portfolio optimization for power plants: the impact of

FCN Working Paper No. 11/2010

Portfolio Optimization for Power Plants:

The Impact of Credit Risk Mitigation and Margining

Joachim Lang and Reinhard Madlener

September 2010

Institute for Future Energy Consumer Needs and Behavior (FCN)

Faculty of Business and Economics / E.ON ERC

FCN Working Paper No. 11/2010

Portfolio Optimization for Power Plants: The Impact of Credit Risk Mitigation and

Margining

September 2010

Authors’ addresses: 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) Faculty 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]

Portfolio optimization for power plants: the impact of credit risk

mitigation and margining

Joachim Langa and Reinhard Madlenerb1

a E.ON AG, Controlling / Corporate Planning, E.ON Platz 1, 40479 Dusseldorf, Germany

b Institute for Future Energy Consumer Needs and Behavior (FCN), Faculty of Business and

Economics / E.ON Energy Research Center, RWTH Aachen University,

Mathieustrasse 6, 52074 Aachen, Germany

September 2010

Abstract

The aim of this study is to analyze the impact of credit risk mitigation via margining on the optimal

portfolio selection for power plants. We develop a model to estimate margining cashflows that is

based on the clearing framework of the European Commodity Clearing AG (ECC), on stochastic

commodity price tracks, and on a pre-defined hedging strategy. To evaluate an assumed set of power

plants, we calculate the discounted cashflow for each power plant in conjunction with a market model

and a Monte Carlo simulation on commodity price tracks. The valuation of the power plants is done

with and without credit risk mitigation by means of margining. The resulting differences in the values,

with and without margining, are analyzed with the mean-variance portfolio approach of Markowitz, to

specify the consequences of margining on the efficient frontier of possible power plant portfolios. We

find that the consideration of margining for power plant portfolio selection is relevant, as it can

markedly change the composition of efficient portfolios on the efficient frontier.

Key words: Margin@Risk, credit risk mitigation, margining, collateralization, risk capital, power plant valuation, portfolio optimization, cashflow planning

JEL Classification Nos.: G11, G17, G32, L94, O16

Acknowledgements and Disclaimer: The authors are especially grateful to Jan Daugart, Otmar Sachsse,

Christoph Waidacher, Stefan Balster and Damian Robinson for the many fruitful discussions and informative

support that helped immensely to develop this paper. Furthermore, we would like to thank Jochen Kley and Ulf

Klostermann as well as the E.ON Group for generously enabling the sabbatical year of Joachim Lang. Note that

the views expressed in this paper are those of the authors and do not necessarily reflect the views of E.ON AG. * Correspondence. Tel. +49 241 80 49 820, fax. +49 241 80 49 829; E-mail: [email protected] (J. Lang),

[email protected] (R. Madlener).

1 Introduction

In recent years, after the financial crisis in the banking sector from 2007–2009, credit risk

mitigation has gained significant importance in the markets. As billions of Euros have had to

be raised to save several banks from bankruptcy by nations all over the world, institutions like

the European Commission are now calling for a stronger general control, especially for

derivative markets, via the application of centralized clearing mechanisms (EUCOM

2009a,b). In this context “a tailor-made proposal for the EU level oversight of electricity and

gas spot markets is foreseen“ (EUCOM 2009c, p.2). Nevertheless, the additional needs for

risk capital in cash or cash equivalents for the resulting clearing requirements will certainly

increase for the utilities in the European markets, as the majority of the trades are still done in

the OTC markets (EEX GB 2009, pp.19, 82). We showed earlier (Lang/Madlener 2010) that

margining requirements might differ between power plants of dissimilar fuel types and might

therefore impact the optimality of existing but also future power plant portfolios. Margins

represent “collaterals posted with the future exchanges clearing company by an outside

counterparty to ensure the eventual performance” (Reilly/Brown 2000, p.1206).

The aim of this study is to analyze the impact of credit risk mitigation via margining on

the optimal portfolio selection for power plants, using the mean-variance approach of

Markowitz (1952). The remainder of the paper is organized as follows. Section 2 gives an

overview of the relevant literature, with a particular focus on portfolio selection problems in

the financial and the electricity sector, combined with issues concerning credit risk or the

mitigation of it. Furthermore, we investigate to what extent margining in the evaluation of

power plants has already been recognized in the literature, and provide an overview of our

proceeding. Section 3 explains the methodological approach adopted to pursue the analysis

outlined in section 4. Section 5 summarizes the results and shows further research

opportunities.

2 Existing literature on solutions for portfolio selection problems

2.1 Portfolio optimization and portfolio selection problems in combination with credit risk

Since Markowitz’ mean-variance portfolio theory (MPT) with its determination of the

“efficient frontier” (Markowitz 1952), as well as the further developments by Tobin (1958,

1965), portfolio optimization techniques have become standard in today’s financial sector.

Steinbach (2001) gives an overview of a broad variety of different sources with regard to the

2

foundation of the Markowitz model, different applications and further developments,

especially for issues related to market risk. Also, with regard to credit risk, the MPT is a well-

known tool and has found its way into operational applications in the financial sector.

Altman/Saunders (1998), for example, use the MPT to estimate an optimal composition of

bond and loan portfolios. Further use can be found in Bennett (1984), who applies the MTP to

loan portfolios in the context of global bank lending.

Besides the profound application and further development of portfolio optimization and

portfolio selection techniques in the world of finance, those techniques are also used for

optimization problems in the energy sector. One of the first approaches was implemented by

Bar-Lev/Katz (1976), who applied the mean-variance method for the optimization of power

plant portfolios in the US with regard to an efficient fuel diversification. Further work with

the mean-variance method was conducted by Awerbuch/Berger (2003), who analyzed the

efficiency of the Power Generation portfolio in the EU by calculating the efficient frontier

using the output per production cost (fuel, O&M, construction period costs) in kWh/cent, the

standard deviation of the different input factors and the corresponding cross-correlation

between them. Krey/Zweifel (2006) analyzed the Swiss and the US electricity markets with a

cost-based application of portfolio theory on different production capacities. A more recent

application of portfolio theory is Roques et al. (2007), where the authors focus on

diversification incentives in liberalized energy markets, and Madlener/Wenk (2008), who

analyze optimal technology choice for peakload and baseload power plant investments in the

Swiss market. Both approaches are moving away from the pure “cost-only” approaches of

former studies and introduce also the revenue component by using discounted-cashflow

models to calculate a relative net present value in £/kW (Roques et al. 2007) or a lifetime

return yield (Madlener/Wenk 2008). With regard to the risk assessment, both approaches use

the standard deviation as a measurement for the implied risk. An application of the mean-

variance approach on cogeneration (or combined-heat-and-power, CHP) plants can be found

in Madlener/Westner (2009a,b).

More applications of the MPT method for markets in other countries can be found in

Jansen et al. (2006) on an optimal renewable energy portfolio in the Netherlands and in

Munoz et al. (2009) for an analysis on an optimal renewable portfolio in Spain.

Borchert/Schemm (2007) show the general application of the MPT on a fictional portfolio of

wind plants in Germany by using the conditional value-at-risk (CVaR) technique as a risk

metric for their analysis. A study on the optimal configuration of generation assets for the

Californian market is available in Bates/White (2006), and for conventional assets in the

Taiwanese market (Huang/Wu 2006). Another study is Zhu/Fan (2010), who evaluate China’s

3

2020-medium-term plans for generating technologies. A further application of the mean-

variance approach with the CVaR as a risk metric can also be found in Schemm (2008). He

applies Markowitz’ portfolio theory (MPT) to model and analyze investment decisions with

utility functions from diverse investors based on the applied optimization algorithms.

Nevertheless, all of the named approaches are focusing on market risk, as they analyze

the impact of changes in the underlying input costs for the commodities or the prices achieved

for the output. None of the approaches mentioned covers credit risk management, or

specifically reviewed the impact of credit risk mitigation applying margining, or risk capital

in general on the optimal selection of power plant portfolios.

2.2 Conclusions from the literature review

So far, the impact of credit risk mitigation on the value of power plant portfolios and its

impact on possible investment decisions have not yet been investigated. Especially the aspect

of margining in the context of power plants is a fairly new issue, as a consequence of the

rather new derivative markets for electricity products in Europe. In an earlier paper

(Lang/Madlener 2010), we showed the necessity for the consideration of margining in the

valuation of power plants. We analyzed the differences in the risk capital needs for alternative

fuel types and worked out the reasons for the major differences. In the present paper, we

sophisticate and extend our first approach by analyzing the impact of credit risk mitigation not

only on a single plant level but on power plant portfolios and investment decisions for

different expansion options. We develop a stochastic market model in conjunction with a

Monte Carlo simulation to estimate margining cashflows. For this, we used the clearing

framework of the European Commodity Clearing AG (ECC) and a linear hedging strategy.

We conduct a discounted cashflow (DCF) valuation of a power plant portfolio with and

without the recognition of credit risk mitigation via margining. The output of our net present

value (NPV) calculations for the “operative” cashflows and the margining needs will be used

to derive the efficient frontier of the possible portfolio combinations based on Markowitz’

mean-variance approach (MPT), as we think this method provides a profound tool for our

task2. The resulting differences for the values are analyzed to identify the consequences of

2 Contrary to continuous and short-term trading decisions for commodities such as electricity, the investment

decision of building a new power plant or selling parts of a generation portfolio (disinvestments) is generally not

done on a continuous basis. Power plants are, in dependency on the applied technology, built for a period of 20-

50 years and are themselves not an object frequently traded. Therefore power plant portfolio structures are

regularly reviewed (see, e.g., E.ON CMD Generation 2009). However, this is done on a discrete (e.g. once a

year) but not continuous basis (e.g. similar to hourly trades on the spot markets).

4

margining for the value of power plant portfolios and the efficient frontier. For the margin

calculations, we use a risk metric that we refer to as “Margin-at-Risk” (MaR) as a

reminiscence to the standard Value-at-Risk (VaR) approach, with a specific definition that fits

the purpose of estimating the value of margining cashflows over a longer time horizon. To

analyze the impact of different components in our portfolio optimization, we undertake

several sensitivity analyses. Figure 1 gives an overview of the procedure followed in this

study.

Portfolio optimizationDetermination of the efficient frontier for different

scenarios

Determination of asset value and risk parameters in simulation runs

DCF valuation for each power plant and new

build opportunity

Calculation of margining cashflow and respective value per pp.

Plant specific data

Efficiency

Deterministic hedging

strategies

Determination of expected economic

generation

Market model • Assumption on price duration curves• Stochastic commodity spot and futures prices• Assumptions on volatilities • …

Availability

Fixed costs

Capacity

…

Evaluation and sensitivity analysis

Lifetime

Other var. costs

CalculationsInput parameters

Embedded into a Monte-

Carlo simulation

Figure 1: Procedure followed in this study Source: own illustration

3 Methodological approach

3.1 DCF valuation of the power plants

3.1.1 General remarks

Markowitz applied the expected rate of return to measure the success of a possible portfolio.

He stated that for the application of the mean-variance model, it is necessary to have “useful

procedures” (Markowitz 1952, p.91) to determine the relevant risk and return measures. In the

financial markets, there is the opportunity to use directly the expected change of

share/security prices for the determination of the expected rate of return. However, for the

application of the method to power plant portfolios the expected rate of return is somewhat

harder to identify: the question arises as to which basis could be used for the rate of return, as

no liquid market with “stock prices” for power plants is available. A possibility of solving this

issue is to use the expected NPV of the underlying assets (see e.g. Roques et al. 2008,

Madlener/Wenk 2008, Madlener/Westner 2009a, b).

5

In our analysis we focus on capacity expansions, i.e. expansions of the existing stock of

power generation plants. To this end, we employ the entity method3 to calculate the DCF and

the NPV as a measure of the return4 and for the evaluation of the cashflows stemming from

margining. The NPV is generally calculated as the sum of all expected yearly free cashflows

(FCF) discounted by a factor based on a plant-specific interest rate r, as depicted in (1) (here:

mid-year convention):

∑=

−+=

T

ttr

FCFENPV1

5.0)1()(

. (1)

The parameters and calculations are discussed in more detail in section 3.2.2.

3.1.2 Determination of the FCF for power plants

With regard to the operative business, we model the net operating profit after tax (NOPAT) as

operative cashflow of the relevant power plants based on the major influencing factors of the

profitability of the plant, starting from the expected revenues less variable costs, fixed costs,

and taxes. For obvious reasons, a main focus point is the commodity pricing. For the sake of

simplicity, we do not cover aspects like the usage of secondary fuels, cogeneration or heat-

only generation. The recognition of start-up and down-time costs is modeled in a simplified

way. Table 1 gives an example of the FCF determination for this study.

3 The entity method uses for the NPV calculation the free cashflow determined from the cashflow of the

operative business minus the cashflow from investing activities and without the cashflow from financing

activities (see Volkart 2007, pp.314-324). 4 Besides the NPV approach a variety of different ways for the valuation of assets or projects exists, such as the

Internal Rate-of-Return method (IRR) or annuity-based approaches, the usage of multipliers, the Real Options

approach or value-based approaches like the Economic-Value-Added (EVA) method etc. (for more detailed

explanations in the standard literature, see, e.g., Bruns/Meyer-Bullerdiek 2008 or Kruschwitz 2007). However,

the discussion on the applicability of the NPV vs. the stated alternatives (see, e.g., Volkart 2007, p.287ff) will

not be a subject of this study.

6

Table 1: Determination of the yearly Free Cashflow

Item for DCF calculation Short name Illustrating example Unit Determination for this

studyAverage achieved electricity price in €/MWh Pavg 53 €/MWh Simulation resultRunning hours p.a. LF 6000 h Simulation resultAvailability in % p.a. Av 90% Plant-specific assumptionCapacity in MW Cap 800 MW Plant-specific assumptionPower generation Vel = Cap*Av*LF 4320000 MWh Simulation result

Revenues in € R = Vel * Pavg 228,960,000 € Resulting calculation

Fuel volume (in t (coal) or MWh (gas)) Vcoal / Vgas 1,544,400 t Simulation resultFuel costs in €/t ; €/MWh(th) Pfuel -60 €/t Simulation resultTotal fuel costs in € VCfuel 92,664,000 - € Simulation resultTotal fuel costs in €/MWh(el) MCfuel -21.45 €/MWh Simulation resultCO2 Emissions in t Vco2 3,672,000 t Simulation resultCO2 Costs in €/t Pco2 -15 €/t Simulation resultTotal CO2 costs in €/MWh(el) MCco2 -12.75 €/MWh Simulation resultTotal CO2 costs in € VCco2 55,080,000 - € Resulting calculationOther variable costs in €/MWh(el) MCother -2.5 €/MWh Plant-specific assumptionOther variable costs in € VCother 10,800,000 - Resulting calculation- Total marginal costs in € VCTotal =VCother+VCco2+VCfuel 158,544,000 - € Resulting calculationTotal marginal costs in €/MWh(el) MCTotal =VCTotal / Vel -36.7 €/MWh Resulting calculation= Gross margin in € GM = R - VCTotal 70,416,000 € Resulting calculation

Personnel cost FCpers 7,000,000 - € Plant-specific assumptionOperation & maintenance FCO&M 24,000,000 - € Plant-specific assumptionOther fixed costs FCother 1,600,000 - € Plant-specific assumption- Total fixed costs FCTotal = FCother+FCO&M+FCpers 32,600,000 - € Plant-specific assumption

= EBITDA EBITDA = GM - FCTotal 37,816,000 € Resulting calculation- Depreciation -D 36,800,000 - € Plant-specific assumption= EBIT EBIT = EBITDA - D 1,016,000 € Resulting calculation- Taxes (30%) -T 304,800 € General assumption= Net operating profit after tax (NOPAT) NOPAT=EBIT-T 711,200 € Resulting calculation

+ Depreciation +D 36,800,000 € Plant-specific assumption- Running Investments -Inv 3,680,000 - € Plant-specific assumption= Free Cashflow FCF 33,831,200 € Resulting calculation

3.2 Recognition of margining cashflows

3.2.1 General assumptions

In addition to the FCF stemming from the operative business, we further model the necessary

cash requirements for possible margins for the clearing requirements for the trades with

futures or forwards. An example calculation of the applicable margins for the trades at the

European Energy Exchange AG (EEX) is given in Lang/Madlener (2010). The relevant

collateralization volume is calculated by the respective clearing company (such as the ECC)

on a daily basis with regard to the corresponding price development and the change of the

volume position of the traded assets (Bruns/Meyer-Bullerdiek 2008, pp.447ff; ECC

Margining 2008, p.7). Analogously to Lang/Madlener (2010), the following main

assumptions apply for this study:

• Application of the clearing rules of the ECC for commodity trades with futures (cf. ECC

Margining 2008, pp.10-25; ECC Clearing 2009, chapters 3.5 & 4.2). We only use the

Variation Margin (VM) and the Additional Margin (AM) to calculate the relevant cash

7

requirements. For the assessment of commodity spot and futures prices, we used a

simplified market model (see sections 3.4–3.6 below);

• No minimum trading volumes of the energy exchange, i.e. it is possible to sell single

Megawatt-hours (MWh);

• 100% of all trades are effected on the same power exchange, offering netting possibilities

between short and long positions for the relevant products traded;

• The liquidity of the commodity markets is sufficient. The company acts as a “price taker”

without feedback of its trades on the corresponding market prices;

• The underlying company applies a two-year hedging period using only futures (for details,

see also section 3.3). Trades for electricity and relevant input factors, such as coal, gas,

and CO2, are done simultaneously without speculation on the corresponding spreads per

MWh of electricity produced;

• All valuations are based on yearly cashflows.

