Financial Products,

and CreditPortfolioView by McKinsey. Kealhofer (2003) describes the shortcomings of the

basic Merton model and introduces the improved KMV-Merton model that can be used to

endogenously and accurately calculate expected default probabilities. Altman studied the

predictability of corporate defaults based on the analysis of financial ratios (Altman 1968).

Altman’s model is also known as the “Z-Score formula” for forecasting bankruptcy. Based on

his original model, Altman (1989) investigates the relationship between rating-based

mortality rates and expected mortality-based rates on return spreads. Altman and Saunders

(1998) give an overview of the developments in credit risk measurement since the 1980s.

Löffler (2004) compares a rating-based approach with a market-based approach to introduce

credit risk measures when building an investment portfolio. After analyzing historic data from

1983 until 2002 he was unable to demonstrate the superiority of either approach. Even before

the EC published their intentions to oblige users of financial derivatives to clear these

derivatives (European Commission 2009a, 2009b), the impact of clearing had been discussed

in the scientific community. Bliss and Steigerwald (2006) give an overview of the

implications of the introduction of a CCP and alternative structures to secure credit risk. They

argue that one of the problems of introducing a CCP is the current information asymmetry in

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the market. Market participants with superior information than others can be expected to

oppose more transparent markets. Since all clearing members of the CCP are treated equally,

this approach gives companies a low-risk option to deal with low rated partners who would

not have met internal risk management requirements otherwise. Hence, central clearing

increases the potential number of trading partners and thus market liquidity. Duffie and Zhu

(2009) investigate the effects of replacing bilateral clearing by central clearing. They conclude

that a CCP can reduce necessary collateral and eliminate unnecessary circles of exposure.

However, this is only true if the CCP is properly used. They show that the introduction of a

second CCP for the same derivative class impairs the netting effect of the users. The

repercussions of clearing are evaluated by Pirrong (2009). One of the issues with CCP is the

effect on other creditors of a defaulting company. Pirrong argues that the reduced default

losses, as a result of central clearing, do not necessarily imply a social gain, because other

creditors of the defaulting party suffer additional losses. Rausser et al. (2009) look at

centralized clearing from a government policy perspective. They argue that it is very

challenging to clear a large share of OTC contracts, because their complexity makes it

impossible to determine their value on a daily basis. Hull (2010) has recently argues that

centralized clearing should be mandatory for all types of derivatives within three years. A

higher percentage of cleared OTC contracts increases the netting efficiency of a CCP.

Literature on margining needs in the electricity industry is still very scarce. Lang and

Madlener (2010a,b) analyze the impact of margining costs in the electricity sector for the

valuation of a power plant and power plant portfolios. They investigate the size of margining

costs for different types of energy. Margining costs are found to have a significant impact and

thus ought to be taken into consideration when valuing new investment projects.

2.2 Conclusion from the literature review

The current body of literature includes the interaction of different types of risk. In addition,

the measurement and the management of credit risk have been examined. Research on

corporate default and the associated cost is mostly based on regular debt. Clearing as one way

to mitigate credit risk is mostly viewed from a global perspective. The present study is

focused on the financial impact of different ways to mitigate the credit risk of a company

rather than an economy as a whole, with a special focus on the electricity industry. The costs

resulting from defaulting derivatives contracts are examined and compared with the costs

associated with clearing. The combination of a binomial default model and an exposure model

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for futures contracts makes it possible to calculate the costs of defaulting counterparties in a

commodity derivative setting. At the same time, the margining needs for an energy

commodity portfolio are modeled. The frequency distributions of both costs, determined by

Monte Carlo simulation, are compared through the use of a value-at-risk (VaR) approach.

Finally, by building the model around a power portfolio, it is possible to assess the impact of

different fuel mixes on the costs of margining and default.

3 Methodology

3.1 Initial set-up

The objective of this study is to quantify the costs of counterparty default in comparison to the

costs of margining. In order to accomplish this, a financial model is developed. Fig. 1

illustrates its basic setup. The model for calculating the margining costs and the model for

calculating the costs of default are both based on the same underlying data and assumptions.

The total quantity of electricity generated is assumed to be 1 TWh per year. This amount of

electricity is split up equally into base-load and peak-load. The technologies used to generate

the energy are differentiated between outright power, coal power, and gas power. The

category “outright power” is comprised of nuclear power plants and run-of-river power plants.

It is assumed that these technologies have negligible fuel and CO2 emissions costs and thus

neither fuel nor CO2 certificates need to be hedged. The sales volume of electricity and the

purchasing volume of fuel and CO2 certificates are based on the total generation volume and

the generation fuel mix. The model uses the price trajectories of selected futures contracts

traded on the European Energy Exchange (EEX).

We assume that all hedging activities are executed using futures contracts. These

standardized derivatives are very common instruments for hedging commodity price risk in

the electricity industry, because the commodities involved do not have any distinguishing

features and the markets are very liquid (see Pschick 2008, p.276 f.). The margining model is

based on the underlying price tracks and the hedging approach2. The model is used to

calculate the margining account balance (MAB) for 2009. In order to fulfill the margining

requirements, it is assumed that the company sets up a cash reserve (CR) in the form of a

credit line, or liquid assets. The financing costs of this CR are assumed to be equal to the costs

of margining.

2 The terms “hedging approach” and “hedging strategy” are used synonymously in this paper.

6

Fig. 1: Model structure of the study

The default model is based on the same underlying fundamentals. A portfolio of contracts is

modeled to compute the costs of default. The exposure at default (EAD) is calculated for each

contract based on the movements of the underlying price trajectory for the years 2007-2009.

The frequency of default is based on published historic default rates and a typical partner

structure of incumbents of the German electricity sector. The major input of the financial

model is the quantity of generated electricity and the fuel mix used for its generation. It is

assumed that the total volume of electric energy VA,EL can be forecasted perfectly for the

years 2010 and 2011. Furthermore, we assume that the VA,EL is 1 TWh for each year between

2009 and 2011. The technologies used to generate the electricity are outright power, coal

power, and gas power. Major input factors for the cost calculations for the thermal power

plants are the efficiencies of the coal- and gas-fired power plants (ηCoal, ηGas). The futures that

are used to hedge electricity are traded in the unit € per MWhel. The coal used for power

generation is traded in USD per ton, natural gas is traded in € per MWHth, and CO2

certificates are traded in € per ton. Based on the total power generation and the respective

efficiencies of the power plants, it is possible to calculate the amounts of coal, gas and CO2

certificates needed for power generation, as well as the shares of base-load vs. peak-load3.

The annual required quantity of coal VA,Coal is represented by equation (1):

3 Base-load contract: Monday through Sunday, 24 hours; peak-load contract: Monday through Friday, 8:00 AM

until 8:00 PM (for more information, see Konstantin, 2009, p.45).

Fuel AllocationGeneration Volume

Hedging ApproachSales VolumePrices Tracks

Exposure at DefaultMargining Account

Balance

Historic Default Rates

Partner Portfolio

Frequency of DefaultCosts of DefaultCosts of MarginingFinancing Costs

Cash Reserve

7

. (1)

VA,El is the total quantity of electrical energy generated during year A. YCoal is the yield factor

of thermal energy per kg of fuel. ηCoal is denoted as the efficiency of the coal power plant and

the SA,Coal is the fuel allocation share of coal in the firm’s portfolio during year A. The annual

quantity of gas VA,Gas is calculated using the equation (2):

. (2)

To account for the fact that gas is traded in the higher heating value (HHV) notation, but the

efficiencies of power plants are calculated based on the lower heating value (LHV) notation,

YGas is used as a correction factor. For natural gas, the HHV/LHV ratio is equal to 1.1 and has

to be taken into consideration for calculation purposes (cf. Petchers 2003, p.47).

The amount of carbon dioxide omitted, VA,CO2, is calculated based on the generation

shares of gas and coal:

( ). (3)

SA,C is the share of the fuel allocation and eC is the CO2 emission factor, measured as the

weight of emitted CO2 per unit of generated electric energy. For hedging purposes, it is

necessary to differentiate the expected amount of power generation in the delivery year

between base-load electricity and peak-load electricity. Note that it is not the aim of this study

to forecast the base-load vs. peak-load ratio of an electricity provider. Therefore, it is assumed

that the ratio between peak-load and base-load electricity is known. The share of base-load

electricity is referred to as αBase and the share of peak-load electricity is αPeak. The sum of αBase

and αPeak has to equal unity.

