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Page 1: THE MODERN PORTFOLIO THEORY APPLIED TO WIND … · THE MODERN PORTFOLIO THEORY APPLIED TO WIND FARMS FINANCING ... The Modern Portfolio Theory (MPT), or “Markowitz ... The next

THE MODERN PORTFOLIO THEORY APPLIED TO WIND FARMS FINANCING

Patricia Chaves, Dr. Kai Mönnich*, Peter Spengemann*,Carl von Ossietzky Universität Oldenburg, Faculty II – Ecological Economics

* DEWI GmbH, Ebertstr. 96, 26382 Wilhelmshavencontact: [email protected]

Summary

The increase in the participation of wind energy in the global energy matrix observed in the last years raises thenecessity to investigate alternatives to improve the economic performance of the projects. In this context, thisPhD research, developed on a co-operation between the Micrositing and the Technical Due Diligencedepartments of the German Wind Energy Institut (DEWI GmbH) and the University of Oldenburg (faculty ofEconomics), will address the application of the Modern Portfolio Theory (MPT) to Wind Farms (WF). In a fewwords, the general objective is to investigate, by comparison with the performance of single projects, the eventualfinancial benefits of bundling several WF projects in a portfolio.

1. Introduction and Initial Assumptions

The Modern Portfolio Theory is traditionally areference on the analysis of investments in financialassets like bonds, stocks, etc., which returns arealways conditioned to a determined level of risk.From the economical point of view, a wind farmproject is a real asset investment. Its return isuncertain and volatile [1]. In this sense, the initialunderstanding of this investigation is that thetheoretical background of the MPT can also beapplied on the analysis of investments in wind farms.

The theory proposes that the risk of financialinvestments can be reduced by allocating theresources in a portfolio of assets which returns areindependent from each other (diversification). In thecase of wind farms, the independence of the return isrelated to the fact that the income of one farm isdirectly connected to its energy production, which onthe other hand, depends on aspects particular toevery project, such as its geographical location (localwind regime), turbine type and energy potentialcalculations. Further on, the return of wind farms is afunction of its fixed and operational costs, as well astaxes and the tariff paid by the project’s off-taker. Forthese parameters, commercial issues (EPCcontracts, O&M, etc.) as well as local aspects suchas incentive politics for the promotion of renewableenergies might significantly distinguish one project tothe other.

The initial premise of our portfolio analysis is that therisk of the investment in a WF project is function ofthe overall uncertainty of the Annual EnergyProduction (AEP) of the plants. The goal is then tounderstand the different parameters contributing tothe overall uncertainty and how do these parametersdiffer from one project to the other, so that acorrelation between the uncertainty on the AEP ofthe projects can be established. As described insection 2, the lower the correlation between theuncertainties, the lower the portfolio’s overall risk (eq.2). The final step to conclude the investigation is togenerate a portfolio’s cash flow so that the individualeconomical performance of the projects can becompared to the portfolio one. The following

research questions summarise the key issues thatwill be addressed along the work.

Research Questions:• How much can the risk of the investment in wind

farms be reduced by bundling projects in aportfolio?

• What are the main aspects of a WF projectcontributing to the portfolio effect (reduction ofrisk due to diversification)?

• What is the improvement on the overall financialperformance of investments?

2. The Modern Portfolio Theory

The Modern Portfolio Theory (MPT), or “MarkowitzPortfolio Selection”, conceived in the context offinancial assets, proposes that the expected return ofa portfolio of assets (in our case wind farms) is theweighted sum (W) of the individual return of all singleasset composing the portfolio (eq. 1). Further on, thetheory states that the overall risk exposure of aportfolio of different risky assets with normallydistributed outcomes does not exclusively depend onthe risks of the single assets. Rather, it isincreasingly dominated by the co-variance risks asthe number of assets in the portfolio increases (eq.2) [1]. Therefore, the strategy to improve theperformance of investments is to build a portfolio ofassets which returns are as low correlated aspossible (fig.1).