3.2.2 Calculation of the Variation Margin (VM) value impact

The VM covers the risk of price changes in open positions and is calculated by the ECC in a

daily run on every single contract of each product (“mark-to-market valuation”; ECC Clearing

2009, p.44ff). The total amount of cash VM(t), needed to cover all margining needs for all

products i = 1, …,n at time t=1,…,T, can be written as:

(∑ ∑∑∑= = =

−−=

−==n

i

n

i

T

ttitiit

T

ti ppvtVMTVM

1 1 1,1,1

1)()()( ). (2)

The required margining cashflows can be seen analogously to cashflows from working capital

(see Lang/Madlener 2010, pp.37f). Since changes in the working capital are relevant for the

determination of the Free Cashflow (see Meyer 2007, pp.61, 72, 75ff; Volkart 2007, p.320),

this implies the need for considering the discounted changes of the margining cashflows over

the period of consideration, to calculate the present value from the cashflows of the total VMt

requirement p.a. For this, we can use the NPV formula:

( )1

1 1

( )(1 ) (1 )

T Tt tVMt

VM tt t

E VM VME FCFNPVr r

−

= =

−= =

+ +∑ ∑ t (3)

and simply insert the VM calculation from (2). In addition, we assume that all cashflows of a

period (e.g. a year) are equally distributed throughout the year (mid-year convention). For

this, we deduct 0.5 from the exponent (cf. Pratt 1998, p.31):

8

( )( )∑

∑∑=

−= =

−−−−−

+

⎟⎠

⎞⎜⎝

⎛−−−

=T

tt

n

i

T

ttitiittitiit

VM r

ppvppvENPV

15.0

1 11,2,2,1,1

)1(

)())((. (4)

Note that (4) implies that the VM is calculated as the sum over all commodities and therefore

reflects the netting possibilities between long and short positions.

Besides the direct influence of commodity prices and the respective open positions on the

absolute value of the required margin in a day-to-day time horizon5, a company will

undoubtedly keep a certain minimum risk capital that is adjusted regularly, but not on a daily

basis. In the banking sector, this risk capital is often referred to as “economic capital”, a

measure of banks that is used to estimate the absolute level of internal capital needed for

running the business, and to cover economic effects of risk-taking activities (see BIS

Economic Capital 2009, p.1; Saita 2007, p.7). The financing of the respective risk capital

might be done with equity but also loans and loan guarantees, triggering a certain need for

negotiations with the companies or banks offering those refinancing possibilities. Therefore,

for practical reasons, companies might fix their maximum risk capital available for trading

activities on a monthly, quarterly, or even yearly basis.

To estimate the required risk capital for market and credit risks, practitioners in the

banking or financial sector often apply the Value-at-risk (VaR) concept, which gives the

maximum potential loss (V0-V) with regard to an original value V0 that a business can

generate in a given time horizon within a defined percentage of a scenario (Saita 2007, p.25),

so that the probability of P(V0-V > VaR1-α) < α. Originally developed by JPMorgan (see

Jorion 2007, p.17) the VaR approach to measure the potential downside risk is meanwhile an

established standard procedure in today’s market- and credit risk management, especially in

the financial sector (see, e.g., Jorion 2007; Saita 2007, pp.25ff; BIS Derivatives 1998; pp.4,

18ff; JPMorgan 1997) and several analogous methods, such as the Earnings-at-Risk (EaR;

Saita 2007, p.134) or the Cashflow-at-Risk (CfaR; Hager/Wiedemann 2004) have been

developed. Also in the electricity and other energy-related sectors, the VaR and its further

developments, such as the Expected Shortfall / Conditional VaR (cf. Rockafeller/Uryasev

2000, 2002), are risk metrics used for the risk quantification for the commodity markets (see,

e.g., Borchert et al. 2006, pp.35ff; Pilipović 1998, pp.189ff; Denton et al. 2003).

The VaR can generally be derived for any probability distribution. In the case of standard

normally distributed variables (e.g. returns, prices), the daily VaR at a confidence level p =

(1-α) can be calculated based on the starting value for an asset V0 multiplied by the standard

5 The ECC, for example, generally calculates the necessary VM and the other margins daily, based on the

respective settlement price differences of the actual day vs. the day before, but also on an intraday basis.

9

deviation or volatility σ and the corresponding multiplier k1-α of the confidence level (see

Saita 2007, p.29; Jorion 2007, pp.106ff):

σαα ⋅⋅= −− 101 kVVaR . (5)

With regard to the application to energy prices (e.g. in the case of an asset-backed generator

who wants to sell electricity), we can interpret the VaR as the potential downside risk of

lower (for power sales) or higher (for purchases) commodity prices. Figure 2 illustrates this

issue, assuming that a generation company expects an electricity price of 50 €/MWh at the

given time of delivery with a possible standard deviation σ = 15 €/MWh and a standard

normally distributed risk profile6. In this case, the probability that the price will fall below (50

€/MWh – 2.326*15 €/MWh =) 15.11 €/MWh is < 1% and the VaR99% for each MWh as

absolute loss can be written as7

( )99% 1 2.326 15 € / €35VaR MWh MWh= ⋅ − ⋅ ≈ 8. (6)

As cash requirements for margining for the VM result from commodity price increases (for

short positions) or decreases (long positions), they actually represent the exact “opposite” risk

to the market risk, as long as the risk distribution over the time period is symmetrical.

Assuming that a trader A would sell 1 MWh of electricity of an existing power plant two

years ahead of delivery at a price of 50 €/MWh, he would cover the risk of a possible price

decrease in the year of delivery. The counterpart B of the trade would have to cover this

possible downside risk with the corresponding margins9. Conversely, the energy exchange

would ask trader A to meet the margin requirements in the case that the prices for the open

short position10 were to rise.

Note that this symmetry between the market risk and the margining risk is only given for

symmetrical distributions. However, commodity prices, and with them the value of the open

positions of a trader, often follow a non-symmetrical distribution, e.g. a log-normal

distribution. Nevertheless, for the sake of simplicity, we assume a standard-normal distributed

risk hereafter.

6 The standard normal distribution is used for example for the determination of the Additional Margin parameter

used by the ECC for the calculation of the Additional Margin (ECC Margining, p.19). 7 See also Jorion (2007), p.21. 8 For a more general explanation, see, e.g., JPMorgan (1997), p.8. 9 See ECC Clearing (2009), p.30. 10 The energy exchange considers a single sale of electricity as a short positioning regardless of a possible power

plant the trader might have in order to fulfill the delivery.

10

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

-15.0 -11.3 -7.5 -3.7 0.0 3.8 7.5 11.3 15.0 18.8 22.5 26.3 30.0 33.8 37.5 41.3 45.0 48.8 52.5 56.2 60.0 63.7 67.5 71.2 75.0 78.7 82.5 86.2 90.0 93.7 97.5 101.3105.0108.8112.5116.3120.0

μPel = 50 €/MWh; σ = 15 €/MWh

μ - 2.326σ μ + 2.326σ

Electricity price Pel

Confidence level of 99% --> 2.326σ--> ~ Pel=15,11 €

Confidence level of 99% --> 2.326σ--> ~Pel= 84,89 €

"Market risk" "Liquidity risk for margining"

Figure 2: Market- vs. liquidity risk from margining (short position) Source: own compilation

Henceforth, we use for the liquidity risk resulting from margining the term “Margin@Risk

(MaR)”11 apart from the known VaR, which generally describes the corresponding market

risk. We define the MaR as the maximum potential cash requirement for a hedged position for

the purpose of margining, that a business faces over a given time horizon within a defined

confidence level. For the example given above we can write

€35~/€15326.21%99 =⋅⋅= MWhMWhMaR . (7)

Generally, the VaR approach is only used to estimate the risk potential for the short term of

several days12. However, with regard to a possible application for a longer time horizon, the

usual way to enlarge the applicable time horizon of the VaR is to assume that returns / price

changes are serially uncorrelated, so that, for example, the daily volatility can be multiplied

by the square root of the time horizon T (Saita 2007, p.43; Jorion 2007, pp.106ff).

TkmTMaRMaR daydayyear ⋅⋅⋅=⋅= − σααα 10 (8)

In (9) the depicted volume m0 for the portfolio is taken as a fixed position for the time horizon

of the MaR of the trading portfolio.

11 So far, we could not find any reference in the literature regarding the “Margin@risk”. However, at E.ON

Group, this term is already used by practitioners from E.ON Energy Trading to describe the named liquidity risk.

Note that the calculation procedure might differ from the one used in this study. 12 The Basel Committee for Banking Supervision, for example, proposes a one- to ten-day horizon, see BIS

Basel II (2005), section 42, p.264.

11

Hedging function:

1 : 02

1( ) :2

21 :

...

i

linear ii i

i i

i

Sfor the hedging period tS

Sf t for the hedging period t SS

for the delivery period S t SS

with S hedging period in days for product i

⎧ ≤ ≤⎪⎪⎪= ≤ ≤⎨⎪⎪

− <⎪⎩365≤ +

(9)

Assuming a constant hedging policy and constant total volumes V p.a., the cumulated position

in this example after the first full hedging period (730 days) would be stable at

VtttVtttV

dttfVdttfVdttfVmSS

S

S

St

⋅=+++−

⋅=⎟⎟⎠

⎞⎜⎜⎝

⎛+

++⎟

⎠⎞

⎜⎝⎛ −⋅=

++= ∫∫∫+

5.1730

3652730730730

36573021

)()()(2/

0 30 2

365

1321

1

. (10)

Figure 3 shows the case of a single product (e.g. the sale of electricity) assuming a hedging

horizon of two years upfront the delivery year with a linear hedging strategy, i.e. on every

trading day an equal share 1/S of the expected total yearly production volume of the delivery

year is sold via futures. In the delivery year, the position is then linearly reduced back to zero,

see (9).

0%10%20%30%40%50%60%70%80%90%

100%110%120%130%140%150%160%

t0 Start t+1 Start t+2 Start t+3 Start t+4Delivery t+2 Delivery t+3 Cumulated position Delivery t+4

Hedging period S1

Hedging period S2

Hedging period S3

Hedged volume mt

tx

∫

∫

∫

+

+

=+

2/

0 3

2/ 2

365

1

)(

)(

)(

i

i

i

i

i

S

S

S

S

St

dttfV

dttfV

dttfVm

Figure 3: Hedging volumes based on a linear hedging strategy and a constant delivery volume Source: own compilation

However, the underlying volume might change over time in dependency on the hedging

strategy and the hedged volume. At a power exchange, normally each contract for a certain

12

delivery year is traded as a separate product13 and the total margining requirement is

calculated for each single product14. With regard to the estimation of the total risk capital

needed for the cumulated amount of the, e.g., net short position of a portfolio of all electricity

contracts, i.e. the risk of multiple products or time-slots for delivery, the portfolio MaR at a

certain point in time can be calculated as follows (cf. analogously for the calculation of VaR:

Saita 2007, p.37; Borchert et al 2006, p.319):

∑ ∑∑= = ≠

⋅⋅+=n

i

n

i ijjijii

Portfolioelect MaRMaRMaRMaR

1 1,

2 2 ρ (11)

with i; j = 1,..,3 serving as an indicator for the delivery year (“product”) and ρi,j representing

the correlation between the margins of the underlying hedging years.

Using a two-year hedging horizon and standard normally distributed volatilities for, e.g.,

a set of electricity sales contracts, the can be written as PortfoliotMaR

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⋅⋅+

⋅⋅+

⋅⋅

⋅+

⋅+⋅+⋅

= −

3,23322

3,13311

2,12211

23

23

22

22

21

21

21 2

ρσσρσσ

ρσσ

σσσ

α

mmmm

mm

mmm

kMaR Portfolioelect . (12)

In this equation, σi represents the price volatility and mi denotes the hedged positions of year i.

By recognizing the respective hedging strategies over the two-year hedging horizon for the

delivery periods i=1,...,3 and the expected generation volumes Vi to be hedged, we can write

for, e.g., the short position in electricity at point in time t:

⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

⋅⋅⋅+

⋅⋅⋅+

⋅⋅⋅

⋅+

⋅⎟⎠⎞⎜

⎝⎛+⋅⎟

⎠⎞⎜

⎝⎛+⋅⎟

⎠⎞⎜

⎝⎛ ⋅

=

∫∫∫∫

∫∫

∫∫∫

+

+

+

−

3,220 223

2/

0 33

2,120 221

365

11

3,13

2/

0 331

365

11

23

22/

0 3322

2

0 2221

2365

11

21

)()(

)()(

)()(

2

)()()(

ρσσ

ρσσ

ρσσ

σσσ

α

SS

SS

S

SS

S

SSS

S

Portfoliot

dttfVdttfV

dttfVdttfV

dttfVdttfV

dttfVdttfVdttfV

kMaR (13)

13 See EEX Products (2007a,b; 2008 a,b). 14 The ECC offers netting possibilities for short and long positions for products which can be attributed to the

same so-called margin classes or margin group (for reference, see ECC Margining 2008, chapters 6&7). In

addition to this, the ECC nets the overall margin payments for the accounts.

13

3.2.3 Recognition of netting effects between the short and long positions

Eq. (13) shows the calculation of the MaR for a portfolio of electricity futures contracts when

the expected energy of a run-of-river plant is sold to the market without the need for possible

input factors. However, in the case of a thermal power plant, the long positions from input

factors, such as fuel and CO2 certificates, would have to be recognized in the portfolio’s MaR

as well. This means, assuming that a trader always locks in a certain “Clean Dark Spread” or

“Clean Spark Spread”15 instead of speculating on the spreads, that one has to consider the

netting effects between the short- and long-positions of the portfolio. On a daily time horizon,

the clearing company would simply net the total payment requirements from the short

position less the payment requirements from the long position (see, e.g., ECC Margining

2008, p.15).

In a one-day period, the resulting change in the margining requirement would be the

potential increase (decrease) of the electricity position less the increase (decrease) of the input

position. Given the assumption that the price volatilities are standard normally distributed and

the prices are perfectly correlated ( )1, =jiρ , we can write:

( dayCoCO

dayfuelfuel

dayelecelec

dayCO

dayfuel

dayelec

day

mmmk

MaRMaRMaRMaR

221

2

σσσα ⋅−⋅−⋅⋅=

−−=

− ). (14)

However, commodity prices are generally not perfectly correlated and with this, we also have

to consider portfolio effects (see, e.g., Jorion 2007, p.164ff) in the total volatility of the

resulting spread:

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+

++

++

=

2,22

2,22

,

22

22

2222

2

COfuelCOfuelCOfuel

COelecCOelecCOelec

fuelelecfuelelecfuelelec

COCOfuelfuelelecelec

dayspread

wwww

ww

www

ρσσρσσ

ρσσ

σσσ

σ . (15)

In (15) the units of the term in brackets have to be aligned to the same unit (e.g. €/MWhel).

The unit for the CO2 costs is transferred to € per MWhel by multiplying with the factor

efuel/ηfuel with ηfuel representing the efficiency per fuel type and efuel covering the marginal CO2

emission per unit of fuel. In the case of coal as fuel, the conversion from $ per metric ton of

15 Clean Dark Spread: marginal electricity price per MWhel less marginal coal and CO2 costs per MWhel for, e.g.,

a coal-fired power plant; Clean Spark Spread: Marginal electricity price per MWhel less marginal gas and CO2

costs per MWhel for, e.g., a Combined-Cycle Gas Turbine (CCGT).

14

coal can be done by multiplying with (FX-Rate/(ηfuel x 6.978 MWhth/t)16. The weighting

factors wi are used to account for the netting by using

welec = 1 (short position) and wfuel; wCO2 =(-1) (long position).

For the resulting net margin requirements we can then write:

dayspreadelec

day mkMaR σα−= 1 . (16)

Inserting (16) in (13) results in:

⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

⋅⋅⋅+

⋅⋅⋅+

⋅⋅⋅

⋅+

⋅⎟⎠⎞⎜

⎝⎛+⋅⎟

⎠⎞⎜

⎝⎛+⋅⎟

⎠⎞⎜

⎝⎛ ⋅

=

∫∫∫∫

∫∫

∫∫∫

+

+

+

−

3,22,0 223,

2/

0 33

2,12,0 221,

365

11

3,13,

2/

0 331,

365

11

23,

22/

0 332

2,

2

0 222

1,

2365

11

21

)()(

)()(

)()(

2

)()()(

ρσσ

ρσσ

ρσσ

σσσ

α

spread

S

spread

S

spread

S

spread

S

S

spread

S

spread

S

S

spread

S

spread

S

spread

S

S

Portfoliot

dttfVdttfV

dttfVdttfV

dttfVdttfV

dttfVdttfVdttfV

kMaR. (17)

ji ,ρ in this case represents the correlation of the margining requirements between the years of

consideration. Finally, the relevant cashflow to calculate the value for the Variation Margin

needs is the year-on-year change of the calculated yearly MaR amount17.