3.2 Hedging model

3.2.1 Hedging rationale and background information

The hedging strategy for electricity, coal, gas, and CO2 derivatives is designed around the

quantities calculated using the total expected generation volume and the prevailing fuel mix.

In order to determine the cost of margining, as well as the cost of default, the hedging

strategy needs to be considered first. Through the use of hedging instruments, the market risk

and thus the cashflow volatility is minimized. In the German market, for example, the existing

incumbents hedge nearly 100% of their power generation already several years upfront the

delivery year (see Lang and Madlener 2010a). However, with the hedging of market risks, the

8

risk of defaulting counterparties arises at the same time. The chance that a counterparty

defaults and cannot fulfill its contract obligations is considered to be part of the credit risk.

3.2.2 Hedging mechanics

This study considers a time frame from Jan 1, 2009 until Dec 31, 2009. From a hedging

perspective, three delivery periods (2009, 2010, and 2011) are taken into consideration. One

complete hedging cycle consists of a two-year hedging period and a one-year delivery period.

The hedge with the delivery period 2009 has been hedged during 2007 and 2008. In addition,

we consider the implications of the hedges for the delivery periods of 2010 and 2011. In order

to make the different hedging strategies tangible, we employ a randomized approach to

approximate real hedging behavior. The accumulated hedged volume VH,C(t) at any point in

time is the share of the total annual quantity VA,C of the commodity C that has been hedged up

to period t. This volume is calculated based on the total duration of the hedging period T, the

total quantity of the commodity VA,C that has to be hedged over the entire hedging period, and

the period under consideration t. In addition, a randomized, normally distributed noise factor

R(t) (with R(t) ~ N(0;0.014)) is used in the model in order to render the model more realistic.

( )

( ). (4)

According to our assumptions, the total hedging period T is 730 days. The type of hedge is

determined by the exponent x. For example, a factor x = 0.5 represents a hedging strategy

following a square root function, x = 1 would represent a linear hedging procedure and x = 2

would cover a hedging procedure in accordance with a quadratic function.

Thus, based on this equation, other faster and slower hedging volume developments are

possible, depending on the size of the exponent. An actual hedge can have different forms

(see Fig. 2), but the hedge always starts at a hedging volume of zero. It is assumed that 100%

of the generated electricity quantity and the corresponding fuel and CO2 certificates are

hedged in each hedging cycle. The hedging path is modeled on the basis of a randomized x-

factor within a Monte Carlo simulation with 5000 draws. The exponent x, describing the

shape of the hedging function, can take values between 0.5 and 2.0, all with the same

likelihood. Therefore, during all periods the following equation holds:

( ) ( ). (5)

The daily additionally hedged volume vH,C in any given period t is calculated as follows:

9

Fig. 2 Real hedging behavior vs. simulated hedges

( ) ( ) ( )

[ ( ) ]. (6)

The additional daily hedge is equal to the difference of the accumulated hedges in the

periods t and (t-1). It is assumed that the power generation is constant throughout the delivery

year. Therefore, the hedged volume decreases linearly during the delivery period:

( )

( ). (7)

The hedged volume VD,C(τ), that remains during the delivery period, depends on the total

length of the delivery period Т and the period of consideration τ. In the last period τ = Т, all of

the hedged volume has been delivered and all financial instruments of the delivery time frame

are settled.

3.3 Margining model

One central element of this study is the calculation of the margining account balance and the

resulting costs. Analogously to Lang and Madlener (2010a) this study focuses on the effects

of the variation margin and the additional margin according to the rules of the European

0%

20%

40%

60%

80%

100%

120%

Real Hedge

Simulated Hedge

Lower Boundary

Upper Boundary

Q 1

/ Y

ear

1

Q 2

/ Y

ear

1

Q 3

/ Y

ear

1

Q 4

/ Y

ear

1

Q 1

/ Y

ear

2

Q 2

/ Y

ear

2

Q 3

/ Y

ear

2

Q 4

/ Y

ear

2

10

Commodity Clearing AG4 (ECC). The ECC calculates the variation margin every day and the

customer has to deposit the account changes according to

( ) ( ( )) ( ( ) ( )), (8)

where pC(t) denotes the price of commodity C in period t. The change of the variation margin

vmC of a commodity C in a certain period t is calculated based on the accumulated hedged

volume of said commodity VH,C until the day (t–1) and the price change between period (t–1)

and period t. The accumulated position of the variation margin VMC is calculated by adding

the individual variation margining balances of the different commodities C for n contracts

over the total time T:

( ) ∑ ∑ ( )

∑ ∑ (( ( )) ( ( ) ( )))

. (9)

In addition to the variation margin, the additional margin (for a definition, see ECC 2010a,

p.37) for derivative trades is calculated in the model. Contrary to the variation margin, the

additional margin is computed based on the notional value of the futures contract. Henceforth,

it increases the margining needs:

( ) ∑ ∑ ( ( ) )

. (10)

The accumulated additional margin AM for all commodities is calculated based on the

accumulated hedged quantity VH,C of each commodity C in period t. An additional margin

parameter5 is used whose value also depends on the type of commodity. These additional

margin parameters are frequently updated by the ECC based on the past volatility of the

commodity prices. Furthermore, an expiry month factor (EMF) EMFC,t is used to account for

potentially increased losses shortly before delivery (ECC 2010a, p.19 f). For all hedged

quantities, which take 30 days or less to deliver, the EMF equals unity6.

4 For more detailed information about the different types of margins, and their definitions, see ECC (2010a, p.10

f). 5 The additional margin parameters used in this study are based on the factors published on the ECC website on

Aug 5, 2010 (see ECC 2010b). The factors used for the additional margin parameters are: Electricity Peak: 3.20

€/MWh; Electricity Base: 2.40 €/MWh; Coal: 5.90 $/t (for calculation purposes 4.50 €/t); Gas: 1.70 €/MWh and

CO2 Emissions: 1.20 €/t.

6 The expiry month factors used in this study are based on the factors published on the ECC website on Jan 18,

2010. The factors used for the expiry month factor are: Electricity Peak: 2.5, Electricity Base: 2.5, Coal: 1, Gas:

1.5, CO2 Emissions: 1.

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Fig. 3 Development of the margining account balance

In order to calculate the actual costs of margining, assumptions need to be made about the

implementation of the margining payments. The netted sum of the margins required by the

ECC represent the amount of cash necessary to comply with the margin requirements. Fig. 3

illustrates the fundamental mechanics of margining costs. Every company needs to be able to

fulfill all margin requirements within a short period of time, otherwise the positions will be

settled. However, large sums of money to refill the margining account cannot be financed at

short notice. Therefore, it is assumed that a company sets up a cash reserve (CR) that is used

to settle the margining account daily. Further, it is assumed that the company commits to the

size of the CR for one year. This CR has to be sufficiently large to fulfill all margining

requirements. If perfect foresight is assumed, the optimum CR level, CRPF, is equal to the

maximum value of the margining deficit during the CR commitment year (A). In that case, the

CR would be exactly large enough to fulfill all necessary margining requirements:

( ( )) (11)

Assuming no perfect foresight, the CR in this study is modeled by assuming that the values of

the MAB of the past year are normally distributed. The mean and standard deviation of the

past year’s MAB are used to compute the MAB-VaR7. The MAB-VaR is based on the

average margining account balance μ(MABA-1) of the past year and the standard deviation of

the MAB σ(MABA-1). The factor ω determines the confidence level of the risk:

( ) ( ). (12)

7 For more detailed information about the value-at-risk methodology, see Jorion (2001) and Saita (2007).

2008 2009

MA

B

Time

Margin Surplus

Margin DeficitCash Reserve

0

MAB-VaR

Normal Distributionof MAB

Perfectforesight CRPF

CRVar

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We assume that the entire CR is kept for one year and financed at an interest rate iFin.

