the modern portfolio theory applied to wind farm financing sven barkemeyer, dewi gmbh
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THE MODERN PORTFOLIO THEORY APPLIED TO WIND FARM FINANCING Sven Barkemeyer, DEWI GmbH Patricia Chaves, Carl von OssietzkyUniversity Oldenburg. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
SITE ASSESSMENT . WIND TURBINE ASSESSMENT . GRID INTEGRATION . DUE DILIGENCE . KNOWLEDGE . CONSULTANCY
THE MODERN PORTFOLIO THEORY APPLIED TO WIND FARM FINANCINGSven Barkemeyer, DEWI GmbH
Patricia Chaves, Carl von Ossietzky University Oldenburg
Page 2
• 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
Introduction
Page 3The 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
Page 4The Modern Portfolio Theory
Graphically depicted the formula looks like this:
Variance - Covariance Matrix
TermsianceCo
N
j
N
jkkjkj
TermsVariance
j
N
jjPFPF wwwE
var
1 1,
2
1
22 *2)var(
Page 5
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´)
Input
Page 6
Portfolio Lower Saxony / Germany:
Description of Portfolios
Source: GoogleEarth™
Monthly Production Data / Portfolio Lower Saxony
0
50
100
150
200
250
300
350
400
Jan.0
3
Jul.0
3
Jan.0
4
Jul.0
4
Jan.0
5
Jul.0
5
Jan.0
6
Jul.0
6
Jan.0
7
Jul.0
7
MW
h/M
on
th/M
W_I
nst WF 1
WF 2
WF 3
WF 4
WF 5
Page 7
Portfolio Northern Germany:
Description of Portfolios
Source: GoogleEarth™
Monthly Production Data / Portfolio Northern Germany
0
50
100
150
200
250
300
350
400
Jan.0
3
Jul.0
3
Jan.0
4
Jul.0
4
Jan.0
5
Jul.0
5
Jan.0
6
Jul.0
6
Jan.0
7
Jul.0
7
MW
h/M
on
th/M
W_I
nst WF 1
WF 2
WF 3
WF 4
WF 5
Page 8
Portfolio Germany:
Description of Portfolios
Source: GoogleEarth™
Monthly Production Data / Portfolio D
0
50
100
150
200
250
300
350
400
Jan.0
3
Jul.0
3
Jan.0
4
Jul.0
4
Jan.0
5
Jul.0
5
Jan.0
6
Jul.0
6
Jan.0
7
Jul.0
7
MW
h/M
on
th/M
W_
Ins
t WF 1
WF 2
WF 3
WF 4
WF 5
Page 9
Assumptions for Economic Calculations:
Description of Portfolios
Page 10Output
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
Page 11Output
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.
Page 12Output
Assessment of Portfolio-Effects
Uncertainty of
c) Correlation of Operational Data
Correlation Matrix:
Correlation-Matrix Portfolio Germany IndependencyWF 1 2 3 4 51 1,00 0,87 0,83 0,76 0,85 0,182 0,87 1,00 0,98 0,95 0,89 0,073 0,83 0,98 1,00 0,95 0,83 0,094 0,76 0,95 0,95 1,00 0,85 0,075 0,85 0,89 0,83 0,85 1,00 0,11
Overall-Portfolio-Independency 10,4%
Page 13Output
Assessment of Portfolio-Effects
Uncertainty of
d) Long Term Data Correction
Variance / Covariance Matrix:
Page 14Output
Calculation of overall uncertainty for• every single wind farm• the wind farm portfolio • the wind farm portfolio with portfolio effects
Page 15Results
Wind Farm Portfolio Uncertainty Overview:
Page 16Results
Overview of DSCR – Values for the three Portfolios
DSCR-Values of Wind Farm Portfolio ´Germany´
1,72
1,300,91
2,231,85
1,46
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
P50 P90 incl. PF-Effects P90 w/o PF-Effects
DSC
R
Minimum
Average
DSCR-Values of Wind Farm Portfolio ´Lower Saxony´
1,45
0,91 0,91
1,98
1,48 1,47
0,00
0,50
1,00
1,50
2,00
2,50
3,00
P50 P90 incl. PF-Effects P90 w/o PF-Effects
DSC
R
Minimum
Average
DSCR-Values of Wind Farm Portfolio ´Northern Germany´
1,37
0,75 0,74
1,93
1,25 1,25
0,00
0,50
1,00
1,50
2,00
2,50
3,00
P50 P90 incl. PF-Effects P90 w/o PF-Effects
DSCR
Minimum
Average
Page 17Summary
• 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
Page 18The End
Thank you for your attention!