3.2.4 Calculation of the Additional Margin (AM) value impact

The AM is meant to protect the ECC against possible additional close-out losses from open

positions in futures and options of a defaulted trader, which have to be closed out on the next

trading day or the day after, at possibly worse prices in comparison to the last settlement

prices used for the so-far paid margins. For single futures positions without margin classes,

the total Additional Margin for all traded products is calculated as follows18:

(∑ ∑==

⋅⋅⋅=n

i

m

tititiitt EMFAMPcvnpAM

11

)

. (18)

where npit is the net position of a certain product/contract i at a certain time t, cvi the standard

contract volume of contract i (e.g. for a monthly futures contract for baseload electricity

delivery in January, this would be 1 MW x 24 h x 31 day = 744 MWh), AMP the Additional

16 One standard traded metric ton of coal equals about 6,000,000 kcal/t (or 6.978 MWh/t), see EEX Products

(2007a). 17 This implies that the trader would close out his position in the case that the absolute margining payment would

be higher than the maximum value of the so calculated MaR. 18 ECC Margining (2008), p.22f.

15

Margin Parameter19 and EMF the Expiry Month Factor (relevant only in the delivery

month).20

From (18) we can see that, although the AMP and the EMF are adjusted from time to

time, the calculation of the AM is a linear function in dependency on the hedged volume of a

position21. For the Additional Margin it is irrelevant whether a net position is a net short or a

net long position. This makes the estimation of the MaR for the valuation of the cashflow

stemming from the Additional Margin much simpler. The estimated maximum cash

requirement for the AM in a specific year for a specific product is therefore the maximum of

the expected hedged volume of the respective year multiplied by the AMP and – for the

hedged volumes of the delivery month – in addition by the EMF.

For a two-year hedging horizon and with the recognition of the applied hedging strategies

we can write:

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⋅⎟⎠⎞⎜

⎝⎛+

⋅⎟⎠⎞⎜

⎝⎛+⋅⋅⎟

⎠⎞⎜

⎝⎛ ⋅

=

∫

∫∫∑

+

==

it

S

it

S

itit

S

Sn

iTot

yeariAM

AMPdttfV

AMPdttfVEMFAMPdttfVMaxMaR

0 22

2/

0 33

365

11

0...,

)(

)()( (19)

The total AM is then simply the sum of all MaRAM for all commodities, i.e.

year

COAMyear

fuelAMyear

elecAMyearAM MaRMaRMaRMaR 2,,, ++= . (20)

The AM is additive to the VM. The EMF is only valid in the month of delivery and the

underlying monthly volumes; otherwise, this factor is equal to unity22.

3.3 Determination of the discount rate

For the valuation of assets, the discount rate is generally represented by the weighted average

cost of capital (WACC) of the underlying company. It is calculated based on the relevant

interest rate for liabilities iL, adjusted by the so-called “tax shield” (rtax denotes the tax rate),

weighted with the share of the liabilities L from the total capital TC of the company plus the

corresponding weighted equity costs iEq23:

19 The AMP and the EMF are standard parameters which are fixed by the ECC and published on the website of

the EEX on a regular basis. 20 For a detailed description of the contained parameters, see ECC Margining (2008), p.17ff. 21 The AMP and the EMF are fixed for each commodity (electricity, coal, gas, CO2) but are not differentiated

between the different maturities of each product (delivery in t, t+1, t+2 etc.). 22 See ECC Parameters (2010). 23 See, e.g., standard literature, such as Brealey/Myers (2000), pp.543ff; Volkart (2001), pp.114ff.

16

TCEqi

TCLriWACC EqtaxLtaxadj ⋅+⋅−= )1( . (21)

The interest rates for the liabilities are determined based on the actual financing cost of the

company and on a risk-free interest rate plus a premium for the risk of default, that the

donator of the liability (e.g. a bank) adds (Volkart 2001, p.149). A common way to determine

the interest rate for the equity is generally by using the Capital Asset Pricing Model (CAPM;

Sharpe 1964). The interest rate for the equity is calculated by using the risk-free interest rate

plus a certain risk premium for the individual market, multiplied by the so-called β-

coefficient, representing the relative risk of the individual company’s engagement vs. the total

market24. With regard to the valuation of power plants, one could argue for the use of project-

or plant-specific WACC in order to represent the different operating risks or also different

dependencies from commodity price development, for example, of a nuclear power plant vs. a

coal power plant. However, as the individual WACC would be to some extent subjective25,

and as they would cause evaluation effects in the relative comparison between the different

plants, we refrain from individual WACC and use one single WACC for all power plants of

7% after tax and a general tax rate for Germany of 30% on the earnings before interest and tax

(EBIT) of the power plant26.

Nevertheless, the question arises as to which WACC should be used for the valuation of

the margining cashflows. One possible assumption would be that the WACC used for

discounting the cashflows from margining should be lower than the WACC used for

discounting cashflows from the operative business. First of all, the capital used for the

purpose of margining is not dependent on any operational risk but purely dependent on the

underlying open positions and the price developments of the commodity markets. Second, the

utility could finance this risk capital with an individual loan agreement with a bank at the

normal company-specific loan interest rate, which is certainly lower than the total WACC of

the company. However, the risk capital that is to be held by the utility company for the

purpose of margining is also relevant for the rating of the company, as is any other loan or

cash position. It limits the possibility of refinancing (under the assumption that the company

does not want to lower the general rating) and, therefore, influences not only the trading-

related business, but also other funding-relevant issues, such as the payment of dividends or

24 For reference, cf. e.g., Volkart (2001), p.24f, or Johnson (1999), p.189ff for the determination of the β-

coefficient for privately held companies. 25 Volkart (2001), p.42 names this issue in a general remark for the Swiss and US markets. 26 The EBIT is assumed to be equal to the EBT, since we estimate the free cashflow before financing costs,

which we then discount with the WACC.

17

investments. In addition to this, the necessary risk capital for margining can be seen as part of

the working capital of a power plant (see Lang/Madlener 2010), and has therefore the same

requirement as the power plant itself. As a consequence, for this study we have used the same

WACC requirements for the margining cashflows as for the cashflows from the operative

business.

3.4 Market model and the estimation of the power plant dispatch

3.4.1 General approach

A central aspect of any power plant valuation is the underlying assumptions for the input and

output factors of the power plants. In this study, we model a simplified but integrated spot and

futures market model that allows us to perform the analysis on the impact of margining on the

portfolio optimization and at the same time offers the possibility to run transparent sensitivity

analysis on the outcomes. Figure 4 gives an overview of the general approach, which is

explained in the following sections.

Market model with Monte Carlo simulation

Average monthly Spot prices forall commodities

);0(~

)(

,,

,,,

dtNanddtdZ

withdZVdtVLkdV

iviv

iviviiivvi

εε

σ

=

⋅+−=

iiiii dZVdtPLkdP +−= )(

Dispatch tool

Assumptions / input parameters for stochastic processes

ean reversion rates, volatilities, distributions

g-term fuel prices and resulting NEC Level for Power prices

on expectationorrelation rates between commoditiesedging functionice duration curve structure

…

• M

• Lon

• Inflati• C• H• Pr•

Average monthly and weightedyearly Future prices for all commodities

Conversion to hourly price duration curveDispatch derived as intersection of the yearly average commodity prices and the sPDC

••

iTt

T

t

iT FtfF ,)( ⋅= ∑

)1()()sin(

)1(4

)4

)(1(

),(ln

exp),),(( )(

)(22

2)(

)(

tT

tT

TtT

tT

etdzt

e

Le

TtSe

TttSF −−

−−

−−

−−

−⋅⋅+

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

−+

−−−+⋅= α

α

α

α

β

ασ

ασλ

Power plant DCF and margining - calculation

Figure 4: Overview of the applied market model Source: own compilation

3.4.2 Determination of the expected power generation per plant

To estimate the impact of margining on the value of power plants, it is necessary to determine

the underlying open positions and, with this, to estimate for the respective economic

generation p.a. of the underlying assets in the delivery years. In the case of baseload power

18

plants, such as run-of-river-, nuclear- or lignite power plants, this task is relatively simple, as

those run-times mainly depend on factors like the underlying maintenance cycles and less on

the volatility of commodity prices. With regard to the estimation of other thermal power

plant’s dispatch, the so-called “unit commitment problem” (UCP), this task becomes more

complex. Sheblé (1994) names more than 80 different articles that are concerned with the

UCP and that are offering different mathematical approaches to it. The general principle of all

models, however, is comparable and mainly based on the judgment of the hourly electricity

price vs. the then given marginal costs of each power plant. Figure 5 shows a comparison of

the hourly spot market electricity price vs. the daily spot market prices for gas for standard

state-of-the-art combined-cycle gas turbine (CCGT)27 for the year 2008 for the German

electricity market.

-50-40-30-20-10

0102030405060708090

100110120130140150160170180190200

1 501 1001 1501 2001 2501 3001 3501 4001 4501 5001 5501 6001 6501 7001 7501 8001 8501

Spot price electricity 2008 Marginal costs based on spot price 2008Average marginal costs 2008 (Spot price)

€/MWh

hoursLoad factor basedon actual marginal costs: 4318 h p.a.Load factor based on average marginal costs: 4268 h p.a.

Figure 5: Comparison of electricity prices vs. marginal costs of a CCGT Source: Based on spot market prices of 2008, data from EEX, own illustration

The modeling of the prices for primary fuels and electricity for the dispatching model can be

differentiated in the way the underlying assumptions are determined: pure stochastic models

resolve the electricity and the input factor prices based on stochastic processes (e.g. Kern

2006; Lucia/Schwarz 2002; Thomson et al. 2004; EnBW 2005). More fundamental models

determine the electricity prices of the market and the dispatch of all power plants by

comparing supply and demand in the market under utilization of deterministic or stochastic

commodity prices (e.g. Kramer 2002; Borchert 2003;, Anderson/Philpott 2002) for each 27 Assumptions: efficiency (LHV): 44%, fuel: natural gas, assumed transport/flexibility charge: 2.5 €/MWh(th),

other variable costs: 1 €/MWh(el); CO2 emission per MWh (el): 0.374 t/MWh(el).

19

single hour in the underlying period. Further reference to different approaches for the

modeling of electricity markets can be found in Ventosa et al. (2005). The major focus of

these models is the application for the short- and mid-term time horizon (one to three years),

for example, to derive possible hedging strategies in the power trading (e.g. Fleten et al.

2002). Although even for the short- to medium-term periods the estimation of prices and

power dispatch can only be done within a range of uncertainty, the estimation of a price

development is still feasible, as in general the market participants have information on

expected power demand, maintenance cycles of power plants28, existing and newly built

capacity in the market etc. However, in long-term models aimed at the evaluation of power

plants, it is questionable as to what extent an hourly price in a 40- or even 50-year time period

can be estimated in a reasonable manner.

To cope with this uncertainty, practitioners inter alias use deterministic price tracks and

scenarios based on fundamental models, fixing certain assumptions on newly built

investments, development of the yearly demand and prices for primary fuels, such as coal and

gas etc. This approach reduces complexity in the underlying decision variables in order to

focus on the impact of general trends on the value of power plants, for example, for the

purpose of long-term portfolio decisions (see, e.g., E.ON Generation 2009). In contrast, quite

a lot of information on the probability distributions of the outcomes is lost, leaving less room

for the estimation of risk capital, as required for our study.

Thus, for the purpose of this study, we combine a possibility to include the stochastics for

the modeling of energy prices, in order to approximate the possible dispatch p.a. for the

thermal power plants, with the possibility of fixing certain market environment assumptions

to test the impact of changes on the optimal portfolio choice.

In a first step, we convert the hourly prices of a year into a sorted hourly price duration

curve (sPDC)29. In the case that the marginal costs of a power plant are pretty stable over the

period of a year (e.g. when the costs for fuel, CO2 and other variable costs are hedged), we

can approximate the dispatch of the power plant by the intersection of the sPDC with the level

of the marginal costs (Figure 6)30. In mathematical terms, the sPDC can be written as a vector

of the hourly prices differential compared to the baseload power price, multiplied by the

baseload power price expressed as a scalar.

28 In Germany, for example, some incumbents publish their expected maintenance cycles and expected power

dispatch on the Internet: see, e.g., http://www.eon-schafft-transparenz.de or http://www.transparency.eex.com. 29 The sPDC represents the hourly power spot price of a year, sorted in descending order from the highest price

to the lowest price of the year, cf. Machate (2008), p.454. 30 Some reference to such an approach can be found in the literature, e.g. Pfaffenberger/Hille (2004), chapter 8.7.

20

http://www.eon-schafft-transparenz.de/

http://www.transparency.eex.com/

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

⋅=Ρ⋅=

base

elec

base

elec

base

elec

basehourlyelecbase

Pp

PpPp

PPsPDC

8760

2

1

... (22)

-50-40-30-20-10

0102030405060708090

100110120130140150160170180190200

1 501 1001 1501 2001 2501 3001 3501 4001 4501 5001 5501 6001 6501 7001 7501 8001 8501

hourly marginal costs 2008 corresponding to electricity price average marginal costs 2008 (Spot price) sorted spot price electricity 2008

Loadfactor based on average marginal costs: 4268 h p.a.

€/MWh

hours

partly loadfactor overestimation

partly loadfactor underestimation

Figure 6: Dispatch determination based on sPDC Source: comparison based on spot market prices of 2008, data from EEX

3.4.3 Determination of the underlying spot market prices

Keeping the vector of the sPDC constanthourlyelecΡ 31 and modeling the yearly baseload power

price Pbase, we reach for every year in our valuation a separate yearly sPDC. To calculate the

average yearly baseload price Pbase, we use an arithmetic mean-reverting process for the

yearly price movements32 and, as a second factor, the implied volatility of the process as

stochastic variable, as proposed by Borchert et al. (2006), p.98f33.

iiiii dZVdtPLkdP +−= )( (23)

31 For our model we use as Base Case the shape of the average sPDC over the years 2002-2009, based on the

German spot market data provided by the EEX. 32 For a reference on the use of mean-reverting models for energy commodity prices, see, e.g., Pilipovic (1998),

pp.63ff.; a more detailed analysis is given in Gibson/Schwarz (1990). 33 For the parametrization of the stochastic processes, see section 3.6.

21

dtdZ

withdZVdtVLkdV

iviv

iviviiivvi

,,

,,, )(

ε

σ

=

⋅+−=

(24)

where dPi is the price change of product i; ki the reversion speed of the actual price Pi to the

mean-reversion level L;; dZi represents a Wiener process; dVi is the change in the variance of

the price; kv the reversion speed of the actual variance Vi to the mean-reversion level Lv,i,, and

dZv,i represents a Wiener process for the variance.

We choose a monthly resolution in our model. Thus, we can compute the yearly average

product price by calculating the arithmetic average of all monthly product prices over a one-

year time period. The prices for all commodities are modeled analogously. All commodity

price modeling is done with prices expressed in logarithms (see Borchert et al. 2006, p.58).

In order to account for the fact that electricity prices in a market are highly correlated

with the underlying price developments of the primary fuels (cf., e.g., Roques et al. 2008,

p.1836) as a result of constant price setting of the underlying merit order and the respective

marginal cost, we model the price movements for electricity, coal, gas, and CO2 as correlated.

As a requirement for the Monte Carlo simulation software employed34, we use the Spearman

rank-order correlation coefficients35, as depicted in Table 2.

Table 2: Spearman rank correlation coefficients for the commodity prices 2007-2009

2007 - 2009 Elec. Base monthly

Elec. Base daily Coal $/t Coal €/t Gas CO2

Elec. Base monthly 1 0.809 0.705 0.678 0.759 0.436Elec. Base daily 1 0.627 0.612 0.681 0.347

Coal $/t 1 0.967 0.818 0.163Coal €/t 1 0.846 0.118

Gas 1 0.260CO2 1

Source: own computation based on EEX prices

34 When applying our power plant valuation tool we use Oracle’s CrystalBallTM for the Monte Carlo simulation. 35 The Spearman rank correlation coefficient is a non-parametric statistic, quantifying the correlation between

two variables without assuming an implied probability distribution or causal relationship of the variables. For the

calculation we used the following formula:

4)1()(

4)1()(

4)1())()((

22

1

22

1

1

2

+−

+−

+−

=

∑∑

∑

==

=

nnyRnnxR

nnyiRxR

i

n

iYi

n

iX

n

iYiX

SPXYρ .

22

The outcome of our dispatch model is used as an input for our hedging procedure, assuming

perfect foresight. By using a fixed sPDC-vector with volatile stochastic prices, we

assume a fixed market environment with a stable relation of power prices between the peak

and off-peak hours. This is certainly not the case for all years to come, due to the changes of

the merit order from a variety of influencing factors. However, it gives us the possibility of

more meaningful sensitivity analysis in order to investigate the impact of different market

environments on the value and risk capital needs for the power plants by changing the shape

of the sPDC.

hourlyelecΡ

3.4.4 Applicability of the sPDC approach

One could argue that a weakness of applying the sPDC concept is a certain loss of

information:

• The movement and change in the form of the yearly modeled sPDC stems only from the

stochastically modeled baseload power price. The underlying assumption of a stable

relationship between the ranked hourly prices does not occur in the real world. However,

it offers the opportunity of a sensitivity analysis on the impact of a change of the market

environment (i.e. the merit order) and the resulting change in the sPDC form on the

margining requirements.