Additionally, it is assumed that during times of a margin surplus8 the trader is entitled to

interest payments on the positive account balance (see Fig. 3). We assume further that the

short-term interest rate iDay paid by the bank offsets the financing costs of the CR during times

of a margin surplus. As a result, financing costs are higher in the case of a margin deficit and

lower in the case of a margin surplus. In the model, the daily costs of margining are calculated

by the following equations:

( ) ( ) for ( ) (13)

( ) for ( ) . (14)

For the purpose of this study, costs are denoted as positive numbers. In the case where

margining results in an interest surplus, this surplus is denoted as a negative number. The

daily interest cash flows have to be accumulated over one year in order to calculate the annual

costs of margining CM,A:

( ) ∑ ( ) . (15)

Even if the funds needed for fulfilling the margining requirements are sourced with off-

balance sheet instruments, they can still affect the rating of a company. The rating agencies

have extensive knowledge of a company’s financing activities. The process to determine a

company’s rating includes the consideration of off-balance-sheet exposure (Langohr and

Langohr 2008, p.189). Therefore, the exposure to finance margining influences the rating. A

rating downgrade, due to a worsened debt position, can trigger contract penalties and increase

external financing costs. Such a contract penalty could be the immediate closure of the

contract (von Nitzsch and Rouette 2008, p. 92). Hence, margining costs have to be

considered, no matter how they are financed.

3.4 Default model

3.4.1 Basic setup

In the previous sections, the hedging approach and the margining model were discussed. In

this section, we present the setup of the default model. As a first step, we determine the

frequency of defaults of the portfolio. Furthermore, we identify the exposure at default of

8 A positive margining balance hereinafter is referred to as “margin surplus”.

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each contract. However, instead of calculating the loss distribution analytically, as in the

CreditRisk+ approach (CreditRisk+ 1997), we utilize a Monte Carlo simulation. The resulting

distribution of default losses is then used to analyze the cost impact of counterparty default

and to conduct a sensitivity analysis. The basis for the loss calculation due to the default of

trading partners is a portfolio of contracts with 500 different futures contracts9. The contracts

are modeled as short positions for base-load and peak-load electricity and long positions for

the different fuel types and CO2 certificates. The losses LPort incurred by the portfolio can be

described as

∑ ( ) . (16)

EADi represents the exposure at default of contract i, RRi stands for the corresponding

recovery rate10

(RR), and bi is a binomial variable that takes the value of unity in the case of a

default and is equal to zero otherwise (Jorion 2001 p.332):

( ). (17)

The probability of bi being unity, the case of default, is referred to as the “default probability”

(DP). The variable takes the value unity with the probability DPi and the value 0 with the

probability (unity–DPi). Each contract i has a specific DPi depending on the company’s

expected condition (Borchert et al. 2006, p.385). The hedging cycle influences the average

duration of a derivative contract. In the case of linear hedging, the average duration of a hedge

is one and a half years. In th ecase of a square root this period is longer and for a quadratic

hedge this period is shorter. It is the assumption that this has an impact on the probability of

default of a contract. The default probability DPi of contract i depends on the duration of

interaction AТ(i) of said contract and the one-year default probability DPA of that contract:

( )

( ). (18)

We assume that shorter interaction times lead to a lower risk of counterparty default. A longer

interaction time with a counterparty leads to a higher risk of partner default during the time of

interaction. Each company, and therefore each different contract, has a certain default

probability and a certain exposure. The shape of the cost distribution depends on the DP, the

number of different contracts, and the exposures of the different contracts. The expected value

9 In order to account for the impact of the number of different contracts/trading partners, a sensitivity analysis is

conducted.

10 The recovery rate (RR) represents the share of a financial obligation that can be recovered in the case of

counterparty default.

14

of the losses is called the (expected) “credit loss” (CL). Over the years, assuming that all other

factors remain constant, this will be the average amount of losses that will be incurred by that

particular credit portfolio. The unexpected credit loss is the difference between the expected

value of credit losses and the de facto occurred credit loss. It is possible to calculate a credit

loss value-at-risk (CL-VaR) with a certain confidence level. For example, the CL-VaR99

represents the maximum credit loss at a 99% confidence level. This means that in 99% of the

time the credit losses of the portfolio will be lower than the CL-VaR99 level. Since the

expected credit loss occurs on average every year, these losses have to be anticipated in the

form of a credit reserve (CR). The CR is the amount that has to be set aside in anticipation of

expected credit losses. The size of the CR is equal to the present value of the expected credit

losses. These losses have to be quantified in advance in order to calculate the effective return

on investment of the portfolio. The unexpected losses have to be buffered with an equity

reserve. The size of the equity reserve has to be equal to the difference between the present

value of unexpected credit losses (at a certain confidence level) and the credit reserve (see

Jorion 2001, p.332 f).

3.4.2 Determination of the default probability

In order to model an entire portfolio of partner contracts, we use publicly available data ont

the partner structure of typical German energy providers. We assume that the current rating

describes the economic condition of the partner accurately. According to Pschick (2008,

p.281), external ratings by rating agencies are used by three quarters of the surveyed

companies in the electricity industry. Hence, this approach is utilized to model the default

probability of the counterparties. The default probability of each partner contract is based on

the historic default rates published by the three largest rating agencies Fitch, Moody’s, and

Standard & Poors (S&P). As a base for the partner portfolio considered in this study, we

analyze typical partner structures of incumbents of the German electricity sector. The partner

structure of these exemplary companies suggests that the majority of trading partners have an

A-rating or better.

15

Fig. 4 Partner structures of incumbents of the German electricity industry Sources: EON (2010, p.137); ENBW (2010, p.191); Vattenfall (2010, p.77); RWE (2010, p.13)

Fig. 4 illustrates the partner structure of typical incumbents of the German electricity sector.

Instead of fixing the portfolio shares to a specific percentage, we assume a flexible partner

portfolio. Each counterparty is simulated as an individual contract. The partner portfolio is

illustrated by Fig. 5.

Fig. 5 Partner portfolio design Source: Own assumptions

The pie chart represents the long-term average of the rating group distribution. Each rating

segment has an expected value of partner share, which is normally distributed. For example,

the chart on the right hand side of Fig. 5 illustrates the long-term distribution of one rating

E.ON Counterparty Structure

19,4%

50,2%

6,0%

1,4%

23,0%

AAA; AA+; AA; AA-

A+; A; A-

BBB+; BBB; BBB-

BB+; BB; BB-

Other

Vattenfall Counterparty Structure

45,8%

41,1%

9,9%3,2%

AAA; AA+; AA; AA-

A+; A; A-

BBB+; BBB; BBB-

Other

ENBW Counterparty Structure10,2%

82,4%

0,4%2,6%4,5%

AAA; AA+; AA; AA-; A+

A; A-

BBB+

BBB; BBB-

Other

RWE Customer Structure

13,0%

41,0%

20,0%

26,0%

Private and commercial

Industrial and corporate

Distributors("Stadtwerke")

Trading / Wholesalemarket

E.ON Counterparty Structure

19,4%

50,2%

6,0%

1,4%

23,0%

AAA; AA+; AA; AA-

A+; A; A-

BBB+; BBB; BBB-

BB+; BB; BB-

Other

Vattenfall Counterparty Structure

45,8%

41,1%

9,9%3,2%

AAA; AA+; AA; AA-

A+; A; A-

BBB+; BBB; BBB-

Other

ENBW Counterparty Structure10,2%

82,4%

0,4%2,6%4,5%

AAA; AA+; AA; AA-; A+

A; A-

BBB+

BBB; BBB-

Other

RWE Customer Structure

13,0%

41,0%

20,0%

26,0%

Private and commercial

Industrial and corporate

Distributors("Stadtwerke")

Trading / Wholesalemarket

0,000%

1,000%

2,000%

3,000%

4,000%

5,000%

6,000%

7,000%

5,0

%

5,6

%

6,2

%

6,8

%

7,4

%

8,0

%

8,6

%

9,2

%

9,8

%

10

,4%

11

,0%

11

,6%

12

,2%

12

,8%

13

,4%

14

,0%

14

,6%

15

,2%

16

,0%

10%

20%

50%

5%

5%

10%

AAA

AA

A

BBB

BB

Other

16

class with an expected share of the portfolio of 10%. The actual partner portfolio is different

for each run of the Monte Carlo simulation. That way, it is possible to implicitly model

potential rating migrations of the counterparties.