To apply the MPT to WF projects means to establisha portfolio of farms, in which the individual productionof the constituting plants are as much independentas possible. In other words, to combine plantslocated in regions with different wind regimes,operating under different conditions (turbine types,power curves, etc.).

Equation 1: Expected Return of a Portfolio

∑= )()( iiPortfolio REWER

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Equation 2: Overall risk of a Portfolio

∑ ∑∑+= jijiiiPortfolio WWW σσσ 222

where:

σ2Portfolio is the variance of the portfolio;

σi, σj are respectively the variance of assets “i” and“j”;

σi,j is the co-variance between the assets, andρij is the correlation coefficient between farms “i”and “j”.

Fig. 1.: Example of a portfolio of two different financialassets (A and B). Unequal “Risk x Return” curves aregenerated for different correlation coefficients (r) [3].

3. Methodology of Investigation

The investigation is carried out based on casestudies relying on data from wind farms in operation.The next diagram (fig.2) illustrates the researchapproach to be applied.

Fig.2.: Research approach of the portfolio analysis.

The input of the portfolio analysis is the informationon the annual energy production, overall uncertainty,the P values and the cash flow of the single farmsconsidered in the portfolio. The initial step is the

detailed analysis of the uncertainties involved in theAEP in a project by project basis, so thatindependencies, or correlation aspects between theprojects can be identified. From this analysis, acorrelation coefficient (ρPORT) will be quantified. Theexpected return of the portfolio is solely the sum ofexpected returns of the single projects, and the risk,or uncertainty of the portfolio, will be determinedaccording to the correlation coefficient (eq.2). Withthis parameters (expected return and uncertainty), Pvalues (P75, P90, etc.) can be obtained, andconsequently the cash flow.The conclusions will be based on the comparison ofproject financing parameters (Debt Service CoverRatio, IRR, NPV, etc.) between the single projectsand the portfolio.

4. Preliminary Findings

Portfolio assessments developed in the past indicatethat there are mainly three aspects with potential tocorrelate between different wind farms: the Windresource, that here we call “geographicaldiversification“, technical characteristics (wind turbinetypes and power curves) and wind potentialcalculations [1].

- Geographical Diversification: The geographicaldiversification is relatively simple to assess, andrepresents the degree of independence between thewind regime on the farm’s sites. It is the factor thatexpresses the seasonal aspect of the farm’sproduction. Depending on the farm location, the windavailable for one project might complement the lackof wind in another one, so that the overall productionof the portfolio is not so volatile as when theproduction of the farms is considered individually. Inshort words the geographical diversification can besummarised as: ”if the wind is not blowing inGermany, then it may be blowing in Italy” [2].

- Technical Diversification: The technicaldiversification is resultant from the variety of windturbine types, power curves and technologies utilisedin the projects considered. By a deep understandingof the technical characteristics of the wind turbines,its suitability to the site, availability and theuncertainties involved in the determination of itspower curves, it is possible to establish a correlationfactor between the risks related to the technicalaspects of the farms in the portfolio.

- Wind Potential Calculations: It is common practiceby project developers to order yield assessments forthe projects under investigation from differenttechnical advisers. Although the assessments followbasically a similar approach results may vary quiteconsiderable in some cases. A detailed analysis ofthe different studies can identify the independence ofgiven assumptions as well as the resultinguncertainties, so that a certain correlation also forthis aspect can be established.

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5. References

[1] Hulsch, F., Strack. M: Exploiting Portfolio Effectsin Diversified Project Bundles – A quantitativeanalysis of potentials and implications forFinancial Engineering, DEWEK 2006;

[2] Dunlop, John: Modern Portfolio Theory MeetsWind Farms, the journal of private equity, 2004,pages 83-95;

[3] S. Awerbuch, M. Berger: Applying PortfolioTheory to EU Electricity Planning and Policy-making, IEA/EET Working Paper, Feb. 2003.

[4] Strack, M., W. Winkler: Analysis of Uncertaintiesin Energy Yield Calculation of Wind FarmProjects, DEWI Magazine Nr. 22, Feb. 2003;

[5] H. Markowitz: Portfolio Selection: Efficientdiversification of investment, 2nd. Edition, 1990;