• In addition, we lose the information of seasonal input prices and the respective marginal

costs, resulting in a certain inherent mismatch to the seasonal input factor prices and thus,

in deviations in the total dispatch volume, the resulting spreads and gross margins (Figure

6). Table 3 shows the result of an analysis of this effect for a state-of-the-art coal-fired

power plant and a CCGT for the years 2007-2009. Especially the CCGT has higher

deviations within the results, as a consequence of higher seasonal changes of the gas

prices compared to the coal prices36. However, the resulting error is still acceptable for the

purpose of this study. Also, note that as we always compare the impact on the optimal

portfolio with and without margining but always on the same data set, there is no

mismatch for our study.

36 Although the coal prices also have a higher volatility in absolute terms per currency, compared to the gas

prices (e.g. in €/t of coal vs. €/MWh(th) of gas), the impact of this volatility in the marginal costs is significantly

lower in the relevant notation in €/MWh(el), see Lang/Madlener (2010).

23

Table 3: Comparison of yearly dispatch volume, spreads, and margins Comparison: loadfactor p.a.

in h p.a. Unsorted Elec. Curve

Sorted Elec. Curve

% of former value

Unsorted Elec. Curve

Sorted Elec. Curve

% of former value

2007 5,845 5,327 91% 3,772 3,182 84%2008 6,358 6,076 96% 4,318 4,268 99%2009 6,280 6,222 99% 5,291 4,937 93%

Comparison: average clean spread of the yearin €/MWh

2007 14.06 14.23 101% 8.84 9.46 107%2008 19.31 18.99 98% 10.96 11.44 104%2009 10.46 10.49 100% 7.60 7.52 99%

Comparison: average margin p.a.in €

2007 82,206 75,784 92% 33,331 30,105 90%2008 122,769 115,397 94% 47,337 48,811 103%2009 65,687 65,282 99% 40,187 37,112 92%

Coal fired power plant Gas fired power plant

Source: own calculations based on EEX commodity prices 2007-2009

• The approach assumes a power plant that can be switched on and off, independently of

start-up and take-down times etc. To address this issue, we use a power-plant-specific

correction factor on the efficiency (resulting in higher marginal costs and thus in lower

dispatch volumes) and we deduct an expected unavailability from the derived dispatch

volume of the model.

• Furthermore, we lose the information on the relationship of peakload prices or off-peak

prices vs. the baseload prices37 because we sort the prices in descending order. The

approximation of the peakload prices as the average price on the first most expensive

3120 h of the sPDC is not completely valid (Table 4), because over a year some of the

highest prices of the year also occur during off-peak times.

Table 4: Comparison of the average peak price margins (compared to baseload price) for the

years 2004-2009 with the approximation based on the sPDC of the respective years

Year Base price Peak price Off Peak price

Peak- vs. Baseload

price

Off-Peak vs.

Baseload Base price Peak price Off Peak

price

Peak- vs. Baseload

price

Off-Peak vs.

Baseload 2004 28.6 38.0 23.3 133% 82% 28.6 39.6 22.4 139% 78%2005 46.0 63.0 36.6 137% 80% 46.0 68.8 33.3 150% 72%2006 50.8 73.3 38.3 144% 75% 50.8 79.7 34.8 157% 69%2007 38.0 56.1 27.9 148% 74% 38.0 62.9 24.2 166% 64%2008 65.7 88.8 53.3 135% 81% 65.7 94.7 49.8 144% 76%2009 38.9 51.3 32.0 132% 82% 38.9 55.8 29.5 143% 76%

Average 44.7 61.8 35.2 138% 79% 44.7 66.9 32.3 150% 72%

Original data non-sorted price curve Approximation based on sorted price curve

Source: own calculations based on EEX prices

37 Peak times are generally defined as the period from Monday to Friday 8 am-8 pm (in total 3120/3132 h a

year), off-peak times: Monday to Friday 8 pm-8 am on the next day and the weekends as well, baseload: Monday

to Sunday 0 am-0 pm (8760 h/8784 h p.a.), see EEX Products (2008b), p.6.

24

Nevertheless, these caveats are acceptable, as we will compare the valuation of power plant

portfolios with and without the recognition of margining, but always based on the same

modeling scenario for the dispatch of the power plants. Thus, the variation of the price

duration curve for the sensitivity analysis in section 4 will be done in a consistent manner. In

addition to this, the determination of the relevant prices of the commodities stems from

futures contracts, as outlined in section 3.5 below, and is not taken from the dispatch model.

Therefore, with regard to the determination of the spread of the peakload price to the baseload

price, we do not use the spread from the sPDC but instead model this spread as a stochastic

mean-reverting process.

3.5 Determination of the futures prices for commodities

Within the literature, a variety of possibilities exist to model the price development of futures

for commodities. In our case, we want to apply a method that offers the possibility to model

futures prices for a certain time period upfront the year of delivery (hedging period). Borchert

et al. (2006, p.123), for example, propose the application of forward-price-curve (FPC)

models that do not only model single price movements for each time step dt, but single- or

multifactor models for the determination of the complete FPC from the first relevant trading

day until maturity. Examples of single-factor models can be found in Clewlow/Strickland

(1999) and Schwarz (1997), who address especially the issue of the increasing volatility over

the trading period of the futures. Extensions of the single factor models are multi-factor

models, such as those introduced in Schwarz (1997), Koekkebakker/Ollmar (2001), and

Pilipovic (1998), which allow to address further aspects of futures price developments.

A central issue for the modeling of yearly cashflows of power plants is to receive the

average achieved electricity-, fuel- and CO2-certificate prices to determine the respective

yearly operating margin (see section 3.1.2) based on a two-year hedging period. To this end,

we use the volume-weighted average of all realized prices during the hedging period in

combination with a two-factor model.

To determine a futures price development, we first apply the arbitrage-free single-factor

model of Schwarz (1997). With this, we can write the FPC as a function of the spot market

prices, the volatility of the futures and spot prices σ as well as the mean-reversion factor k:

⎟⎟⎠

⎞⎜⎜⎝

⎛−+−−−+⋅= −−−−−− )1(

4)

4)(1(),(lnexp),),(( )(2

22)()( tTk

TtTktTk e

kkLeTtSeTttSF σσλ . (25)

Factor k, on the one hand, represents the rate at which the forward price approaches the spot

market price at the time of maturity. On the other hand, the mean-reversion rate of the spot

market prices to the long-term price level. t=0 represents the beginning of the hedging period

25

and T the day on which the delivery starts. The long-term price Lt for the future in the

Schwarz model is adjusted by the market price of energy risk λ and a factor σ2/4k (see

Clewlow/Strickland 2000, p.93). As we use a yearly cashflow model, with one volatility

figure for each delivery year, we simulate the volatility σ as time-dependent and log-normally

distributed, following a mean-reverting stochastic process (see section 3.4.3)38.

The single factor model of Schwarz allows a general movement of the futures prices

against the spot prices with an increasing impact at the end of the maturity and therefore

fulfils the no-arbitrage criteria. However, it leaves only little room for smaller movements in

the earlier part of the hedging period which might occur randomly, for example, due to

changes in market expectations for the delivery period39.

Thus, to account for smaller movements of the futures prices (including a mean-reverting

behavior) already at earlier stages of the hedging period, we adjust the model by a second

factor and impose a further movement based on a stochastic and time-dependent sinus

function onto the forward curve. In order not to disturb the general trend of the single factor

model towards the spot prices, we use a diminishing factor (1-e(-k(T-t)) towards the delivery

year:

)1()()sin(

)1(4

)4

)(1(

),(ln

exp),),(( )(

)(22

2)(

)(

tTk

tTk

TtTk

tTk

etdzt

ek

kLe

TtSe

TttSF −−

−−

−−

−−

−⋅⋅+

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

−+

−−−+⋅= β

σ

σλ . (26)

The factor β increases the amplitude of the sinus function and therefore gives a possibility to

modulate the futures price variation derived from the second factor at each point in time

individually for each of the commodities. To account for the high correlation between the

futures prices of one product for different delivery periods, we assume for simplification a

correlation of one for the stochastic processes dzi(t). Finally, we model the relevant price for

the product i with delivery in T for the valuation as volume-weighted prices, depending on the

hedging strategy f(t):

iTt

T

t

iT FtfF ,)( ⋅= ∑ . (27)

38 We modeled the futures price for each single delivery year as a separate product Fi(S(t),t,T). For simplification

of the notation, we left out the notification of the product i in the formulas shown. 39 In the chart shown in Appendix C, one can see that the futures prices (in this case, an electricity baseload

contract) for a certain delivery year generally follows the trend of the spot prices. However, it also has smaller

price changes that do not necessarily correspond to the spot price movements.

26

3.6 Parameterization of the market model

3.6.1 Spot price development

All prices in the market model are calculated in logarithms. The level of detail is based on

monthly data. We therefore use for all commodities the month-by-month changes of the EEX

commodity prices over the period 2007-2009, to derive the necessary volatilities (for CO2

only the NAP II period 2008-2009 is recognized). The distribution for the commodity price

processes was derived by a time series analysis for each of the commodities using a standard

“goodness-of-fit-test” (Anderson-Darling test40), contained in Crystal BallTM for the

distribution fitting on the data that was available from the EEX (see Appendix A). For the

commodities under consideration (electricity (baseload and peakload), coal, gas, CO2), we

assume a mean-reversion factor of the stochastic processes for the monthly average price to

the expected long-term level Lt (that we model as new entry costs, see below) of 0.3466,

representing a half-life41 for each commodity of 24 months42. For the mean-reversion

processes of the volatilities, we use a factor of one. Table 5 gives an overview of the

assumptions made.

Table 5: Major assumptions for the stochastic spot price processes

Product Mean-reversion level Assumed mean-reversion rate Distribution

Mean-reversion level of

volatility σ

Volatility σ(σ)

Mean-reversion

rate of volatility σ

Distribution

Electricity base Derived from NEC-Approach 0.3466 log-normal 0.209 0.081 1 log-normal

Peak premium over base price

Derived from Data series 2003-2009 - - 0.317 0.081 1 log-normal

Coal 71 €/t, inflated over the years 0.3466 log-normal 0.176 0.071 1 log-normal

Gas 17.5 €/MWh (th), inflated over the years 0.3466 log-normal 0.246 0.139 1 log-normal

CO2 17.2 €/t, inflated over the years 0.3466 log-normal 0.159 0.052 1 log-normal

Source: own assumptions

40 For reference, see Anderson/Darling (1952) and Duller (2008), pp.116ff. 41 The half-life of a price process represents the time until the price difference of the process, compared to the

expected long-term mean-reverting level of the commodity price, has decayed by half. It can be calculated by

t1/2 = ln 2/k , see Borchert et al. (2006), p.94. 42 A possibility to estimate the mean-reversion rate is by applying linear regression (see Skorodumov 2008).

However, due to a limited original data set for a thorough estimate on a monthly average price level, and the

generally high correlation between the commodities, we use the same assumption for all commodities.

27

In addition, we assumed a sustainable coal price level of 71 €/t in real terms, based on the

average coal price API#2 CIF ARA for the years 2007-200943. Correspondingly, we assumed

a sustainable real gas price level of 17.5 €/MWh44 based on our starting year for the

valuation. For the sustainable CO2 price level, we used the average spot price of the NAP II

period from Jan 2008 – Dec 2009 at 17.2 €/t (in real terms). To receive the nominal prices

over the valuation time period, we inflated the named price levels with 2% p.a. As natural gas

is traded based on the higher heating value (HHV), but efficiencies for power plants are

generally represented as efficiencies of the lower heating value (LHV), we convert our gas

prices by multiplying them by a factor of natural gas of roughly 1.11x45. With regard to the

sustainable level for the electricity prices, we use the necessary new entry cost level of a state-

of-the-art power plant. The new entry costs represent the average price level for a power plant

in €/MWh, that is necessary to cover the full costs of the expansion power plant assuming a

certain amount of full-load running hours46. For this study, we apply the stochastic prices for

coal, gas, and CO2 to determine the variable costs in combination with assumptions on (1) the

price-setting hours based on the expected full-load hours, (2) capital requirements (investment

volume), (3) capital costs, as well as (4) fixed and other variable costs (see Table 6).

The economic rationale behind this approach is our assumption that in the future the

power prices will have to reach at least a certain minimum value that will cover the costs of

the existing newly built power plants, otherwise the investments already made will not cover

their cost of capital. The approach is clearly a simplification. More sophisticated fundamental

models, that compare the expected supply and demand for a price determination, could

probably give a better educated guess about future developments based on more influencing

factors. However, the approach adopted offers a sufficiently accurate market model that

provides comparable results in a fairly stable market environment (only depending on the

stochastics in the commodity prices) in the beginning, which can then be transparently altered

in a sensitivity analysis to see the impacts on the original focus of this study.

43 Coal price notation as from EEX in $/t converted with the daily interbank FX rates from Bloomberg, non-

trading days assumed to have the same prices as the last trading day before. 44 Gas price notation as from EEX for the period of Jul 2007 – Dec 2009. For the period Jan 2007 – Jun 2007,

TTF prices from Bloomberg are used as an approximation. 45 A quite good explanation of HHV vs. LHV can be found in the European Fuel Cell Forum document

http://www.efcf.com/reports/E10.pdf . 46 New entry cost approximations are regularly published by the power generation companies, showing the

necessary electricity price to foster expansion investments into the respective power market (see, for example,

EDF 2008, pp.53-61 or E.ON IR1 2009, p.24).

28

http://www.efcf.com/reports/E10.pdf

Table 6: Major assumptions for new entry costs calculation (coal power plant)

Basis (2010) Further developmentInvestment volume in €/kW 1570 inflatedWACC pre tax 10% stablePre-tax capital service (annuity) 10.23% stableThermal efficiency 46% stableEconomic life time in years 40 stableFull load hours 7500 stableFixed costs in €/kW 37.7 inflatedFuel costs stochastic stochasticCO2 costs stochastic stochasticother variable costs in €/MWh 2.5 inflated

Source: own assumptions47

3.6.2 Future price development

For the monthly futures product for each single delivery year, we use the same mean

reversion rate as shown for the spot market prices (cf. Clewlow/Strickland 1999, p.6). For the

year-by-year change in the absolute level of the futures price, we use the volatilities as shown

in section 3.9. For the second factor in the futures price calculation, we assumed β = 2 for coal

and electricity, and β = 1 for CO2 and gas. According to the underlying forward price data48,

we found a slightly higher average peak price premium above baseload compared to the spot

market at dp/b = 0.36 (price difference in logarithms) that we used as long-term price premium.

For the volatility of the futures peak price premium, we find a factor of σp/b-premium = 0.02 and

a log-normal distribution. The interest rates are assumed to be stable, resulting in an assumed

constant inflation rate of 2% and a constant WACC for all periods.

3.7 Assumptions and data set for the power plant portfolio

Tables 7–11 summarize the assumed power plant portfolio and the included expansion

options (marked with “NB”) for our study with the major components for the valuation

analysis. Most parameters are our own estimates. However, the parameters are broadly in line

with other references: for parameters such as the lifetimes, depreciation periods, efficiencies,

CO2-free-allocation, and emission factors cf., e.g., Konstantin (2009, pp.280ff, 290). For the

investment costs, we made our own assumptions based on RWE data (RWE Investments

2009). For the fixed costs (operation & maintenance, personnel, insurance etc.) for the hard

coal-fired power plants (HCPs) and the gas-fired power plants (CCGTs), we assumed a

certain fixed cost degression for newer plants as a result of lower personnel requirements and

47 Investment costs coal: average from expected costs for PP Eemshaven (NL) and Wola (PL): €3.7 bn for 2360

MW, see RWE Investment (2009). 48 For the analysis of the peak price premia, we used the average daily settlement prices for the yearly futures

with delivery in 2007-2010 over the time period 24 months before the delivery year started.

29

operational improvements. For nuclear power plants (nukes) we estimated total fixed costs

(details as above but including nuclear waste management and decommissioning costs),

including further capital expenditures (capex) for maintenance of approx. 200 €/MW. Note

that the fixed costs must not include the cost of capital, because we first estimate the

operational cashflow, which we discount with the WACC. For the HCPs, the last expansion

option represents a power plant with the possibility of carbon capture and storage (CCS),

resulting in significantly higher investment costs and lower total efficiency. All Euro numbers

stated below are discounted to the starting year 2010. For the load factors of the run-of-river

plants, we used our own assumptions based on the data provided by E.ON for several power

plants in Germany49. To reflect potential changes in the water inflow from year to year, we

model the dispatch as a standard normally-distributed variable with the expected values in %

of the year and the corresponding standard deviations, as shown in Table 9. In addition, we

assume a correlation for the dispatch for all RoR-plants of unity.