3.4.3 Determination of the exposure at default

The EAD for a futures contract is more challenging to calculate than the EAD for a loan or a

bond. Typically, the EAD of loans and bonds is constant over time. In contrast, the EAD of

futures varies, based on the current value of the futures contract. Depending on the price

movement of the underlying commodity and the point of sale, the EAD of a financial

derivative varies every day. The exposure at default in period t of a contract i is calculated by

( ) ( ( ) ( ̅̅ ̅̅ )) ( ̅̅ ̅̅ ), (19)

where pC,i(t) is the current price of the commodity in period t, and pC,i(th) is the price that was

locked in by the hedge in period th. The magnitude of the EAD also depends on the contract

size vH,C,i that was fixed in th. The contract size and the time of sale are determined by the

hedging strategy. A portfolio of commodity futures contracts is the sum of all contract

exposures:

( ) ∑ ( ) ∑ (( ( ) ( ̅̅ ̅̅ )) ( ̅̅ ̅̅ ))

. (20)

Each hedge is locked in at th,i. In this setup of the EADPortfolio,theo, each individual EAD can be

positive or negative. Depending on the price developments, it is theoretically possible that the

EAD is negative and, therefore, a partner default would be in the hedging company’s favor.

That would be the case if electricity prices were increasing and, due to the defaulting partner,

it would be possible to sell the identical futures contract that have just gone into default with

the same maturity date at a higher price. However, the different EADi of this model are

assumed to be always positive for each transaction, because trading partners will not default

on contracts which are still “in the money” (Altman and Saunders 1998 p.1727). For

modeling purposes, we assume that the EAD of any defaulting contract is always larger than

or equal to zero and works towards the company’s disadvantage:

( ) . (21)

The portfolio exposure of the futures contracts has to be larger than or equal to zero as well:

( ) ∑ [ ( )] . (22)

17

Note that negative EADs that would generate a profit in the case of a partner default are

excluded from the portfolio EAD.

3.4.4 Determination of the recovery rate / the loss-given default

For the purpose of this study, three different recovery rate scenarios are used. Besides two

deterministic scenarios (RR=0%, RR=40%) a randomized recovery rate (hereafter referred to

as the “correlated recovery rate”) is used, based on the findings of Hamilton et al. (2004).

They showed that the RRs and ratings are correlated and they quantified the relationship

between historical default rates and historical RRs. The relationship for the years 1982 to

2003 was

. (23)

DR is the default rate of the contract. According to the study, a linear relationship between the

default rate and the recovery rate is sensible. Their regression analysis explained much of the

annual variation of RRs (R2=60%). Therefore, a similar approach for the RR is used in our

study.

3.5 Determination of results

Monte Carlo simulation is employed to simulate the costs of margining and the costs of

counterparty default simultaneously. The randomized hedging approach leads to a different

hedging strategy for each run of the simulation. The hedging strategy is used to determine the

time of sale of each derivative contract. The price of the derivative contract is determined

based on the time of sale. The probability of default for each contract is determined by the

associated rating and the active contract time. In addition to that, the EAD of each contract is

calculated using the futures’ price at the point of sale and the futures’ price at the point of

default. The simulation calculates a frequency distribution of the resulting costs of default

based on the different input factors. The default distributions of the costs of default are then

compared with the distribution of the margining costs using the value-at-risk methodology.

18

4 Financial analysis and results

4.1 Assumptions and results of the base case

4.1.1 Basic assumptions

In section 3 we described the methodological approach of our study. In this section we present

the underlying data applied to the model. Furthermore, the results of the simulation, as well as

the sensitivity analysis, are also presented. All of the simulations are based on a portfolio of

power plants with an assumed total generation of electricity of 1 TWh p.a. For the basic

scenario, the fuel mix is 40% outright power, 40% coal power and 20% gas power. This mix

and the generated volume remain constant over time. In addition, we assume a constant ratio

of 60% base-load electricity and 40% peak-load electricity. Further assumptions with regard

to the efficiencies of the investigated power plant technologies and the energy contents of the

fuel are displayed in Table 1. In order to accommodate the different notations for natural gas,

a correction factor is utilized. This factor corrects the difference between the low heating

value notation of the power plant efficiency and high heating value notation of the gas price at

the EEX.11

Table 1 Assumptions about the power plant efficiencies and yield factors

Source: Own assumptions and calculations based on Lang and Madlener (2010a, p.25)

The applied commodity prices are taken from the EEX notations12

for the time frame from Jan

1, 2007 until Dec 31, 2009. They form the basis for the calculation of the variation margin

and the additional margin according to the rules of the ECC (2010a)13

. It is assumed that on

weekends and during holidays the prices are the same as that on the previous business day.

Instead of a complete cascading of all prices for all products during the delivery period, a

11 The different heating value notations and their purpose are described in Petchers (2003, p.47).

12 For detailed information about the different products traded at the EEX, please refer to EEX (2010).

13 The other margins are assumed to be negligibly small and are therefore not used in the model.

EfficienciesCoal Power ηCoal 44% MWhel/MWhth

Gas Power ηGas 54% MWhel/MWhth,LHV

Energy Contents

Coal Power YCoal,th 6.978 MWhth/ton

Gas Power YGas,th 3.070 MWhel/ton

Gas Correction Factor YGas,LHV/HHV 0.901 MWhth,LHV/MWhth,HHV

CO2 EmissionsCoal Power eCoal 0.777 ton CO2/MWhel,Coal

Gas Power eGas 0.374 ton CO2/MWhel, Gas

19

simplified approach is chosen for the relevant commodities.14

For base-load and peak-load

electricity price developments, we employ the Phelix-base and Phelix-peak annual futures

price. During the delivery period, the daily price notations of the monthly futures are used.

For the price developments of the natural gas, the prices of the Net Connect Germany (NCG)

natural gas yearly futures are applied. During the delivery period, the average of the monthly

futures notations is used. For the first half of 2007, no gas price data were available from the

EEX, so the TTF gas prices of Bloomberg are utilized as an approximation. For the price

developments of coal, the prices of the Amsterdam-Rotterdam-Antwerp (ARA) annual coal

futures are used (API#2). Coal futures are typically denoted in USD. The dollar value per ton

was converted into Euros based on the daily foreign exchange rate published by Bloomberg

for the time between Jan 1, 2007 and Dec 31, 2009. During the delivery period, the daily

notation of monthly coal futures is applied. To reflect the developments of the CO2 prices, the

European Carbon Futures (EUA) quotation of the EXX is used. For the delivery period, the

prices of monthly futures are utilized.

4.1.2 Calculation procedure of margining costs

In this section we describe the development of the MAB and the influence of the CR

commitment procedure. For the margining model, the variation margin and the additional

margin are calculated on a daily basis. Fig. 6 shows a graph of the MAB development based

on the assumptions mentioned above. The positive variation margin for the short position on

electricity during 2009 is partly offset by the variation margin of the long positions in coal,

gas, and CO2 certificates. The additional margin is charged by the ECC independently of the

price movements of the underlying commodities.15

At the beginning of 2009, the model

reaches a steady-state level of the additional margin, because starting at that point, all three

hedging cycles for all delivery years can be calculated.16

14 The simplification process is analogous to Lang and Madlener (2010a, p.26).

15 Technically, the additional margin factors and the expiry month factors are influenced by the price volatility of

the underlying commodity prices. The ECC updates those factors on a regular basis. However, the price tracks

do not influence the calculation of the additional margin directly.

16 The assumed hedging cycle for delivery in 2011 starts on Jan 1, 2009.

20

Fig. 6 Margining account balance 2007-2009 (in €)

The CR needed to cover the margin payments for 2009 is illustrated in Fig. 7. The actually

required CR is displayed by the shaded area below the horizontal axis. Assuming perfect

foresight, the size of the CR is based on the maximum negative MAB of 2009. As part of the

Monte Carlo simulation, the maximum negative level of the MAB in dependency of the

hedging strategy is calculated. The maximum size of the negative MAB of 2009 varies

between €6,275,000 and €9,295,000. For a company that is financed with debt and equity, the

weighted average cost of capital (WACC) needs to be considered (Ross et al. 2008, p.353).

The money used to finance the CR could otherwise be used for internal and external

investment opportunities. Therefore, the capital costs for the CR have to be considered as

opportunity costs. As a simplification, the CR is assumed to be financed at an interest rate iFin

of 7%.17

Furthermore, it is assumed that the margin surplus renders an interest iDay of 2%.18

17 A discussion about the reasonable cost of capital for an electricity producer can be found in Lang and

Madlener (2010b).

18 Both iFin = 7% and iDay = 2% are annual interest rates. The daily rates, used in the model, are iFin/D = 0.01918%

and iDay/D = 0.00548%.

