THE MODERN PORTFOLIO THEORY APPLIED TO WIND FARM FINANCING Sven Barkemeyer, DEWI GmbH

1. THE MODERN PORTFOLIO THEORY APPLIED TO WIND FARM FINANCING Sven Barkemeyer, DEWI GmbH Patricia Chaves, Carl von Ossietzky University Oldenburg

2. Introduction • By creating Wind Farm Portfolios the risk of the investment can be reduced and simultaneously the financing conditions can be improved • While the positive aspect can be regarded as widely accepted the sound quantification of the portfolio effect is still under discussion • An approach that has already been suggested in the past is the application of the Modern Portfolio Theory (MPT) to wind farms

3. The Modern Portfolio Theory • The MPT was developed by H.M. Markowitz in the 1950´s with respect to common investment assets (stocks) • The two relevant parameters in the Markowitz model are: a) Expectancy Value (Return) b) Standard Deviation (Risk) • Expectancy Value is equivalent to the P50-value and is not addressed here • The risk of a portfolio is described by its variance or standard deviation

4. Variance - Covariance Matrix The Modern Portfolio Theory Graphically depicted the formula looks like this:

5. Input Input: • MPT • Production Data of Wind Farms • Economic Assumptions for the Calculation of the Base Case Models • 3 Portfolios (´Lower Saxony´, ´Northern Germany´ and ´Germany´)

6. Description of Portfolios Portfolio Lower Saxony / Germany: Source: GoogleEarth™

7. Description of Portfolios Portfolio Northern Germany: Source: GoogleEarth™

8. Description of Portfolios Portfolio Germany: Source: GoogleEarth™

9. Description of Portfolios Assumptions for Economic Calculations:

10. Output First Step Single Wind Farms: • P50 • Overall risk of every individual wind farm • P75, P90, P95,... Focus on Risk: As we considered operational wind farms (post-operative perspective) the following 4 uncertainty aspects have been considered for every wind farm: Uncertainty of a) Operational Behaviour (Technical Availability) b) Production Data c) Correlation of Operational Data d) Long Term Data Correction

11. Output Assessment of Portfolio - Effects Uncertainty of a) Operational Behaviour (Technical Availability) b) Production Data These aspects are assumed to be completely independent  no Portfolio Effect Uncertainty of c) Correlation of Operational Data d) Long Term Data Correction These aspects correlate to a certain degree between the wind farms that constitute the portfolio.

12. Correlation Matrix: Output Assessment of Portfolio-Effects Uncertainty of c) Correlation of Operational Data

13. Variance / Covariance Matrix: Output Assessment of Portfolio-Effects Uncertainty of d) Long Term Data Correction

14. Output Calculation of overall uncertainty for • every single wind farm • the wind farm portfolio • the wind farm portfolio with portfolio effects

15. Results Wind Farm Portfolio Uncertainty Overview:

16. Results Overview of DSCR – Values for the three Portfolios

17. Summary • Using the MPT a quantification of the portfolio effects has been performed on three wind farm portfolios located in Germany • The risk reducing effects for the two portfolios ´Lower Saxony´ and ´Northern Germany´ were neglectable. • The risk reduction in the ´Germany´ portfolio led to an increase in AEP for the P90 scenario of about 1.5% leading to an increase in the average DSCR from 1.5 to 1.9 • Higher portfolio effects due to increased independency (geographical anticorrelation) can generally be expected for international wind farm portfolios Outlook • This subject is currently investigated in more detail within a doctoral thesis by Ms Patricia Chaves

18. The End Thank you for your attention!