For the sake of simplicity, we assumed only plants for electricity generation with one fuel

type, and without the possibility of co-generation or secondary fuels. Our date for discounting

is January 1, 2010. All expansion power plants are taken into account with their full

investment costs, regardless of the start of operation and possible building time periods before

2010. All fixed costs and other variable costs are inflated starting from the basis in 2010. For

fossil-fired power plants, we assume a reduction in the efficiency of 2% to the shown values

in order to account for the losses during the start-ups etc. The assumed equity ownership for

all plants is 100%.

Table 7: Hard coal power plants in the portfolio including expansion options Power Plant Coal_1 Coal_2 Coal_3 Coal_4_NB Coal_5_NB Coal_6_NB Coal_7_NBCapacity 1600 1400 3000 800 800 800 1200Year of commissioning 1975 1979 1990 2013 2014 2016 2019Lifetime 40 40 40 40 40 40 40End of life 2015 2019 2030 2053 2054 2056 2059Depreciation period 20 20 20 20 20 20 20Efficiency 37% 38% 43% 46% 48% 50% 41%Fuel emission factor 0.342 0.342 0.342 0.342 0.342 0.342 CCSEmission factor per MWh (el) 0.924 0.900 0.795 0.743 0.713 0.684 CCSDispatch in h before availability simulated simulated simulated simulated simulated simulated simulatedGeneral availability 90% 90% 90% 90% 90% 90% 90%Maintenance cycle 4 years 4 years 4 years 4 years 4 years 4 years 4 yearsFixed costs in €/kW (as of 2010) 45 €/kW 44 €/kW 40 €/kW 38 €/kW 38 €/kW 37 €/kW 45 €/kWFuel costs simulated simulated simulated simulated simulated simulated simulatedFuel transport costs (as of 2010) 6 €/t 7 €/t 8 €/t 8 €/t 8 €/t 8 €/t 5 €/tOther var. costs (as of 2010) 2.5 €/MWh 2.5 €/MWh 2.5 €/MWh 2.5 €/MWh 2.5 €/MWh 2.5 €/MWh 2.5 €/MWhFree CO2 allocation until 2012 84.4% 84.4% 84.4% - - - -Investment / other capital expenditure (value 2010) 1600 €/kW 1600 €/kW 1700 €/kW 2500 €/kW


49 Data base is publicly available from http://www.eon-schafft-transparenz.de: Load factor estimates and

availabilities based on average daily load factors and average amount of days running of selected run-of-river

plants over the period Oct 5, 2007 – Dec 31, 2009.

30

http://www.eon-schafft-transparenz.de/

Table 8: Gas-fired power plants in the portfolio including expansion options

Power Plant CCGT_1 CCGT_2 CCGT_3 CCGT_4_NB CCGT_5_NB CCGT_6_NB CCGT_7_NBCapacity 250 300 400 400 400 450 530Year of commissioning 1995 2000 2005 2012 2013 2014 2015Lifetime 30 30 30 30 30 30 30End of life 2025 2030 2035 2042 2043 2044 2045Depreciation period 20 20 20 20 20 20 20Efficiency (before start-up) 48% 52% 54% 59% 60% 60% 61%Fuel emission factor 0.202 0.202 0.202 0.202 0.202 0.202 0.202 Emission factor per MWh (el) 0.421 0.388 0.374 0.342 0.337 0.337 0.331 Dispatch in h before availability Simulated Simulated Simulated Simulated Simulated Simulated SimulatedGeneral availability 95% 95% 95% 95% 95% 95% 95%Maintenance cycle 3 years 3 years 3 years 3 years 3 years 3 years 3 yearsFixed costs in €/kW (as of 2010) 35 €/KW 34 €/kW 32 €/kW 30 €/kW 30 €/kW 30 €/kW 30 €/kWFuel costs Simulated Simulated Simulated Simulated Simulated Simulated SimulatedFuel transport/flexibility charges (in % of gas price) 15% 15% 15% 15% 15% 15% 15%

Other var. costs (as of 2010) 1 €/MWh 1 €/MWh 1 €/MWh 1 €/MWh 1 €/MWh 1 €/MWh 1 €/MWhFree CO2 allocation until 2012 84.4% 84.4% 84.4% - - - -Investment / other capital expenditure (value 2010) ~ 665 €/kW ~ 665 €/kW ~ 665 €/kW 800 €/kW 850 €/kW 850 €/kW 900 €/kW


Table 9: Run-of-river power plants in the portfolio including expansion options

Power Plant RoR_1 RoR_2 RoR_3 RoR_4_NB RoR_5_NB RoR_6_NB RoR_7_NBCapacity 300 220 250 150 100 100 100Year of commissioning 1980 1985 2000 2012 2013 2014 2015Lifetime 50 50 50 50 50 50 50End of life 2030 2035 2050 2062 2063 2064 2065Depreciation period 25 25 25 25 25 25 25Yearly expected dispatch in h before availability 75% 70% 77% 75% 72% 80% 78%

Standard deviation of dispatch (normal-distribution) +/- 3% +/- 3% +/- 3% +/- 3% +/- 3% +/- 3% +/- 3%

General availability 90% 90% 90% 90% 90% 90% 90%Maintenance cycleFixed costs in €/kW (1% of spec. Investment cost, 2010) 30 30 30 30 35 37 45

Other var. costs (e.g. water tax) 5 €/MWh 5 €/MWh 5 €/MWh 5 €/MWh 5 €/MWh 5 €/MWh 5 €/MWhInvestment / other capital expenditure (value 2010) 3000 €/kW 3000 €/kW 3700 €/kW 4500 €/kW

3000 3000 3000 3000 3500 3700 4500

assumed to be included in availability


Table 10: Lignite-fired power plants in the portfolio

Power Plant LGN_1 LGN_2 LGN_3Capacity 500 750 750Year of commissioning 1980 1985 1995Lifetime 35 35 35End of life 2015 2020 2030Depreciation period 20 20 20Efficiency 38% 39% 41%Fuel emission factor 0.410 0.410 0.410 Emission factor per MWh (el) 1.079 1.051 1.000 Dispatch in h before availability Simulated Simulated SimulatedGeneral availability 90% 90% 90%Maintenance cycle 4 years 4 years 4 yearsFixed costs in €/kW (as of 2010) 48 €/kW 45 €/kW 43 €/kWTotal fuel costs (as of 2010) 15 €/t 15€/t 14 €/tOther var. costs (as of 2010) 2 €/MWh 2 €/MWh 2 €/MWhFree CO2 allocation until 2012 84.4% 84.4% 84.4%Investment / other capital expenditure (value 2010) - - -


31

Table 11: Nuclear power plants in the portfolio

Power Plant Nuke_1 Nuke_2Capacity 2500 2500Year of commissioning 1985 1986Lifetime 35 35End of life 2020 2021Depreciation period 20 20Depreciation like capex like capexDispatch in h before availability 8760 8760General availability 90% 90%Maintenance cycle yearly yearlyFixed costs in €/kW (as of 2010) 150 €/kW 150 €/kWVar. costs incl. fuel (2012) 2 €/MWh 2 €/MWhInvestment / other capital expenditure (value 2010) 50 €/kW 50 €/kW


3.8 Further assumptions for the margin calculation

3.8.1 Additional Margin

For the Additional Margin parameters, we use the latest available parameter at the time of

conducting this study from May 201050: AMP: electricity: 2.4 €/MWh (base); 3.0 €/MWh

(peak); coal: 5.9 $/t; natural gas: 1.7 €/MWh (th); CO2: 1.6 €/t; EMF: electricity: 2.5x; coal:

1x; natural gas: 1.5x; CO2: 1x.

3.8.2 Variation Margin

Besides the hedging volumes for the relevant delivery years, which we derive from our

market model, another important input is the assumptions on the volatilities for the Variation

Margin calculations. Generally, we differentiate between the volatility in the hedging period

(two years ahead of delivery, one year ahead of delivery, both on a monthly basis) and the

volatility in the delivery year, for which we use the spot price volatility. Table 12 shows the

volatility assumptions based on EEX market data for the Variation Margin calculation51. In

addition to this, we assume a MaR calculation based on a standard-normally distributed

margin requirement with a 99% percentile, resulting in a k-factor of approx. 2.326. Due to

space limitations, the issue of non-symmetrical distributions and their impact on the portfolio

optimization is omitted from this study.

50 See ECC Parameters (2010). 51 For each commodity, we derived these input parameters as averages from the yearly averages on daily

notations from 2006–2009 for the products with delivery in 2008–2012.

32

Table 12: Volatilities of futures and Variation Margin calculations

Period ProductMean-reversion level of volatility

σ

Mean-reversion

rate of volatility σ

Volatility σ(σ) Distribution

Electricity 0.06 1 0.01 log-normalCoal 0.09 1 0.02 log-normalGas 0.11 1 0.03 log-normalCO2 0.16 1 0.00 log-normalElectricity 0.21 1 0.08 log-normalCoal 0.18 1 0.07 log-normalGas 0.25 1 0.14 log-normalCO2 0.16 1 0.05 log-normal

Hedging period

Delivery period (analogous to spot prices)


4 Empirical analysis and results

4.1 NPV calculation scenarios and results

For our portfolio optimization analysis, we run a Monte-Carlo simulation with 10,000 draws

to derive the expected NPVs, the standard deviation, the relevant percentiles of the values,

and the value distributions of the “operative business”.

In addition, we calculate as well the corresponding figures for the risk capital

requirements for the AM and the VM for all existing power plants and expansion options in

our example portfolio. As a sensitivity, we estimate the impact of different market

environments on the risk capital requirements for power plants and possible subsequent

changes in the optimal portfolio choices. For this we keep all parameters of our simulation

constant (ceteris paribus assumption) besides the underlying normalized sPDC form, which

we use to calculate the dispatch for the years.

-150%

-100%

-50%

0%

50%

100%

150%

200%

250%

300%

1 401 801 1201 1601 2001 2401 2801 3201 3601 4001 4401 4801 5201 5601 6001 6401 6801 7201 7601 8001 8401

2007 2009 Curve based on hourly median 02-09

% of Baseload price

hour

Figure 7: Applied sPDCs for the simulation (normalized to the respective yearly baseload prices) Source: own compilation based on EEX data

33

Our Base Case is a curve derived from the hourly median of all sPDC over the years 2002-

2009 for the German market. Scenario 1 (Sc07) uses the German sPDC of the year 2007;

Scenario 2 (Sc09) uses the sPDC of the year 2009. Figure 7 shows the differences between

the curves. The Sc07 uses a curve that is significantly steeper for a broader range of hours at

the beginning of the curve. Especially for the spread-steered power plants this leads to a

significant reduction of the generation volume accompanied by an increase of the realized

spreads. In contrast, the Sc09 has a comparable steepness for the first 3500 hours to our Base

Case but then the curve becomes significantly flatter, resulting in increasing load factors and a

reduction in the realized spreads.

By using a linear hedging function over a two–year time horizon (for a description cf.

Lang/Madlener 2010), our model leads to the following results for the single power plants

depicted in Table 1352. The implied changes of the total generation volumes in the price

duration curve scenarios influence the margin needs for the coal, gas, and lignite-fired power

plants. As we keep all other parameters constant, the effect works in the same direction for all

power plants. Comparing now the total margining requirements for the expansion power

plants (in our example with their investment costs), we can see that there is a relative

advantage of coal-fired power plants compared to the CCGTs. Their margining requirements

are between 5-8% of the investment costs, compared to 13-14% of the CCGTs (Base Case).

These results correspond quite well to the results from our previous study (Lang/Madlener

2010) with comparable percentages for coal-fired (6-9%) and gas-fired power plants (16-

18%), respectively.

The values for the run-of-river plants stretch out between approx. 4-5%, due to the

relatively high investment costs. However, if we also take the NPV (incl. the value for

margining) without the investments53, the difference between coal-fired and gas-fired power

plants shrinks significantly. Valuewise, the scenarios only influence the merit-order-

dependent power plants (coal, gas, lignite), due to the stable output for the nuclear and the

run-of-river plants. In Sc07 we can see the volume indicated value losses for all these power

plants.

For the Base Case, compared to Sc09, the numbers for the CCGTs and the expansion

coal-fired power plants remain quite stable. However, we find some significant value

increases for the lignite-fired and the existing coal-fired power plants. In the following

section, we use the results from above for further portfolio analysis.

52 All values represent expected values derived from our model (note that unless stated differently all values are

given in million €). 53 In order to obtain the NPV without investment costs, we simply add the discounted investments to the NPV.

34

Table 13: Results from NPV simulation model (Base Case )

Power plant

Capacity in MW

Discounted investment

in €/kW

Avg. Full-load-hours

p.a. in h

Avg. discounted

clean spread in €/MWh

Avg. discounted

gross margin p.a.

NPV Std.Dev. NPV AM VM Total

NPV

Std. dev. Total NPV

Total margin in % of

investment


investment + NPV

CCGT1 250 3,579 21 19 100 12 (7) (6) 86 12 13.7%CCGT2 300 4,089 24 29 205 16 (11) (10) 184 15 10.3%CCGT3 400 4,339 25 43 361 22 (16) (16) 329 21 9.1%

NB_CCGT4 400 677 4,939 26 52 170 22 (18) (20) 133 21 13.9% 8.5%NB_CCGT5 400 672 5,054 26 54 164 21 (17) (19) 128 20 13.5% 8.4%NB_CCGT6 450 628 5,054 26 60 181 22 (18) (21) 142 21 13.6% 8.3%NB_CCGT7 530 621 5,169 27 73 212 25 (20) (24) 168 24 13.3% 8.1%

HC1 1600 4,051 25 159 478 77 (22) (28) 428 73 10.4%HC2 1400 4,162 25 146 607 78 (29) (37) 541 74 10.9%HC3 3000 4,873 27 392 2,881 199 (107) (148) 2,626 188 8.8%

NB_HC4 800 1,310 5,295 28 117 4 46 (33) (53) (83) 43 8.2% 8.2%NB_HC5 800 1,310 5,545 28 125 24 44 (31) (53) (60) 42 8.0% 7.8%NB_HC6 800 1,265 5,770 29 132 43 41 (28) (50) (35) 38 7.7% 7.4%NB_HC7 1200 1,611 6,735 32 256 (99) 56 (29) (74) (203) 54 5.3% 5.6%LGN1 500 6,311 22 70 269 40 (13) (14) 242 39 10.0%LGN2 750 6,309 23 111 614 69 (32) (33) 549 67 10.6%LGN3 750 6,585 26 128 1,140 75 (23) (62) 1,054 72 7.5%Nuke1 2500 7,884 55 1,077 3,533 171 (37) (175) 3,321 166 6.0%Nuke2 2500 7,884 55 1,077 3,776 176 (39) (187) 3,549 171 6.0%ROR1 300 5,913 52 92 781 19 (5) (24) 752 19 3.7%ROR2 220 5,518 52 63 597 14 (4) (19) 575 13 3.7%ROR3 250 5,519 52 72 891 16 (5) (25) 860 16 3.4%

NB_ROR4 150 2,537 5,937 52 46 161 10 (3) (16) 142 9 5.1% 3.6%NB_ROR5 100 2,960 5,711 52 30 30 6 (2) (10) 18 6 4.0% 3.6%NB_ROR6 100 2,983 6,358 52 33 48 6 (2) (11) 34 6 4.5% 3.9%NB_ROR7 100 3,458 6,210 52 32 (30) 6 (2) (10) (42) 6 3.5% 3.9%

Base Case (expected values)

Table 14: Results from NPV simulation model (Sc07)

Power plant

Capacity in MW


in €/kW


p.a. in h

Avg. discounted


Avg. discounted

gross margin p.a.

NPV Std.Dev. NPV AM VM Total

NPV

Std. dev. Total NPV


investment


investment + NPV

CCGT1 250 2,954 23.6 17 87 12 (6) (5) 75 12 13.1%CCGT2 300 3,390 26.6 27 187 16 (9) (9) 169 16 9.5%CCGT3 400 3,615 27.7 40 334 23 (14) (14) 307 22 8.2%

NB_CCGT4 400 677 4,170 29.9 50 148 23 (15) (17) 116 21 11.9% 7.7%NB_CCGT5 400 672 4,280 30.0 51 144 22 (14) (17) 113 21 11.5% 7.5%NB_CCGT6 450 628 4,278 30.0 58 160 23 (15) (18) 127 22 11.6% 7.4%NB_CCGT7 530 621 4,387 30.3 70 189 26 (17) (21) 151 25 11.4% 7.2%

HC1 1600 3,374 27.7 149 418 81 (19) (21) 378 77 9.4%HC2 1400 3,479 28.2 137 541 82 (25) (28) 488 78 9.8%HC3 3000 4,150 30.4 378 2,704 217 (93) (126) 2,485 204 8.1%

NB_HC4 800 1,310 4,580 31.1 114 (31) 50 (29) (47) (107) 47 7.3% 7.5%NB_HC5 800 1,310 4,854 31.5 122 (5) 48 (28) (48) (80) 45 7.2% 7.3%NB_HC6 800 1,265 5,118 31.7 130 20 45 (25) (46) (51) 42 7.0% 6.9%NB_HC7 1200 1,611 6,447 33.1 256 (107) 57 (28) (70) (205) 55 5.1% 5.4%LGN1 500 5,788 22.3 64 241 45 (12) (13) 216 43 10.4%LGN2 750 5,838 23.4 102 556 78 (30) (31) 495 75 11.0%LGN3 750 6,222 25.9 121 1,070 85 (22) (59) 988 81 7.6%Nuke1 2500 7,884 54.6 1,077 3,535 172 (37) (175) 3,322 167 6.0%Nuke2 2500 7,884 54.7 1,077 3,777 176 (39) (187) 3,550 171 6.0%ROR1 300 5,914 51.8 92 781 20 (5) (24) 752 19 3.7%ROR2 220 5,520 51.9 63 597 14 (4) (19) 575 14 3.7%ROR3 250 5,519 51.9 72 891 16 (5) (25) 860 16 3.4%

NB_ROR4 150 2,537 5,938 52.0 46 161 10 (3) (16) 142 9 5.1% 3.6%NB_ROR5 100 2,960 5,712 52.0 30 30 6 (2) (10) 18 6 4.0% 3.6%NB_ROR6 100 2,983 6,359 52.0 33 48 6 (2) (11) 34 6 4.5% 3.9%NB_ROR7 100 3,458 6,211 52.0 32 (30) 6 (2) (10) (42) 6 3.5% 3.9%

Scenario 2007 (expected values)

35

Table 15: Results from NPV simulation model (Sc09)

Power plant

Capacity in MW


in €/kW


p.a. in h

Avg. discounted


Avg. discounted

gross margin p.a.