-25,000,000

-20,000,000

-15,000,000

-10,000,000

-5,000,000

0

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

01.01.07

01.04.07

01.07.07

01.10.07

01.01.08

01.04.08

01.07.08

01.10.08

01.01.09

01.04.09

01.07.09

01.10.09

Variation Margin Total Margining Account Additional Margin Electricity Base Additional Margin Electricity Peak

Additional Margin Coal Additional Margin Gas Additional Margin CO2

Additional Margin Additional Margin (including EMF) Variation Margin Electricity Base Variation Margin Electricity Peak

Variation Margin Coal Variation Margin Gas Variation Margin CO2

21

Fig. 7 Annual cash reserve commitment

The size of the CR used to settle the margining needs is based on perfect foresight and

therefore equal to the largest negative MAB during 2009.

4.1.3 Calculation procedure of the default costs

The underlying trading portfolio is simulated based on a set of 500 individual contracts /

partners. Each contract has its individual rating and the corresponding default probability. The

assumed portfolio is made up of six different rating classes with an individual share of the

total portfolio. The shares of the different rating classes are based on the disclosed partner

structures of German incumbents of the electricity industry (see Fig. 4 in section 3.4). The

highest rating class is AAA (10% of the total portfolio). The other classes are AA (20%), A

(50%), BBB (5%), BB (5%) as well as “other” (10%). The default probabilities are based on

historic default rates published by Fitch (2010, p.12), Moody’s (2009, p.31), and S&P (2010,

Table 25). It is assumed that the default probability of rating class AAA is 0%. The default

probabilities of the other rating classes are AA (0.066%), A (0.075%), BBB (0.280%), BB

(1.332%), and “other” (3.910%). Based on historical default rates, each contract is randomly

assigned with a default probability and the expected costs of default are calculated. The rating

class “other” of the model is assumed to have the same properties as the rating class

“speculative grade” by the rating agencies.

-10.000.000

-5.000.000

0

5.000.000

10.000.000

15.000.000

20.000.000

Cash Reserve Margin Surplus Margining Account Balance

22

4.1.4 Financial analysis of the base case

Based on the assumptions about the margining model and the default model, the costs for both

types of risk are calculated. Fig. 8 illustrates the frequency distributions of the margining

costs as well as the costs of default, determined by the Monte Carlo simulation. The costs of

margining are based on three different CR commitment periods. To calculate the costs of

default, three different RRs are modeled. These include an RR of 0%, one of 40%, and one

correlated RR19

.20

Fig. 8 Frequency distribution of margining and default costs

The base case of the model assumes a CR commitment period of one year. Table 2 displays

the results of the Monte Carlo simulation. The average costs resulting from an annual

commitment to the CR are €384,000. These costs are significantly higher than the average

costs of default €67,000, assuming an RR of 0% (€40,000, assuming an RR of 40%).

Therefore, looking at the average costs for both types of risks, margining is significantly more

expensive than the intentional acceptance of counterparty default risk. Nevertheless, while

looking at the tail risk, the difference is less striking. The default costs are lower than

€406,000 (RR = 0%) at a confidence level of 95%. The margining costs, assuming an annual

CR commitment, are €465,000 at the same confidence level. Hence, in this respect, the cost

differences are significantly smaller, although the margining costs are still higher than the

costs of default. In extreme cases, the costs of default can exceed the costs of margining. The

maximum costs of default (RR = 0%) are €1,478,000 and the maximum costs of margining

are €538,000 (annual CR commitment). In section 4.2 the base case analysis is extended for

19 As described in section 3.4.1, the recovery rate was calculated as: RR = 50% - 6 × Default Rate.

20 It is assumed that only contracts that are “out-of-the-money” would default (Altman and Saunders 1998,

p.1727).

23

an enquiry on the impact of different price movements on the relationship between the costs

of margining and default.

Table 2 Financial cost analysis of the base case (in 1000 €)

Furthermore, the length of the CR review cycle has a significant impact on the costs of

margining. In the case of a quarterly review cycle and perfect foresight, the CR is equal to the

maximum negative MAB of the quarter. If the maximum MAB of the quarter is positive, the

CR is assumed to equal zero. A new deal structure with more chances to update the size of the

CR could decrease the costs of margining substantially21

. In the set of basic assumptions, an

active management of the CR for margining would reduce the necessary capital requirements

and thus, could significantly reduce the cost of the employed capital. For example, a switch

from an annual CR commitment to a quarterly CR review for the assumed year in the example

reduces the costs of margining from €384,000 to €23,000 for 2009. Assuming fully flexible

financing possibilities with a daily CR update for the margining requirements, the costs of

margining during 2009 would further decrease. In fact, using the historical price tracks from

2007 until 2009, this practice would lead to a result with a positive interest. However, the

transaction costs for the CR adjustment would increase as well with the number CR updates.

Hence, the optimal CR commitment period is a trade-off between CR financing costs and CR

adjustment transaction costs. Due to space limitations, we leave the development of a possible

optimization algorithm to further research. The determination of the size of the CR has a

major impact on the costs of margining. Throughout the study it is assumed that the

margining account balance of 2009 can be forecasted perfectly and the CR is chosen based on

the forecast information. In reality, it is not possible to forecast the MAB of the following

year perfectly. Therefore, the CR level used in the study is a best case scenario. Hence, real

margining costs are likely to be higher, assuming a different forecasting procedure of the CR.

21 Please note that no other transaction costs are considered.

Statistics: Cost Analysis Mean Minimum Maximum VaR 99% VaR 95% VaR 90%

Margining CostsPerfect Foresight

Annual CR Update 384 318 538 496 465 443

Quarterly CR Update 23 -26 103 85 68 58

Daily CR Update -94 -127 -41 -52 -64 -71

Default Costs

RR correlated 40 0 773 181 243 427

RR = 0% 67 0 1,478 303 406 695

RR = 40% 40 0 887 182 244 417

24

This makes the fact that margining is on average always more expensive than the costs of

counterparty default even more striking.

4.2 Impact of the economic environment: Scenario analysis

In order to get a different view of the effects of the price developments on the costs of

margining and the costs of default, three different price development scenarios, in addition to

the base case mentioned above, are simulated. In the base case, the historical price tracks of

futures contracts traded at the EEX are used. In order to examine the impact of different

commodity prices, a situation with increasing prices (Scenario 1), low price volatility

(Scenario 2) and decreasing prices (Scenario 3) is analyzed. Scenarios 1 and 3 are designed as

mirror images of each other. The prices start out at the same level, and the absolute change

over the three year period, as well as the price volatility, are identical. Scenario 1 describes an

economic climate during a growth period. Over the period of three years the prices for base-

load electricity increase by roughly 60%. Prices for peak-load electricity increase by 59%

over three years. Futures prices for coal, gas, and CO2 certificates increase by 50%, 52%, and

52%, respectively. In Scenario 2 the effects of a lower price volatility are analyzed. The price

of base-load electricity decreases by less than 1% on average per year. On average, the price

for peak-load futures increases by 5% annually. The prices for futures on coal, gas, and CO2

certificates change plus 8%, minus 2%, and minus 7%, respectively, during the assumed

trading period. Due to the low price changes, the volatility of this set of prices is lower than

the volatility of Scenarios 1 and 3. The prices of Scenario 3 decrease substantially over the

time period of three years. The price for the base-load futures decreases by 60% from €80.8 at

the beginning to €32.4 at the end of the trading period. Over the same time period, the prices

for peak-load electricity, coal, gas, and CO2 certificates drop by 59%, 50%, 52%, and 52%,

respectively. These price tracks are symmetrical to the upside case in Scenario 1. Taking these

price tracks, the costs of margining using a one-year CR commitment are calculated. In

addition, the costs of default, assuming a 0% and a correlated RR, are simulated.