NPV in mio. €

Std.Dev. NPV in mio.€

AM in mio.€

VM in mio.€

Total NPV in mio.€

Std. dev. Total

NPV in mio.€


investment


investment + NPV

CCGT1 250 4,034 19.0 19 97 13 (8) (7) 81 12 16.2%CCGT2 300 4,824 20.2 29 204 16 (13) (12) 179 15 12.3%CCGT3 400 5,172 20.7 43 360 22 (19) (20) 321 21 10.8%

NB_CCGT4 400 677 5,850 22.1 52 168 21 (21) (23) 124 20 16.3% 10.1%NB_CCGT5 400 672 5,958 22.3 53 161 20 (19) (23) 118 19 15.7% 9.8%NB_CCGT6 450 628 5,958 22.3 60 178 22 (20) (25) 133 21 15.9% 9.8%NB_CCGT7 530 621 6,058 22.6 73 208 25 (23) (28) 158 24 15.4% 9.4%

HC1 1600 4,774 21.0 161 501 80 (26) (29) 446 75 11.0%HC2 1400 4,920 21.2 146 626 78 (34) (40) 552 73 11.9%HC3 3000 5,670 23.0 390 2,921 187 (123) (170) 2,628 176 10.0%

NB_HC4 800 1,310 6,006 24.2 116 0 44 (37) (60) (97) 42 9.3% 9.3%NB_HC5 800 1,310 6,180 25.0 124 21 43 (35) (60) (73) 40 9.0% 8.8%NB_HC6 800 1,265 6,326 25.8 131 41 39 (30) (57) (46) 37 8.6% 8.2%NB_HC7 1200 1,611 6,917 30.9 256 (99) 55 (30) (74) (204) 53 5.4% 5.7%LGN1 500 6,721 22.2 75 291 34 (14) (15) 262 33 9.8%LGN2 750 6,666 23.3 117 657 60 (33) (35) 589 58 10.4%LGN3 750 6,835 25.9 133 1,187 67 (24) (64) 1,099 64 7.4%Nuke1 2500 7,884 54.6 1,076 3,529 170 (37) (175) 3,317 165 6.0%Nuke2 2500 7,884 54.6 1,077 3,772 174 (39) (186) 3,546 169 6.0%ROR1 300 5,912 51.8 92 781 20 (5) (24) 752 19 3.7%ROR2 220 5,518 51.9 63 597 14 (4) (19) 575 14 3.7%ROR3 250 5,518 51.9 72 890 17 (5) (25) 860 16 3.4%

NB_ROR4 150 2,537 5,937 52.0 46 161 10 (3) (16) 142 9 5.1% 3.6%NB_ROR5 100 2,960 5,711 52.0 30 30 6 (2) (10) 18 6 4.0% 3.6%NB_ROR6 100 2,983 6,358 52.0 33 48 6 (2) (11) 34 6 4.5% 3.9%NB_ROR7 100 3,458 6,210 52.0 32 (30) 6 (2) (10) (42) 6 3.5% 3.9%

Scenario 2009 (expected values)

4.2 Impact of margining on the efficient frontier

4.2.1 Alternative scenarios influencing the underlying economic generation

The data mentioned above in conjunction with the corresponding correlations (see Appendix

C) between the power plants served as input for the portfolio optimization. For this purpose,

we kept the existing assets for all portfolio combinations stable and altered only the expansion

possibilities with a binary decision to build or not to build54. In addition, we assume a

company that is unrestricted with regard to the funds for the planned investments and the

necessary margining payments.

The introduction of the value of margining cashflows for the total portfolio generally

leads to a significant downward shift of the general portfolio values and thus also to a

corresponding shift of the efficient frontier of the portfolio (Figure 8). Furthermore, we can

see that not only the absolute value level was changed but also the form of the efficient

frontier. By recognizing the value for margining (total value), the efficient frontier remains in

a much smaller range for the standard deviation (€874–930 million) compared to the single-

value case, in which we ignore the margining value (€910–1,065 million). Also, the NPV

range for the efficient frontier was significantly reduced from €16,224–17,253 million (values

54 Resulting in 212 = 4096 portfolio combination possibilities.

36

without margining) to €15,095–15,858 million (total value including margining), indicating a

change in the optimal set of power plants under recognition of margining in the total values.

14,500

14,750

15,000

15,250

15,500

15,750

16,000

16,250

16,500

16,750

17,000

17,250

17,500

850 875 900 925 950 975 1,000 1,025 1,050 1,075 1,100

NPV w/o margining NPV w/ margining Max NPV w/o margining Max NPV w/ margining

Efficient frontier

NPV in million €

Std. dev. in million €

Figure 8: Efficient frontiers of portfolio with and without margining Source: own compilation

However, looking at the efficient frontiers of our Base Case in more detail, we can see that

the recognition of the margining cashflows in the portfolio value only transfers the efficient

frontier to a lower value level, but that the asset combinations within the efficient portfolios

do not change.

14,500

15,000

15,500

16,000

16,500

17,000

17,500

850 875 900 925 950 975 1,000 1,025 1,050 1,075 1,100

NPV w/o margining NPV w/o margining Corresponding portfolios to values w/o margining

inefficient portfolios

CCGT: 4,5,6,7Coal: 4,5,6RoR: 4,5,6

CCGT: 4,5,6,7Coal: 5,6RoR: 4,5,6

CCGT: 4,5,6,7Coal: 6RoR: 4,5,6

CCGT: 4,5,6,7Coal: -RoR: 4,5,6

CCGT: 4,5,6,7Coal: -RoR: 4,6

CCGT: 5,6,7Coal: -RoR: 4,6

CCGT: 6,7Coal: -RoR: 4,6

CCGT: 6,7Coal: -RoR: 4

CCGT: 7Coal: -RoR: 4,6

CCGT: 7Coal: -RoR: 4

CCGT: -Coal: -RoR: 4

CCGT: -Coal: -RoR: -


NPV in million €

Figure 9: Effect of recognizing margining in the portfolio optimization (Base Case) Source: own compilation

37

The only exemptions are, in our example, the coal power plants, which are no longer part of

the efficient portfolios as a consequence of the negative NPV after recognizing the margining

requirements (see Table 13 and Figure 9). This result can also be seen for value changes

resulting from changes in the generation volumes in Sc07 and Sc09 (see figures in Appendix

B). Although there are quite some significant differences on the values and the margin

requirements between the scenarios, the recognition of the margining values did neither

change the NPV- and standard deviation rankings between the expansion plants nor was it

significant enough to profoundly change the correlation matrices between the power plants, as

shown in Table 16 below55.

Table 16: Correlation of NPVs w/ and w/o margining (model output)

(a) Base Case NPV w/o margining BC NPV_CCGT NPV_COAL NPV_LGN NPV_NUKE NPV_ROR

NPV_CCGT 1.0000 0.8676 0.6562 0.6545 0.7970NPV_COAL 1.0000 0.8872 0.8311 0.8508NPV_LGN 1.0000 0.9161 0.7293

NPV_NUKE 1.0000 0.7233NPV_ROR 1.0000

NPV w/ margining BC Total_CCGT Total_COAL Total_LGN Total_NUKE Total_RORTotal_CCGT 1.0000 0.8689 0.6542 0.6581 0.8021Total_COAL 1.0000 0.8839 0.8294 0.8488Total_LGN 1.0000 0.9175 0.7293

Total_NUKE 1.0000 0.7242Total_ROR 1.0000

(b) Sc2007 NPV w/o margining 07 NPV_CCGT NPV_COAL NPV_LGN NPV_NUKE NPV_ROR


NPV_NUKE 1.0000 0.7241NPV_ROR 1.0000

NPV w/ margining 07 Total_CCGT Total_COAL Total_LGN Total_NUKE Total_RORTotal_CCGT 1.0000 0.8451 0.6154 0.6195 0.7570Total_COAL 1.0000 0.8747 0.8188 0.8412Total_LGN 1.0000 0.9048 0.7126


(c) Sc2009 NPV w/o margining 09 NPV_CCGT NPV_COAL NPV_LGN NPV_NUKE NPV_ROR


NPV_NUKE 1.0000 0.7194NPV_ROR 1.0000

NPV w/ margining 09 Total_CCGT Total_COAL Total_LGN Total_NUKE Total_RORTotal_CCGT 1.0000 0.8697 0.6784 0.6632 0.8042Total_COAL 1.0000 0.8919 0.8297 0.8452Total_LGN 1.0000 0.9376 0.7450


55 For the sake of transparency, we have summarized the correlations of the single plants (see Appendix C) to the

level of fuel types.

38

This means for our chosen scenarios that, despite the relative advantage of the coal-fired

power plants compared to the CCGTs with regard to the margining requirements and the

relevant investment volume, and although the standard deviations for the NPV with

margining changed slightly, compared to the one for the NPV without margining (see Tables

13-15), there is no impact on the portfolio sequence on the efficient frontier when margining

is considered. This outcome remains, as long as the overall value of each asset does not turn

negative and as long as the ranking between the NPVs stays the same. An exemption of this

would only be given in a direct comparison between two power plants with the same NPV in

the beginning and different margining requirements, which is not the case in this example.

4.2.2 Alternative scenarios influencing the underlying calculation of the Variation Margin

In 4.1 we covered the effect of the margining on the efficient portfolio by using different

volume scenarios with altered sPDC. To complete the view, we now keep the volumes

constant, but we assume an investor who believes in higher volatilities for the Variation

Margin calculations56. For the simulation, we kept all other parameters equal, but changed the

assumed volatilities for the margin calculations in the hedging years t-2 and t-1 to the same

volatility that we assume for the delivery year (see Table 12). These steps result in

significantly higher VM requirements and correspondingly, in a lower total NPV and higher

standard deviation for each power plant, as depicted in Figure 10.

13,500

14,000

14,500

15,000

15,500

16,000

16,500

800 850 900 950 1,000

NPV w/ margining Corresponding portfolios to values with new volatility NPV w/ margining , new volatility

CCGT: 4,5,6,7Coal: ‐RoR: 4,5,6

CCGT: 4,5,6,7Coal: ‐RoR: 4,6

CCGT: 4,5,6,7Coal: ‐RoR: 4CCGT: 5,6,7

Coal: ‐RoR: 4,6

CCGT: 5,6,7Coal: ‐RoR: 4

CCGT: 6,7Coal: ‐RoR: 4,6CCGT: 5,7

Coal: ‐RoR: 4

CCGT: 7Coal: ‐RoR: 4,6

CCGT: 7Coal: ‐RoR: 4

CCGT: ‐Coal: ‐RoR: 4,6CCGT: ‐

Coal: ‐RoR: 4CCGT: ‐

Coal: ‐RoR: ‐


NPV in million €

Effect of higher volatility forvariation margin calculation

Figure 10: Effect of a higher Variation Margin through higher volatility (compared to Base

Case) Source: own compilation

56 As the volatilities are also used as a multiplier in the margin calculations (see section 3.3.2), this has the same

effect as a change in the assumed confidence level.

39

Still, the sequence of the efficient portfolios remains unchanged for this scenario compared to

the Base Case. The reason is given by the minor influence of the higher VM changes on the

standard deviation of the total NPV (Table 17), the stable value ranking and the only small

changes on the correlations between the power plants (Table 18).

Table 17: Comparison between VM and total NPV of Base Case vs. Base Case with higher VM

volatility in million €

Power plant VM Std. dev. VM

Total NPV

Std. dev. Total NPV

VM Std. dev. VM

Total NPV

Std. dev. Total NPV

NB_CCGT4 20 - 1.3 133 20.5 47 - 4.3 99 23.0 NB_CCGT5 19 - 1.3 128 19.6 46 - 4.1 95 21.9 NB_CCGT6 21 - 1.4 142 21.0 49 - 4.4 107 23.4 NB_CCGT7 24 - 1.6 168 23.7 56 - 5.0 128 26.5 NB_HC4 53 - 3.4 83 - 43.4 106 - 6.8 136 - 44.0 NB_HC5 53 - 3.4 60 - 41.7 107 - 6.6 114 - 42.4 NB_HC6 50 - 3.1 35 - 38.4 102 - 6.1 86 - 39.2 NB_HC7 74 - 3.0 203 - 53.9 148 - 7.9 277 - 55.0 NB_ROR4 16 - 0.7 142 9.3 32 - 1.3 127 9.5 NB_ROR5 10 - 0.4 18 5.7 20 - 0.8 8 5.8 NB_ROR6 11 - 0.5 34 5.9 22 - 0.9 24 6.1 NB_ROR7 10 - 0.5 42 - 5.5 21 - 0.8 52 - 5.6

Base Case, higher volatilityBase Case

Source: model output

Table 18: Value correlations of Base Case vs. Base Case and higher VM volatility NPV w/ margining BC Total_CCGT Total_COAL Total_LGN Total_NUKE Total_ROR

Total_CCGT 1.0000 0.8689 0.6542 0.6581 0.8021Total_COAL 1.0000 0.8839 0.8294 0.8488Total_LGN 1.0000 0.9175 0.7293


NPV w/ margining BC, changed Volatitlity Total_CCGT Total_COAL Total_LGN Total_NUKE Total_ROR




4.3 Comparison of relative portfolio values

So far, we have only compared the absolute values of the portfolio for which power plants

with a larger capacity and comparably higher values (or lower in the case of negative values)

may dominate the effects. To mitigate this issue, we will now compare the results by looking

at a relative NPV (in €/kW) for the portfolios. When the portfolio optimization is done based

on relative values in €/kW, the optimal portfolio composition looks somewhat different

40

(Figure 11), as, for example, also combinations with the coal-fired power plants are

considered in the efficient portfolios, including the recognition of margining cashflows.

650

700

750

800

850

900

950

1,000

1,050

1,100

1,150

49 51 53 55 57 59 61 63 65

NPV w/ margining Corresponding portfolios to values w/o margining NPV w/o margining

CCGT: -Coal: -RoR: -

CCGT: -Coal: -RoR: 4

Std. dev. in €/kW

NPV in €/kW CCGT: 7Coal: -RoR: 4

CCGT: 6,7Coal: -RoR: 4,6

CCGT: 5,6,7Coal: -RoR: 4

CCGT: 5,6,7Coal: -RoR: 4,5,6

CCGT: 4,5,6,7Coal: -RoR: 4,6

CCGT: 7Coal: 7RoR: 4

CCGT: 5,6,7Coal:7RoR: 4,6

CCGT: 5,6,7Coal:6,7CCGT:

4,5,6,7Coal: 5,6,7

CCGT:6,7Coal: 6RoR: 4

CCGT: 5,6,7Coal: 7

CCGT: 6,7Coal: 7RoR: 4

CCGT: 7Coal: 7RoR: 4,6

CCGT: 4,5,6,7Coal: 6,7RoR: 4,5,6,7

CCGT: 4,5,6,7Coal: 4,5,6,7

CCGT: 6,7Coal: 6,7RoR: 4

Effect of the recognition of margining cashflows

Figure 11: Effect of margining recognition based on values in €/kW (Base Case) Source: own compilation

However, the general movement of the efficient frontier is the same as in the original Base

Case: the efficient frontier is only transferred to a lower value level, but the asset

combinations within the efficient portfolios do not change in this view.

4.4 Sensitivity with regard to commodity prices

For the next sensitivity check, we now change our Base Case by using different long-term

commodity prices for coal and gas, by reducing the long-term mean-reverting level of coal by

10%, and by increasing the mean-reverting level of gas by 15%. In addition to this, we

assume a 1% overyield above capital costs in our new entry cost calculation, resulting in a net

increase in the long-term mean-reverting level for the electricity base price of ~0.5 €/MWh

(including the lower coal costs). By doing so, we are changing the relationship of the power

plant values of the different fuel types: in the original Base Case we stated a scenario in which

the gas-fired power plants performed better than the coal-fired ones. Now, in the new Base

Case, we develop a scenario that favors coal-fired power plants. Table 19 gives an overview

of the new values. Running our Monte Carlo simulation with the optimization of the efficient

frontier for these values, the results change significantly, compared to the original Base Case

(Figure 12). More specifically, due to the change of the power plant values and the

41

corresponding ranking between them, some portfolios that have been on the efficient frontier

for an NPV without the recognition of margining, are now below it.57

Table 19: Expected power plant values with and without changes in commodity prices in million €

Power plant NPV Std. dev. NPV

Total margin

Total NPV

Std. dev. Total NPV

NPV Std. dev. NPV

Total margin

Total NPV

Std. dev. Total NPV

NB_CCGT4 170 22 (38) 133 21 59 19 (32) 27 18 NB_CCGT5 164 21 (36) 128 20 58 18 (31) 27 17 NB_CCGT6 181 22 (39) 142 21 68 19 (33) 35 19 NB_CCGT7 212 25 (44) 168 24 85 22 (37) 47 21 NB_HC4 4 46 (86) 83 - 43 146 45 (93) 53 42 NB_HC5 24 44 (84) 60 - 42 159 43 (91) 68 40 NB_HC6 43 41 (78) 35 - 38 164 39 (84) 80 37 NB_HC7 (99) 56 (103) 203 - 54 109 54 (106) 3 52 NB_ROR4 161 10 (19) 142 9 166 9 (20) 147 9 NB_ROR5 30 6 (12) 18 6 33 6 (12) 21 5 NB_ROR6 48 6 (13) 34 6 51 6 (13) 38 6 NB_ROR7 (30) 6 (12) 42 - 6 (27) 5 (12) (39) 5

Base Case Base Case II, new commodity prices

Source: model output; expansion options only

This means that, due to the change in the underlying commodity price scenario, the

recognition of margining cashflows in the portfolio valuation would alter the choice of an

investor with regard to the efficient portfolio.

15,500

16,000

16,500

17,000

17,500

18,000

800 825 850 875 900 925 950 975 1,000 1,025 1,050



NPV in million €


CCGT: 4,5,6,7Coal: 4,5,6,7RoR: 4,6

CCGT: 5,6,7Coal: 4,5,6,7RoR: 4,5,6

CCGT: 5,6,7Coal: 4,5,6,7RoR: 4,6

CCGT: 4,5,6,7Coal: 5,6,7RoR: 4,5,6CCGT: 5,6,7

Coal: 5,6,7RoR: 4,5,6

CCGT: 5,6,7Coal: 5,6,7RoR: 4,6

CCGT: 6,7Coal: 5,6,7RoR: 4,6

CCGT: 7Coal: 5,6,7RoR: 4,5,6

CCGT: Coal: 6,7RoR: 4,5,6

CCGT: 4Coal: 6,7RoR: 4,6

Comparision of selected portfolio with and without the recognition of margining cashflows

Figure 12: Efficient frontiers w/ and w/o margining (Base Case, changed commodity prices) Source: own compilation

57 For details of the portfolio values of the efficient frontiers, see Appendix D.

42

The main differences of the input parameters for this simulation run compared to the original

Base Case are only the commodity prices and the resulting value differences for the power

plant portfolios. Other parameters, such as the standard deviation per plant (Table 19) or also

the correlations between the power plant values (Table 20), remain quite stable.

Table 20: Correlation between power plants (aggregated) for adjusted Base Case

NPV w/o margining BC, changed Commodities Total_CCGT Total_COAL Total_LGN Total_NUKE Total_ROR


NPV_NUKE 1.0000 0.7154NPV_ROR 1.0000

NPV w/ margining BC, changed Commodities Total_CCGT Total_COAL Total_LGN Total_NUKE Total_ROR




4.5 Replacement of the standard deviation by the total margin

Finally, we analyze the impact of margining on the efficient frontier when the risk parameter

from the x-axis is changed from standard deviation to the total margining requirements. We

use again the data set introduced in section 4.4 with the adjusted commodity prices.

Analogously to the standard deviation, we calculate the portfolio margin under recognition of

the margin correlations between the different power plants. Table 21 gives a summary of the

correlations used 58 of the total margin on fuel type level. Although the correlations are not as

strong as the ones for the power plant values, the generally strong dependency between the

values remains.

Table 21: Correlation between power plants (aggregated) for adjusted Base Case

Correlation total margin, summary TM_CCGT TM_COAL TM_LGN TM_NUKE TM_ROR

TM_CCGT 1.0000 0.7139 0.5525 0.4321 0.5513TM_COAL 1.0000 0.8562 0.5793 0.6857TM_LGN 1.0000 0.7623 0.7024

TM_NUKE 1.0000 0.7702TM_ROR 1.0000


The switch in the risk metrics from a market risk perspective (represented by the standard

deviation) to a risk capital view for margining may imply a change in the efficient set of 58 For a detailed correlation table per power plant, see Appendix C.

43

portfolios. In Table 22 we compare the portfolio set-up on the efficient frontiers (including

margining) of the twelve portfolios with the highest NPV for the two risk types. It is clear that

the margining requirements and the standard deviation of a power plant must have a strong

correlation, as both of them stem from the same degree of uncertainty of the market

parameters (i.e. the commodity price volatility) and representations of the generation

volumes. Thus, the ranking of the efficient portfolio is more or less equal, independently of

the chosen risk parameter. However, in one of the portfolio combinations, the corresponding

standard deviations and the total margin differ (although to a minimal extent), leading to a

changed power plant combination for this portfolio on the efficient frontier.

Table 22: Portfolio ranking for different risk metrics

Portfolio rank on the efficient frontier

Total margin

Std.dev. of NPV

NPV w/ margining

Portfolio combination (Total margin)

Std.dev. of NPV

Total margin

NPV w/ margining

Portfolio combination (Std. dev.)

1 1,327.6 16,311.1 CCGT: 4,5,6,7Coal: 4,5,6,7RoR: 4,5,6

995.05 16,311.1 CCGT: 4,5,6,7Coal: 4,5,6,7RoR: 4,5,6

2 1,274.4 16,307.8 CCGT: 4,5,6,7Coal: 4,5,6RoR: 4,5,6

973.70 16,307.8 CCGT: 4,5,6,7Coal: 4,5,6RoR: 4,5,6

3 1,266.0 16,286.9 CCGT: 4,5,6,7Coal: 4,5,6RoR: 4,6

969.93 16,286.9 CCGT: 4,5,6,7Coal: 4,5,6RoR: 4,6

4 1,250.4 16,281.1 CCGT: 5,6,7Coal: 4,5,6RoR: 4,5,6

959.33 16,281.1 CCGT: 5,6,7Coal: 4,5,6RoR: 4,5,6

5 1,242.0 16,260.20 CCGT: 5,6,7Coal: 4,5,6RoR: 4,6

955.58 16,260.2 CCGT: 5,6,7Coal: 4,5,6RoR: 4,6

6 1,200.0 16,254.6 CCGT: 4,5,6,7Coal: 5,6RoR: 4,5,6

942.32 16,254.6 CCGT: 4,5,6,7Coal: 5,6RoR: 4,5,6

7 1,191.6 16,233.7 CCGT: 4,5,6,7Coal: 5,6RoR: 4,6

938.64 16,233.7 CCGT: 4,5,6,7Coal: 5,6RoR: 4,6

8 1,176.3 16,227.9 CCGT: 5,6,7Coal: 5,6RoR: 4,5,6

928.20 16,227.9 CCGT: 5,6,7Coal: 5,6RoR: 4,5,6

9 1,168.0 16,207.0 CCGT: 5,6,7Coal: 5,6RoR: 4,6

924.55 16,207.0 CCGT: 5,6,7Coal: 5,6RoR: 4,6

10 1,154.9 16,200.6 CCGT: 6,7Coal: 5,6RoR: 4,5,6

916.07 16,200.6 CCGT: 6,7Coal: 5,6RoR: 4,5,6

11 1,133.4 16,186.3 CCGT: 4,5,6,7Coal: 6RoR: 4,5,6

912.45 16,179.7 CCGT: 6,7Coal: 5,6RoR: 4,6

12 1,125.2 912.3 16,165.5 CCGT: 4,5,6,7Coal: 6RoR: 4,6

904.49 1133.87 16,165.9 CCGT: 7Coal: 5,6RoR: 4,5,6


44

5 Summary, conclusions, and scope for further research

The purpose of this study was to analyze possible differences in the optimal portfolio

configuration with and without the issue of credit risk mitigation via the application of

margining. In a first step, we developed a method for estimating future cashflows for

margining requirements based on the requirements of the ECC and a deterministic hedging

strategy, recognizing the possibility of netting between long and short positions. We

implemented this method into a Monte Carlo simulation together with a plant-by-plant

valuation of a pre-defined asset portfolio and possible expansion opportunities. We used a

simplified market model to estimate the potential generation volume for each year of

operation based on stochastically simulated commodity prices for the spot markets and plant-

specific assumptions. Applying Markowitz’ portfolio theory, we analyzed the impact of the

recognition of margining in power plant portfolio optimizations.

Based on our analysis we find that:

• Future margining requirements can be estimated applying a modified Value@Risk

approach. A specialty for an effective prognosis is, on the one hand, the recognition of the

netting possibilities between short and long positions as well as the recognition of the

expected hedging volume and thus the underlying hedging strategy. However, as in any

VaR calculation in practical use, also the MaR calculation needs a continuous and careful

“reality check” by backtesting (see Jorion 2007, pp.139ff) for a substantial risk

assessment.

• Our earlier results from a previous study (Lang/Madlener 2010) are verified; with regard

to the investment cost, CCGTs have comparably higher margin requirements than coal-

fired power plants. However, in a portfolio optimization, this effect might be irrelevant

when the recognition of margining cashflows does not alter the ranking of the NPV or the

underlying risk metric of the assets.

• Depending on the input parameters (in our case, especially commodity prices) and the

resulting value differences between the power plants in the portfolio, the recognition of

margining can alter the structure of the efficient frontier und the efficient portfolio and

thus, ought to be considered in portfolio optimizations.

An improvement of our analysis would certainly be a breakdown of our model into a higher

level of detail: We used several simplifications, such as the application of perfect foresight for

the dispatch in combination with estimates to the share of baseload and peakload products for

the hedge. In addition, we used yearly cashflows, average yearly commodity prices and yearly

MaR calculation without addressing the issue of seasonality or the effective usage level of the

45

assumed total risk capital (i.e. we implicitly assume that the company fixes one level of risk

capital resulting in the need to close positions, when the level is depleted). A higher resolution

with regard to the time would certainly shed more light on the issue and would give a more

detailed view, especially for the developments in the delivery year with the aspect of

cascading of the futures. With this, another improvement would be the recognition of interest

payments on the effectively played margining amounts over a day-to-day time horizon.

However, one has to recognize that banks require banking fees for the handling of the margins

or the recognition of credit lines. Thus, we have assumed in this paper that the payable fees

and the earnings from interest payments offset each other.

In our model we only addressed the usage of futures for the hedge of future deliveries

including the possibility to net open long and open short positions by 100%, as we assumed

that all trades are done with one exchange. Another extension worthwhile considering, is the

integration of options and swaps that are also common in the daily trading business of the

utilities. Furthermore, the fact that utilities do not necessarily run all their trades with one

exchange might alter our assumption that the netting can be done at 100% (best case

assumption). In dependency on the individual trading behavior, the resulting additional

requirements for margining could increase significantly, because in the case of zero netting,

the margining requirements of the short and long positions cannot be deducted but have to be

added instead.

In section 4.5 we showed that the choice of the underlying risk to be optimized (in our

example, the standard deviation as market risk and the margin requirement as liquidity risk),

changed the set-up of the portfolios on the efficient frontier. In order to have an integrated

view of the risk position for power plants, it would certainly be interesting to integrate the

market risk, the credit risk, and the risk from margining into one model, in order to see the

total risk of a company active in the energy markets. We leave these questions for future

research.

46

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Appendices

Appendix A. Data analysis of spot prices (in logs)

A.1 Estimation of probability distributions for spot market price processes

(a) Probability distribution for electricity baseload price

Source: EEX prices, own calculations, data set: Phelix Monthly base price, monthly average for the period

Jan 2003–Dec 2009

(b) Probability distribution for coal price

Source: EEX prices, own calculations, data set: monthly futures for coal price, monthly average price,

Jun 2006–Dec 2009

51

(c) Probability distribution for gas price

Source: EEX prices, own calculations, data set: daily gas price, Jan 2009 – Dec 2009

(d) Probability distribution for CO2 certificate price

Source: EEX prices, own calculations, data set: monthly average CO2 certificate price, Mar 2008 – Dec 2009

(e) Probability distribution for the peak price premium above baseload price

Source: EEX prices, own calculations, data set: peak premium above baseload price based on monthly average

price, Jan 2003 – Dec 2009

Figure A.1: Estimations for commodity probability distributions

52

Appendix B. Efficient frontier analysis for SC2007 and SC2009

14,000

14,500

15,000

15,500

16,000

16,500

17,000

900 925 950 975 1,000 1,025 1,050 1,075


CCGT: 4,5,6,7Coal: 6RoR: 4,5,6

CCGT: 4,5,6,7Coal: ‐RoR: 4,5,6

CCGT: 4,5,6,7Coal: ‐RoR: 4,6

CCGT: 4,5,6,7Coal: ‐RoR: 4

CCGT: 5,6,7Coal: ‐RoR: 4,6

CCGT: 6,7Coal: ‐RoR: 4,6

CCGT: 6,7Coal: ‐RoR: 4

CCGT: 7Coal: ‐RoR: 4,5,6



CCGT: Coal: ‐RoR: 4,6

CCGT: ‐Coal: ‐RoR: 4

Std. dev. In mio. €

NPV in mio. €

CCGT: ‐Coal: ‐RoR: ‐

inefficient portfolio

(a) Efficient frontiers with and without margining, SC2007

14,000

14,500

15,000

15,500

16,000

16,500

17,000

17,500

18,000

800 850 900 950 1,000


CCGT: 4,5,6,7Coal: 5,6RoR: 4,5,6

CCGT: 4,5,6,7Coal: 6RoR: 4,5,6

CCGT: 4,5,6,7Coal: ‐RoR: 4,5,6

CCGT: 4,5,6,7Coal: ‐RoR: 4,6

CCGT: 5,6,7Coal: ‐RoR: 4,6

CCGT: 5,6,7Coal: ‐RoR: 4

CCGT: 5,7Coal: ‐RoR: 4,6

CCGT: 6,7Coal: ‐RoR: 4



CCGT: ‐Coal: ‐RoR: 4

CCGT: ‐Coal: ‐RoR: ‐

Std. dev. In mio. €

NPV in mio. €


(b) Efficient frontiers with and without margining, SC2009

Figure A.2: Effects of recognizing margining in the portfolio optimization Source: own compilation, model output

53

Appendix C. Correlation coefficients for the portfolio optimization

Correlation coefficients Base case (NPV w/o margining)

NPV

_CC

GT1

NPV

_CC

GT2

NPV

_CC

GT3

NPV

_CC

GT4

NPV

_CC

GT5

NPV

_CC

GT6

NPV

_CC

GT7

NP

V_HC

1

NP

V_HC

2

NP

V_HC

3

NP

V_HC

4

NP

V_HC

5

NP

V_HC

6

NP

V_HC

7

NPV

_LGN

1

NPV

_LGN

2

NPV

_LGN

3

NP

V_Nuke1

NP

V_Nuke2

NPV

_RO

R1

NPV

_RO

R2

NPV

_RO

R3

NPV

_RO

R4

NPV

_RO

R5

NPV

_RO

R6

NPV

_RO

R7

NPV_CCGT1 1.00 0.94 0.91 0.77 0.69 0.62 0.56 0.66 0.78 0.84 0.62 0.56 0.45 0.30 0.60 0.73 0.77 0.76 0.74 0.70 0.67 0.65 0.58 0.53 0.49 0.44NPV_CCGT2 1.00 0.97 0.84 0.77 0.72 0.66 0.64 0.76 0.90 0.71 0.65 0.55 0.43 0.59 0.72 0.84 0.75 0.73 0.77 0.74 0.72 0.66 0.61 0.57 0.53NPV_CCGT3 1.00 0.88 0.82 0.76 0.71 0.62 0.74 0.89 0.75 0.70 0.61 0.49 0.58 0.71 0.82 0.74 0.73 0.77 0.78 0.75 0.70 0.65 0.62 0.57NPV_CCGT4 1.00 0.96 0.90 0.85 0.42 0.57 0.78 0.89 0.84 0.74 0.62 0.40 0.57 0.73 0.65 0.63 0.71 0.73 0.75 0.80 0.77 0.74 0.69NPV_CCGT5 1.00 0.97 0.91 0.29 0.48 0.70 0.93 0.90 0.80 0.67 0.28 0.49 0.68 0.58 0.55 0.67 0.70 0.72 0.78 0.80 0.79 0.75NPV_CCGT6 1.00 0.96 0.18 0.40 0.64 0.90 0.93 0.85 0.71 0.19 0.43 0.63 0.51 0.48 0.62 0.65 0.68 0.74 0.77 0.81 0.79NPV_CCGT7 1.00 0.09 0.33 0.60 0.86 0.90 0.90 0.75 0.10 0.36 0.59 0.45 0.41 0.58 0.62 0.65 0.71 0.74 0.79 0.81