Table 3 displays the results of the three different scenarios. Compared to the base case

with slightly decreasing prices and average costs of margining of approx. €384,000, the total

costs in the assumed scenarios differ significantly. The increasing prices in Scenario 1 lead to

much higher average costs of margining €2,100,000. In the case of comparable low price

volatility, the average costs of margining are €1,122,000. The higher costs compared to the

base case are mainly a result of the additional margin: in Scenario 2, the overall price change

25

over the three-year period is only marginal. Therefore, the effects of the variation margin are

smaller, since the calculation of the VM largely depends on the price changes of the

commodities (see eq. (8)). The different prices do not affect the size of the additional margin,

because the calculation of the additional margin does not depend on the commodity prices

(see eq. (10)). The size of the additional margin depends on the factors published by the ECC

and the notional contract volume. During times of decreasing prices, the calculated MAB was

positive throughout 2009. In accordance with the perfect foresight assumption, the

calculations for all CR commitment periods resulted in a CR of zero for the entire year of

2009. This resulted in an average interest surplus of €227,000 based on our assumption of a

2% interest on an MAB surplus. The average costs of default are €67,000 in the base case and

only €26,000 (RR = 0%) during times of increasing prices and €17,000 (RR = 0%) during

times of low price volatility. The average costs resulting from counterparty default in

Scenario 3 are €78,000 (RR = 0%). Hence, for the assumed standard portfolio of an asset-

backed trader, the costs of default are lowest during times of low price volatility and the costs

are especially high during times of decreasing prices.

Table 3 Effects of different economic environments (in 1000 €)

In the base case, the costs of margining are significantly higher than the costs of default. This

is also true for Scenarios 1 and 2. In both of these cases, the average costs of margining are

substantially higher than the costs of default. Also at the 95% confidence level, the costs of

margining are still significantly higher than the costs of default. In Scenario 3 the outcome is

different. Because of a positive MAB, no CR is used, resulting in an interest surplus. In this

case, the costs of counterparty default are higher than the costs of margining. However, it is

unrealistic for a company to risk not being able to fulfill potential margining calls. Although

Statistics: Scenario Analysis Mean Minimum Maximum VaR 90% VaR 95% VaR 99%

Basic AssumptionsHistoric Price Tracks

Costs of Default (RR correlated) 40 0 773 181 243 427

Costs of Default (RR = 0%) 67 0 1,478 303 406 695

Margining Costs (Annual CR Commitment) 384 316 529 443 465 496

Scenario 1Increasing Prices

Default Costs (RR correlated) 15 0 313 59 79 122

Default Costs (RR=0%) 26 0 472 98 128 197

Margining Costs (Annual CR Commitment) 2,100 1,632 2,917 2,482 2,606 2,812

Scenario 2Low Price Volatility


Default Costs (RR=0%) 17 0 385 63 98 186

Margining Costs (Annual CR Commitment) 1,122 884 1,534 1,310 1,364 1,459

Scenario 3Decreasing Prices


Default Costs (RR=0%) 78 0 1,343 343 466 689

Margining Costs (Annual CR Commitment) -227 -343 -161 -177 -172 -166

26

an MAB might be positive as a consequence of mark-to-market value of the trading positions,

a trader would always keep a certain minimum amount of cash as a risk buffer, incurring

additional costs. Nevertheless, the tendency of decreasing prices to lead to lower margining

costs or even an interest surplus can be seen in this example22

. Default costs are lowest during

times of relatively stable prices. This is due to the fact that the EAD depends on the price

movements and remains low during times of low price volatility. Even with the same number

of default occurrences, the total lost volume is lower than in times of increasing or decreasing

prices. Due to the assumption that only contracts with a negative exposure can default, the

costs of default increase both in an environment of increasing as well as an environment of

decreasing prices, compared to a scenario with low price volatility. In the case of decreasing

prices, the electricity providers lose money due to losses on the short positions of the

electricity. In times of increasing prices, the losses are due to partner defaults in the long

positions of fuel and CO2 certificates. Overall, the effect of decreasing prices on the costs of

default is stronger, because the EAD is mainly influenced by the short position in electricity.23

4.3 Impact of a different partner allocation

After exploring the influence of different commodity price developments, the scenario

analysis in this section covers the impact of the partner structure on the costs of default. The

price tracks used in this section correspond to the base case. In order to understand the

influence of the partner structure, three trains of thought are explored. First, what is the

impact if the historic default rates, published by the rating agencies, turn out to be too low to

accurately describe the default probability? In order to answer that question, the default

probabilities of the base case are doubled. The resulting default probabilities are: AAA (0%),

AA (0.132%), A (0.150%), BBB (0.560%), BB (2.664%) and “other” (7.820%). Second, what

is the effect of a financial crisis that adversely influences the partners’ credit-worthiness? This

question is answered by modeling a potential partner downgrade. Each rating class is

downgraded to the next lower class. This results in a counterparty allocation of AAA (0%),

AA (10%), A (20%), BBB (50%), BB (5%) and “other” (15%). Third, what if it is not

22 In this case, the interest earned by the margin surplus is larger than the capital costs for the CR. In all tables,

costs are denoted as positive numbers and the positive interest surplus resulting from margining is denoted as

negative numbers.

23 It can be assumed that the notional value of inputs (fuel & CO2) has to be lower than the notional value of the

output (electricity). The exposures of the futures contracts behave in the same way.

27

sufficient to model each contract individually? If one partner that the company trades several

contracts with defaults, all of those contracts would default at the same time. Therefore, the

number of uncorrelated partner contracts might lead to additional portfolio effects that lower

the costs of default. The answer to this question is modeled by reducing the number of

counterparties from 500 to 100. As a result of this, each of the five commodities is only traded

with 20 different partners. Table 4 displays the results of the cost analysis for the different

partner structures. In addition to the base case, also the costs of a doubled default probability,

a partner downgrade, and a reduction of the partner portfolio are illustrated.

Table 4 Effects of changes of the counterparty structure

In the case of doubled default probabilities, the costs of default increase for the average cost

as well as for the tail risk. However, the average costs of default are €129,000 (RR = 0%) and,

therefore still lower than the average costs of margining (€384,000). Hence, in the long run

(i.e. looking at the average costs), the costs of default are still lower than the costs of

margining, even if the default probabilities of all counterparties are twice as high as the

historical default rates. In the short run, i.e. looking at the tail risk, the costs of default may

exceed the costs of margining. At a 95% confidence level and an RR of 0%, the costs of

default are €612,000. In comparison, the costs of margining at the same confidence level are

€465,000. Nevertheless, these results clearly depend on the assumed RR. Using the correlated

RR with costs of default of €443,000, the costs of margining would be more expensive than

the intentional acceptance of counterparty default risk. In the case of a rating downgrade of all

counterparties, the effects are similar to the effects of doubling the default probability. In the

long run, it is still cheaper to accept counterparty default risk than paying for margining. The

Statistics: Partner Structure Change Mean Minimum Maximum VaR 90% VaR 95% VaR 99%

Base Case


Default Costs (RR=0%) 67 0 1,478 303 406 695

Default Costs (RR=40%) 40 0 887 182 244 417

DoubledDefault Probability

Default Costs (RR correlated) 92 0 1,558 296 443 695

Default Costs (RR=0%) 129 0 1,818 423 612 964

Default Costs (RR=40%) 71 0 1,036 233 335 527

1 Rating Downgrade


Default Costs (RR=0%) 110 0 1,499 385 530 816

Default Costs (RR=40%) 60 0 795 211 295 463

Reduced Partner Portfolio

(100 contracts)

Default Costs (RR correlated) 38 0 3,250 0 57 1,113

Default Costs (RR=0%) 63 0 5,352 0 97 1,906

Default Costs (RR=40%) 38 0 3,211 0 58 1,143

Margining Costs (Annual CR Commitment) 384 316 529 443 465 496

28

average default costs after one rating downgrade are €110,000 (RR = 0%), which is only 28%

of the average costs of margining. From a short term perspective, the costs of margining are

lower than the costs of default if the RR is 0%. The application of the correlated RR, or the

RR of 40%, would lead to lower costs of counterparty default than the costs of margining at a

95% confidence level. The reduction of the number of counterparties has only a marginal long

term effect. Since the production volumes and the underlying default probabilities remain

constant and all of the contracts are uncorrelated, the long-term costs of counterparty default

do not change. However, the short-term effects, on the other hand, are significant as a

consequence of lower diversification effects. The maximum costs of default increase from

€1,478,000 (RR = 0%) in the base case to €5,352,000 (RR = 0%) in the scenario with a

reduced partner portfolio. The effect at a 99% confidence level is similar. However, the effect

at lower confidence levels is different. At a confidence level of 95%, the costs of default are

€97,000 (RR = 0%). Fig. 9 illustrates the potential effects of the partner portfolio size on the

frequency distribution of the default costs. The distribution of the default costs stretches

towards extreme high and extreme low losses as a result of the reduced number of partner

contracts. The average value of the distribution remains constant. But due to the bigger tail,

the VaR 99% level is shifted towards higher losses and the value-at-risk level at a 95%

confidence level is shifted towards lower losses.

Fig. 9 Change of the frequency distribution due to a reduced partner portfolio

Consequently, in all of the cases with modified counterparty structures, margining is still

more expensive in the long run than accepting the risk of counterparty default based on the

underlying set of assumptions. In the short run, assuming an RR of 0%, the costs of

counterparty default are higher after a doubling of the counterparty default rate, or a partner

downgrade of all partners in the portfolio. In the cases of the correlated RR and an RR of

Mean MeanVaR 95 % VaR 95 %VaR 99 %VaR 99 %Losses Losses

Freq

uen

cy

Freq

uen

cy

Before the reductionof contract partners

After the reductionof contract partners

29

40%, the costs of margining are still higher than the cost of counterparty default. The effect of

the number of counterparties differs, depending on the time frame. From a long-term

perspective, the reduction of the number of counterparties does not have an impact. In the

short run, however, the costs of counterparty default, at very high confidence levels, might be

significantly higher than the default costs of the base case and the costs of margining.

4.4 Impact of the fuel mix

In this section of the study, the effects of different fuel mixes on the costs of margining and

counterparty default are tested (100% of outright power vs. 100% coal vs. 100% gas). Fig. 10

contains the data of the resulting margining and default costs, depending on the technology of

power generation used.

Fig. 10 Statistics: Fuel mix analysis and margining costs (in 1000 €)

Table 5 Statistics: Fuel mix analysis and margining costs (in 1000 €)

Statistics: Fuel Mix Analysis Mean VaR 95%

OutrightPower

Default Costs (RR=0%) 63 384

Margining Costs (Annual CR Commitment) -386 -316

Original Mix 40/40/20


Margining Costs (Annual CR Commitment) 384 466

CoalPower



GasPower


Margining Costs (Annual CR Commitment) 1,536 1,755

-500.000

0

500.000

1.000.000

1.500.000

2.000.000

Outright Power

Basic Mix 40/40/20

Coal Power Gas Power

Statistics: Fuel Mix Analysis Mean VaR 95%

OutrightPower


Margining Costs (Annual CR Commitment) -386 -316




CoalPower



GasPower


Margining Costs (Annual CR Commitment) 1,536 1,755

-500.000

0

500.000

1.000.000

1.500.000

2.000.000

Outright Power

Basic Mix 40/40/20

Coal Power Gas Power

30

For outright power, no fuel or CO2 certificates need to be hedged. Therefore, this type of

power does not offer an offsetting effect.24

Outright power generates an average interest

surplus resulting from margining of €386,00025

using the historical price tracks of the base

case. The chart in Fig. 10 illustrates the average costs of margining according to the fuel type.

The decreasing prices during 2009 lead to an interest surplus resulting from margining. The

original mix, where 60% of the energy is generated using spread-based fuels, leads to average

margining costs of €384,000. The electricity generated purely from coal leads to average

margining costs of €788,000 and the gas based electricity results in average margining costs

of €1,536,000. The strong offsetting effect for gas power can be explained by the extreme gas

price movements during the time period of 2008 and 2009.

The effects of the use of outright power are analyzed in more detail. The three scenarios

of section 4.2 are applied to outright power in order to understand its effect. The results of the

sensitivity analysis of outright power are displayed in Table 5.

Table 6 Effects of the sole use of outright power (in 1000 €)

24 The prices of fuel and electricity are assumed to be correlated. Therefore, if electricity is generated using

spread-based fuels, the margining requirements for the short position on electricity are offset by the margining

consequences of the long position on fuel and CO2. For more details about the offsetting effect of the fuel mix,

see Lang and Madlener (2010a, p.28).

25 In the case of an interest surplus, the numbers in the table are negative. Therefore, the VaR 95% level of the

margining costs does not denote the maximum costs, but the minimum interest surplus resulting from margining.

Mean Minimum Maximum VaR 95%

Basic Assumptions Historic Price Tracks

Outright Power

Costs of Default (RR = 0%) 63 0 1,022 384

Margining Costs (Annual CR Commitment) -386 -466 -299 -316


Costs of Default (RR = 0%) 67 0 1,478 406

Margining Costs (Annual CR Commitment) 384 316 529 465

Scenario 1Increasing Prices

Outright Power

Default Costs (RR=0%) 0 0 75 0

Margining Costs (2009 Max MAB) 2,727 2,087 3,811 3,440



Margining Costs (Annual CR Commitment) 2,100 1,632 2,917 2,606

Scenario 2Low Price Volatility

Outright Power


Margining Costs (2009 Max MAB) 1,483 1,174 2,052 1,821



Margining Costs (Annual CR Commitment) 1,123 888 1,525 1,365

Scenario 3Decreasing Prices

Outright Power

Default Costs (RR=0%) 83 0 1,036 487

Margining Costs (2009 Max MAB) -453 -648 -334 -357


Default Costs (RR=0%) 82 0 1,035 453

Margining Costs (Annual CR Commitment) -228 -343 -162 -171

31

With regard to the default costs, the absolute differences between outright power vs. the

original power mix is negligible. In the case of increasing prices, as we assume that the

counterparty will not default on contracts which are still “in the money” (see above), the

average costs of default as well as the tail risk at a 95% confidence level, are zero for outright

power. In Scenario 2, the costs of default for outright power are €11,000 (RR = 0%)

compared to €20,000 for the original mix. In Scenario 3, with decreasing prices, the costs of

default for both types of energy are similar. The average costs of default of outright power are

€83,000 and the costs of default of the basic energy mix are €82,000, assuming an RR of 0%

each time. This can be explained by the EAD of the short and long positions. In the case of

increasing prices, the long positions on fuel and CO2 certificates primarily cause risk of

exposure. Since outright power does not hedge long positions on these items, this is a low risk

of exposure. In the case of decreasing prices, the main risk of exposure is caused by the short

position on electricity. Since the volume of electricity futures contracts is the same for both

fuel mixes, the difference in average costs of default is very low. With regard to the

margining costs, the selected technology portfolio has a major influence. The offsetting effect

of the long position on fuel and CO2 certificates of the original mix reduces the volatility of

the MAB. As a result, the absolute value of the margining costs is always larger for outright

power. In the case of increasing prices, the costs of margining are €2,727,000 for outright

power compared to €2,100,000 for the original mix. During times of low price volatility, the

costs of margining of outright power are 32% larger than the costs of margining of the basic

energy mix. In Scenario 3, outright power leads to a 98% larger interest surplus resulting from

margining. Furthermore, the difference between the maximum costs of margining in Scenario

1 and the largest interest surplus resulting from margining in Scenario 3 is larger for outright

power. Therefore, the costs of margining and the underlying size of the margining account are

more volatile when outright power is used. This is in line with the results of Lang and

Madlener (2010a) showing higher volatility of margining amounts for outright power in

comparison to the margining requirements of other generation technologies.

5 Conclusion

As a result of the financial crisis, the European Commission plans the mandatory introduction

of a centralized clearing and the consequent use of margining for the European derivatives

markets. A major focal point in this context is the expectation of a higher transparency in the

derivative markets and a reduction of the credit risk associated with these products. Due to the

32

still developing derivatives markets in the electricity industry, with a high percentage of the

trades concluded in the OTC market, without centralized clearing, this will have a significant

impact on the electricity industry. This study has focused on the comparison of the costs

resulting from margining and the expected costs of defaulting counterparties. After giving an

overview of current research developments, the basic methodology of the model was outlined.

Furthermore, the setup of the hedging approach, the margining model and the default model

were explained. Thereafter, the results of the basic case were discussed. In addition to that, a

scenario analysis was conducted to test the effects of the economic climate, the partner

structure, and the fuel mix. The results suggest that the use of margining in the electricity

industry is significantly more expensive than the potential costs of defaulting counterparties.