NPV_HC1 1.00 0.88 0.75 0.30 0.19 0.02 0.00 0.95 0.80 0.69 0.72 0.74 0.58 0.55 0.53 0.38 0.27 0.17 0.09NPV_HC2 1.00 0.86 0.50 0.41 0.27 0.07 0.84 0.93 0.81 0.88 0.91 0.70 0.67 0.65 0.52 0.44 0.37 0.30NPV_HC3 1.00 0.73 0.67 0.57 0.43 0.72 0.84 0.95 0.85 0.84 0.86 0.83 0.80 0.71 0.64 0.60 0.55NPV_HC4 1.00 0.97 0.86 0.72 0.31 0.53 0.72 0.62 0.59 0.70 0.73 0.77 0.85 0.87 0.86 0.81NPV_HC5 1.00 0.92 0.77 0.20 0.45 0.67 0.54 0.51 0.66 0.69 0.73 0.81 0.85 0.89 0.86NPV_HC6 1.00 0.87 0.03 0.32 0.57 0.40 0.36 0.57 0.61 0.67 0.74 0.77 0.83 0.86NPV_HC7 1.00 0.01 0.13 0.44 0.20 0.15 0.44 0.50 0.57 0.64 0.67 0.71 0.75

NPV_LGN1 1.00 0.85 0.73 0.74 0.76 0.60 0.57 0.55 0.39 0.28 0.19 0.10NPV_LGN2 1.00 0.87 0.93 0.95 0.74 0.71 0.68 0.56 0.48 0.43 0.36NPV_LGN3 1.00 0.85 0.83 0.88 0.84 0.81 0.72 0.66 0.62 0.57NPV_Nuke1 1.00 0.98 0.80 0.76 0.74 0.64 0.57 0.52 0.44NPV_Nuke2 1.00 0.78 0.74 0.72 0.62 0.55 0.49 0.41NPV_ROR1 1.00 0.97 0.93 0.84 0.78 0.73 0.67NPV_ROR2 1.00 0.96 0.88 0.82 0.77 0.72NPV_ROR3 1.00 0.92 0.87 0.83 0.78NPV_ROR4 1.00 0.97 0.92 0.87NPV_ROR5 1.00 0.97 0.92NPV_ROR6 1.00 0.97NPV_ROR7 1.00

(a) NPV w/o margining Correlation coefficients Base case (NPV w/ margining)

totalCC

GT1

totalCC

GT2

totalCC

GT3

totalCC

GT4

totalCC

GT5

totalCC

GT6

totalCC

GT7

totalHC

1

totalHC

2

totalHC

3

totalHC

4

totalHC

5

totalHC

6

totalHC

7

totalLGN

1

totalLGN

2

totalLGN

3

totalNuke1

totalNuke2

totalRO

R1

totalRO

R2

totalRO

R3

totalRO

R4

totalRO

R5

totalRO

R6

totalRO

R7

totalCCGT1 1.00 0.94 0.91 0.76 0.68 0.62 0.56 0.66 0.78 0.84 0.62 0.56 0.45 0.30 0.60 0.73 0.77 0.76 0.75 0.71 0.68 0.65 0.58 0.53 0.49 0.44totalCCGT2 1.00 0.97 0.84 0.77 0.71 0.66 0.64 0.76 0.91 0.71 0.66 0.56 0.43 0.59 0.72 0.84 0.76 0.74 0.78 0.75 0.72 0.66 0.61 0.57 0.53totalCCGT3 1.00 0.88 0.82 0.76 0.71 0.62 0.74 0.89 0.76 0.70 0.61 0.49 0.58 0.71 0.83 0.75 0.73 0.78 0.79 0.76 0.70 0.65 0.62 0.57totalCCGT4 1.00 0.96 0.90 0.85 0.41 0.57 0.77 0.90 0.85 0.75 0.62 0.39 0.57 0.73 0.65 0.63 0.72 0.74 0.75 0.81 0.78 0.75 0.70totalCCGT5 1.00 0.96 0.91 0.28 0.47 0.70 0.94 0.90 0.80 0.67 0.28 0.49 0.68 0.58 0.56 0.67 0.70 0.72 0.79 0.81 0.80 0.75totalCCGT6 1.00 0.96 0.17 0.39 0.64 0.91 0.93 0.85 0.71 0.18 0.42 0.63 0.51 0.48 0.62 0.65 0.68 0.75 0.78 0.82 0.79totalCCGT7 1.00 0.09 0.32 0.60 0.86 0.91 0.90 0.76 0.09 0.36 0.58 0.45 0.41 0.58 0.62 0.65 0.71 0.75 0.80 0.82

totalHC1 1.00 0.88 0.75 0.29 0.18 0.02 0.00 0.94 0.80 0.69 0.72 0.74 0.58 0.55 0.53 0.37 0.26 0.16 0.08totalHC2 1.00 0.86 0.49 0.40 0.26 0.07 0.84 0.93 0.80 0.88 0.90 0.70 0.67 0.65 0.51 0.43 0.36 0.29totalHC3 1.00 0.72 0.66 0.56 0.43 0.72 0.84 0.95 0.85 0.84 0.86 0.82 0.80 0.70 0.63 0.59 0.54totalHC4 1.00 0.97 0.86 0.73 0.30 0.52 0.72 0.61 0.58 0.70 0.73 0.77 0.85 0.87 0.86 0.81totalHC5 1.00 0.92 0.77 0.19 0.45 0.66 0.54 0.51 0.65 0.68 0.73 0.81 0.85 0.89 0.86totalHC6 1.00 0.87 0.03 0.31 0.57 0.40 0.36 0.57 0.61 0.66 0.74 0.77 0.83 0.86totalHC7 1.00 0.01 0.13 0.44 0.20 0.15 0.44 0.50 0.57 0.64 0.67 0.71 0.75

totalLGN1 1.00 0.85 0.73 0.74 0.77 0.60 0.57 0.55 0.39 0.28 0.19 0.10totalLGN2 1.00 0.87 0.94 0.95 0.74 0.71 0.69 0.56 0.48 0.42 0.36totalLGN3 1.00 0.85 0.84 0.88 0.84 0.81 0.72 0.66 0.62 0.57totalNuke1 1.00 0.98 0.80 0.76 0.74 0.64 0.57 0.52 0.44totalNuke2 1.00 0.78 0.75 0.72 0.62 0.55 0.48 0.41totalROR1 1.00 0.97 0.94 0.84 0.78 0.73 0.67totalROR2 1.00 0.96 0.88 0.82 0.77 0.72totalROR3 1.00 0.92 0.87 0.83 0.78totalROR4 1.00 0.97 0.92 0.87totalROR5 1.00 0.97 0.92totalROR6 1.00 0.97totalROR7 1.00

(b) NPV w/ margining

Correlation coefficients, base case,

total margins

TM_C

CG

T1

TM_C

CG

T2

TM_C

CG

T3

TM_C

CG

T4

TM_C

CG

T5

TM_C

CG

T6

TM_C

CG

T7

TM_H

C1

TM_H

C2

TM_H

C3

TM_H

C4

TM_H

C5

TM_H

C6

TM_H

C7

TM_LG

N1

TM_LG

N2

TM_LG

N3

TM_N

uke1

TM_N

uke2

TM_R

OR

1

TM_R

OR

2

TM_R

OR

3

TM_R

OR

4

TM_R

OR

5

TM_R

OR

6

TM_R

OR

7

TM_CCGT1 1.00 0.93 0.90 0.81 0.75 0.68 0.62 0.47 0.58 0.64 0.51 0.45 0.37 0.23 0.40 0.50 0.54 0.46 0.47 0.46 0.45 0.44 0.38 0.35 0.29 0.26TM_CCGT2 1.00 0.96 0.87 0.80 0.76 0.70 0.47 0.57 0.71 0.57 0.53 0.45 0.33 0.40 0.50 0.62 0.48 0.49 0.54 0.52 0.50 0.45 0.42 0.36 0.33TM_CCGT3 1.00 0.90 0.85 0.80 0.74 0.45 0.56 0.70 0.62 0.57 0.50 0.39 0.39 0.50 0.63 0.48 0.49 0.55 0.56 0.54 0.49 0.46 0.40 0.37TM_CCGT4 1.00 0.92 0.86 0.81 0.41 0.51 0.67 0.69 0.65 0.57 0.45 0.34 0.45 0.57 0.41 0.42 0.49 0.51 0.53 0.56 0.52 0.45 0.43TM_CCGT5 1.00 0.92 0.86 0.33 0.46 0.62 0.74 0.69 0.61 0.49 0.28 0.40 0.54 0.37 0.38 0.46 0.49 0.50 0.53 0.55 0.47 0.45TM_CCGT6 1.00 0.92 0.24 0.40 0.57 0.69 0.73 0.65 0.52 0.22 0.37 0.51 0.33 0.35 0.44 0.46 0.48 0.51 0.52 0.50 0.47TM_CCGT7 1.00 0.14 0.33 0.54 0.65 0.69 0.69 0.55 0.14 0.32 0.47 0.28 0.30 0.41 0.44 0.46 0.50 0.51 0.48 0.51

TM_HC1 1.00 0.78 0.64 0.43 0.29 0.02 0.01 0.85 0.63 0.52 0.42 0.41 0.36 0.35 0.34 0.28 0.22 0.16 0.10TM_HC2 1.00 0.78 0.60 0.49 0.32 0.10 0.67 0.78 0.65 0.56 0.54 0.47 0.45 0.44 0.37 0.34 0.28 0.23TM_HC3 1.00 0.79 0.72 0.61 0.43 0.57 0.74 0.86 0.58 0.59 0.67 0.64 0.62 0.58 0.54 0.46 0.44TM_HC4 1.00 0.92 0.80 0.63 0.41 0.56 0.74 0.45 0.47 0.58 0.61 0.64 0.69 0.72 0.62 0.58TM_HC5 1.00 0.88 0.68 0.30 0.51 0.70 0.41 0.44 0.57 0.60 0.64 0.70 0.72 0.68 0.64TM_HC6 1.00 0.79 0.02 0.37 0.59 0.30 0.33 0.50 0.54 0.59 0.66 0.69 0.66 0.68TM_HC7 1.00 0.01 0.19 0.45 0.17 0.20 0.44 0.50 0.57 0.65 0.68 0.65 0.67

TM_LGN1 1.00 0.71 0.57 0.51 0.49 0.43 0.42 0.40 0.31 0.25 0.19 0.12TM_LGN2 1.00 0.72 0.66 0.65 0.55 0.53 0.51 0.44 0.39 0.33 0.28TM_LGN3 1.00 0.76 0.78 0.88 0.85 0.82 0.72 0.68 0.59 0.54TM_Nuke1 1.00 0.97 0.83 0.80 0.78 0.63 0.56 0.46 0.39TM_Nuke2 1.00 0.85 0.82 0.80 0.66 0.59 0.49 0.42TM_ROR1 1.00 0.97 0.93 0.82 0.77 0.66 0.61TM_ROR2 1.00 0.96 0.86 0.81 0.70 0.66TM_ROR3 1.00 0.90 0.86 0.75 0.71TM_ROR4 1.00 0.94 0.82 0.78TM_ROR5 1.00 0.86 0.82TM_ROR6 1.00 0.95TM_ROR7 1.00

(c) Total margin

Figure A.3: Correlation coefficients for portfolio optimization, Base Case Source: model output

54

Appendix D. Portfolio values for new Base Case with changed commodity prices

Portofolio Std.Dev. In mio.€

NPV w/o margining in

mio.€

Corresponding Total Std.Dev. in

mio.€

Corresponding Total NPV in mio.€

CC

GT4

CC

GT5

CC

GT6

CC

GT7

HC

4

HC

5

HC

6

HC

7

RO

R4

RO

R5

RO

R6

RO

R7

1 1,040.8 18,062.9 995.0 16,311.1 1 1 1 1 1 1 1 1 1 1 1 02 1,036.8 18,030.3 991.2 16,290.2 1 1 1 1 1 1 1 1 1 0 1 03 1,027.2 18,004.3 982.1 16,283.8 1 0 1 1 1 1 1 1 1 1 1 04 1,025.4 18,003.3 980.4 16,284.4 0 1 1 1 1 1 1 1 1 1 1 05 1,021.4 17,970.7 976.5 16,263.5 0 1 1 1 1 1 1 1 1 0 1 06 1,018.5 17,953.2 973.7 16,307.8 1 1 1 1 1 1 1 0 1 1 1 07 1,011.9 17,944.7 967.6 16,257.1 0 0 1 1 1 1 1 1 1 1 1 08 1,006.0 17,916.7 962.7 16,257.9 1 1 1 1 0 1 1 1 1 1 1 09 1,003.4 17,893.6 959.3 16,281.1 0 1 1 1 1 1 1 0 1 1 1 0

10 1,002.0 17,884.0 958.9 16,237.0 1 1 1 1 0 1 1 1 1 0 1 011 998.9 17,877.2 955.2 16,222.4 0 0 0 1 1 1 1 1 1 1 1 012 992.7 17,858.1 950.1 16,230.6 1 0 1 1 0 1 1 1 1 1 1 013 990.8 17,857.1 948.3 16,231.2 0 1 1 1 0 1 1 1 1 1 1 014 988.8 17,825.4 946.3 16,209.7 1 0 1 1 0 1 1 1 1 0 1 015 986.9 17,824.4 944.5 16,210.3 0 1 1 1 0 1 1 1 1 0 1 016 984.7 17,807.0 942.3 16,254.6 1 1 1 1 0 1 1 0 1 1 1 017 977.6 17,798.5 935.8 16,203.9 0 0 1 1 0 1 1 1 1 1 1 018 973.7 17,765.8 932.0 16,183.0 0 0 1 1 0 1 1 1 1 0 1 019 971.8 17,748.3 930.0 16,227.3 1 0 1 1 0 1 1 0 1 1 1 020 969.9 17,747.4 928.2 16,227.9 0 1 1 1 0 1 1 0 1 1 1 021 964.9 17,731.0 923.7 16,169.2 0 0 0 1 0 1 1 1 1 1 1 022 961.4 17,698.5 920.9 16,162.9 0 1 1 1 0 0 1 1 1 1 1 023 957.1 17,688.8 916.1 16,200.6 0 0 1 1 0 1 1 0 1 1 1 024 953.3 17,656.1 912.4 16,179.7 0 0 1 1 0 1 1 0 1 0 1 025 948.5 17,639.9 908.7 16,135.6 0 0 1 1 0 0 1 1 1 1 1 026 944.9 17,621.2 904.5 16,165.9 0 0 0 1 0 1 1 0 1 1 1 027 941.7 17,588.8 902.0 16,159.6 0 1 1 1 0 0 1 0 1 1 1 028 936.2 17,572.4 897.1 16,101.0 0 0 0 1 0 0 1 1 1 1 1 029 932.5 17,539.8 893.4 16,080.1 0 0 0 1 0 0 1 1 1 0 1 030 929.3 17,530.2 890.2 16,132.3 0 0 1 1 0 0 1 0 1 1 1 031 925.6 17,497.6 886.7 16,111.4 0 0 1 1 0 0 1 0 1 0 1 032 923.9 17,488.1 885.4 16,053.6 0 0 0 0 0 0 1 1 1 1 1 033 917.5 17,462.7 879.1 16,097.6 0 0 0 1 0 0 1 0 1 1 1 034 913.9 17,430.1 875.6 16,076.8 0 0 0 1 0 0 1 0 1 0 1 035 905.9 17,378.4 868.1 16,050.3 0 0 0 0 0 0 1 0 1 1 1 036 902.4 17,345.7 864.7 16,029.4 0 0 0 0 0 0 1 0 1 0 1 037 898.8 17,298.9 861.7 16,017.3 0 0 0 1 0 0 0 0 1 1 1 038 895.3 17,266.3 858.3 15,996.4 0 0 0 1 0 0 0 0 1 0 1 039 887.8 17,214.6 851.3 15,969.9 0 0 0 0 0 0 0 0 1 1 1 040 884.4 17,181.9 848.0 15,949.1 0 0 0 0 0 0 0 0 1 0 1 041 881.3 17,131.2 844.9 15,911.5 0 0 0 0 0 0 0 0 1 0 0 042 878.2 17,015.6 841.9 15,802.2 0 0 0 0 0 0 0 0 0 0 1 043 875.0 16,964.8 838.9 15,764.6 0 0 0 0 0 0 0 0 0 0 0 0


55

List of FCN Working Papers

2010 Lang J., Madlener R. (2010). Relevance of Risk Capital and Margining for the Valuation of Power Plants: Cash

Requirements for Credit Risk Mitigation, FCN Working Paper No. 1/2010, Institute for Future Energy Consumer Needs and Behavior, RWTH Aachen University, February.

Michelsen C., Madlener R. (2010). Integrated Theoretical Framework for a Homeowner’s Decision in Favor of an

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.

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).

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.

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.

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.

portfolio optimization for power plants: the impact of

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