According to the model employed, the introduction of centralized clearing, and with this, the

necessity to collateralize all trades, will significantly burden the utilities sector. We find that

in most of the assessed cases it is cheaper for companies to accept and bear the credit risk,

rather than to carry the resulting margining costs. Nevertheless, as expected, the economic

environment has a major impact on the costs of margining and the cost of default. During

times of economic growth and increasing commodity prices, margining costs tend to be

higher, compared to margining costs when price volatility is low. During times of decreasing

commodity prices, margining costs for electricity providers tend to be lower than during times

with stable prices. On the contrary, especially an adverse economic environment with

decreasing commodity prices suggests increasing expected costs of default. The effect of

increasing prices on the expected costs of default for an asset-backed security is in this

comparison not as strong. The reason for this is the fact that counterparties will not default on

contracts which are still “in the money”, as those contracts can, for example, be sold or closed

out by the counterparty. The type of fuel used to generate the electricity has also a significant

impact on the margining costs due to offsetting effects between long and short positions in the

case of positively correlated commodity prices. Outright power, without the need to hedge

fuel or CO2 certificates, does not offer such an offsetting effect and, therefore, increases the

volatility of the margining account balance. Also, for the potential costs of default, the impact

of the fuel mix is relevant. Due to the positive correlation of the commodity prices in the

spread-based business, the exposure at default increases with the price volatility. For outright

power, contrary to the margining costs, increasing commodity prices lead to lower expected

costs of default. Disregarding potential effects from commodity price developments and the

underlying portfolio mix, a further major influence factor for the comparison of the margining

costs vs. the costs of default is the recovery rate for the defaulted contracts. The amount of

33

potential trading partners does mainly affect the short-term credit risk exposure. In the case of

a constant portfolio composition with constant distribution of equally rated positions, the

average (long-term expected) loss remains constant. In the base case of this study historic

price tracks were used to calculate the costs of margining. As an extension of the model, it

would be interesting to include a price forecasting model that can be used to quantify the

expected size of the cash reserve cushion, as well as the expected costs of margining. Further,

the different elements of the model were not correlated with each other in this study. It would

be interesting to simulate correlated default probabilities and price developments based on the

economic climate. Moreover, the expected default probabilities were based on the partners’

ratings and historic default rates. An integrated endogenous approach to quantify the

probability of default could be implemented in order to increase the accuracy of the expected

probability of default. Furthermore, it would be interesting to extend the model, which was

only based on the use of futures, for further hedging tools, such as options and swaps. In

addition to that, the model could be extended to include calculations for potential portfolio

insurance.

Disclaimer

The views expressed in this paper are those of the authors and do not necessarily reflect the

views of the E.ON AG.

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Innovative Residential Heating System, FCN Working Paper No. 2/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, February.

Harmsen - van Hout M.J.W., Herings P.J.-J., Dellaert B.G.C. (2010). The Structure of Online Consumer

Communication Networks, FCN Working Paper No. 3/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, March.

Madlener R., Neustadt I. (2010). Renewable Energy Policy in the Presence of Innovation: Does Government Pre-

Commitment Matter?, FCN Working Paper No. 4/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, April (revised June 2010).

Harmsen-van Hout M.J.W., Dellaert B.G.C., Herings, P.J.-J. (2010). Behavioral Effects in Individual Decisions of

Network Formation: Complexity Reduces Payoff Orientation and Social Preferences, FCN Working Paper No. 5/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, May.

Lohwasser R., Madlener R. (2010). Relating R&D and Investment Policies to CCS Market Diffusion Through Two-

Factor Learning, FCN Working Paper No. 6/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, June.

Rohlfs W., Madlener R. (2010). Valuation of CCS-Ready Coal-Fired Power Plants: A Multi-Dimensional Real

Options Approach, FCN Working Paper No. 7/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, July.

Rohlfs W., Madlener R. (2010). Cost Effectiveness of Carbon Capture-Ready Coal Power Plants with Delayed

Retrofit, FCN Working Paper No. 8/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, August.

Gampert M., Madlener R. (2010). Pan-European Management of Electricity Portfolios: Risks and Opportunities of

Contract Bundling, FCN Working Paper No. 9/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, August.

Glensk B., Madlener R. (2010). Fuzzy Portfolio Optimization for Power Generation Assets, FCN Working Paper

No. 10/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, August. Lang J., Madlener R. (2010). Portfolio Optimization for Power Plants: The Impact of Credit Risk Mitigation and

Margining, FCN Working Paper No. 11/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, September.

Westner G., Madlener R. (2010). Investment in New Power Generation Under Uncertainty: Benefits of CHP vs.

Condensing Plants in a Copula-Based Analysis, FCN Working Paper No. 12/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, September.

Bellmann E., Lang J., Madlener R. (2010). Cost Evaluation of Credit Risk Securitization in the Electricity Industry:

Credit Default Acceptance vs. Margining Costs, FCN Working Paper No. 13/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, September.

2009 Madlener R., Mathar T. (2009). Development Trends and Economics of Concentrating Solar Power Generation

Technologies: A Comparative Analysis, FCN Working Paper No. 1/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November.

Madlener R., Latz J. (2009). Centralized and Integrated Decentralized Compressed Air Energy Storage for

Enhanced Grid Integration of Wind Power, FCN Working Paper No. 2/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November (revised September 2010).

Kraemer C., Madlener R. (2009). Using Fuzzy Real Options Valuation for Assessing Investments in NGCC and

CCS Energy Conversion Technology, FCN Working Paper No. 3/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November.

Westner G., Madlener R. (2009). Development of Cogeneration in Germany: A Dynamic Portfolio Analysis Based

on the New Regulatory Framework, FCN Working Paper No. 4/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November (revised March 2010).

Westner G., Madlener R. (2009). The Benefit of Regional Diversification of Cogeneration Investments in Europe:

A Mean-Variance Portfolio Analysis, FCN Working Paper No. 5/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November (revised March 2010).

Lohwasser R., Madlener R. (2009). Simulation of the European Electricity Market and CCS Development with the

HECTOR Model, FCN Working Paper No. 6/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November.

Lohwasser R., Madlener R. (2009). Impact of CCS on the Economics of Coal-Fired Power Plants – Why

Investment Costs Do and Efficiency Doesn’t Matter, FCN Working Paper No. 7/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November.

Holtermann T., Madlener R. (2009). Assessment of the Technological Development and Economic Potential of

Photobioreactors, FCN Working Paper No. 8/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November.

Ghosh G., Carriazo F. (2009). A Comparison of Three Methods of Estimation in the Context of Spatial Modeling,

FCN Working Paper No. 9/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November.

Ghosh G., Shortle J. (2009). Water Quality Trading when Nonpoint Pollution Loads are Stochastic, FCN Working

Paper No. 10/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November.

Ghosh G., Ribaudo M., Shortle J. (2009). Do Baseline Requirements hinder Trades in Water Quality Trading

Programs?, FCN Working Paper No. 11/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November.

Madlener R., Glensk B., Raymond P. (2009). Investigation of E.ON’s Power Generation Assets by Using Mean-

Variance Portfolio Analysis, FCN Working Paper No. 12/2009, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, November.

FCN Working Papers are free of charge. They can mostly be downloaded in pdf format from the FCN / E.ON ERC Website (www.eonerc.rwth-aachen.de/fcn) and the SSRN Website (www.ssrn.com), respectively. Alternatively, they may also be ordered as hardcopies from Ms Sabine Schill (Phone: +49 (0) 241-80 49820, E-mail: [email protected]), RWTH Aachen University, Institute for Future Energy Consumer Needs and Behavior (FCN), Chair of Energy Economics and Management (Prof. Dr. Reinhard Madlener), Mathieustrasse 6, 52074 Aachen, Germany.

2008 Madlener R., Gao W., Neustadt I., Zweifel P. (2008). Promoting Renewable Electricity Generation in Imperfect

Markets: Price vs. Quantity Policies, FCN Working Paper No. 1/2008, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, July (revised May 2009).

Madlener R., Wenk C. (2008). Efficient Investment Portfolios for the Swiss Electricity Supply Sector, FCN Working

Paper No. 2/2008, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, August.

Omann I., Kowalski K., Bohunovsky L., Madlener R., Stagl S. (2008). The Influence of Social Preferences on

Multi-Criteria Evaluation of Energy Scenarios, FCN Working Paper No. 3/2008, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, August.

Bernstein R., Madlener R. (2008). The Impact of Disaggregated ICT Capital on Electricity Intensity of Production:

Econometric Analysis of Major European Industries, FCN Working Paper No. 4/2008, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, September.

Erber G., Madlener R. (2008). Impact of ICT and Human Skills on the European Financial Intermediation Sector,

FCN Working Paper No. 5/2008, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, September.