This document discusses applying Modern Portfolio Theory (MPT) to determine the optimal energy mix for Ireland. MPT, developed by Harry Markowitz, suggests diversifying assets to maximize returns while minimizing risk. The document provides an overview of MPT concepts like expected return, risk calculation using variance and standard deviation, and the efficient frontier. It then analyzes Ireland's current energy mix, which relies heavily on oil and has limited renewable sources. The document argues MPT can help Ireland develop a more balanced energy portfolio to reduce risk and meet its renewable energy targets in a cost-effective way. Case studies show MPT facilitates evaluating energy sources based on their portfolio costs and risks rather than only levelized costs.

1. Modern Portfolio Theory in future-proo…ng
energy mix of Ireland
Soumyadeep Mukhopadhyay; 17235308
1718 - EC5102 Renewable Energy Economics and Policy
2nd Semester, MEconSc (NREP), NUIG
s.mukhopadhyay1@nuigalway.ie
16th
March, 2018
Abstract
Energy mix of a country needs to be carefully decided to achieve ro-
bust energy security. A Nobel Prize winning asset management concept
introduced by Prof Harry Markowitz in 1952 - "Modern Portfolio Theory"
(MPT) can be applied for this task. MPT suggests a portfolio focussing
on two main concepts, viz. (i) maximizing asset return for any level of
risk and (ii) reducing risk by diversifying a portfolio of unrelated assets.
This article describes the basic concepts of MPT and proceeds to explain
implementation of MPT in energy mix problem using some case studies.
It was concurred that a vast range of externalities and social costs are not
being currently taken into account while deciding on energy mix. Thus
renewables are incorrectly perceived to be more expensive than fossil fuel
sources. Once the cost to society are accounted for by using non-market
valuation techniques, renewables become welfare maximizing and form in-
tegral part of energy mix as recommended by MPT. Especially for Ireland,
determination of energy mix using MPT will ensure that it can achieve
the target of 16% renewable energy in its energy mix by 2020 according
to EU Renewable Energy Directive 2009/28/EC.
1 Introduction
Energy mix is the combination of primary energy sources e.g. fossil fuel, nuclear
energy and renewable energy to meet energy needs of a country- especially
for generating power, providing fuel for transportation and heating or cooling.
Determination of proper energy mix is key to robust energy security of a country
leading to uninterrupted availability of energy sources at an a¤ordable price
(IEA, 2016). For each country, composition of energy mix depends on three
things, viz. (i) availability of resources (domestic/ import), (ii) extent & type of
energy needs, and (iii) policy choices determined by historical, economic, social,
demographic, environmental and geopolitical factors.
1

2. In 2016, the world primary energy mix included 33.3% oil, 28.1% coal, 24.1%
natural gas, 4.5% nuclear energy, 6.9% hydroelectricity and only 3.2% from other
renewables (BP, 2017). It should be noted that the primary energy mix …gures
do not match …nal energy consumption …gures because a signi…cant portion of
primary energy is lost in conversion processes to generate secondary energy.
Final consumption re‡ects demand for re…ned petroleum products, natural gas,
electricity and heat.
This article discusses an e¤ective asset management theory to determine
an e¤ective energy mix for a country. Markowitz’s Portfolio Selection Theory
(Markowitz, 1991) suggests that by investing in portfolios rather than in indi-
vidual assets, investors can lower the total risk of investing without sacri…cing
return, i.e. diversi…cation is the key to reduce asset risk. In …nance, diversi…-
cation is the process of allocating capital in a way that reduces the exposure
to any one particular asset or risk. This concept of portfolio allocation can be
applied to determine energy mix of a country to reduce the risk on it energy
security.
2 Energy mix of Ireland
In energy mix of Ireland in 2016 (Figure 1), oil dominates as a fuel, account-
ing for 48% of the total primary energy requirement (TPER). Renewables e.g.
wind, hydro and others account for only 8% of TPER. Transport continues to
be the largest user, accounting for 42% usage. Losses associated with the gen-
eration and transmission of electricity amounted to 17% (52% of the primary
energy for electricity generation). Natural gas plays a vital role in Ireland’s en-
ergy mix, meeting 27% of Ireland’s TPER. Until 2015, 90% of natural gas was
imported from UK. Corrib …eld came into operation in 2015 to supply up to
56% of gas. However, it will run out by 2025, leaving Ireland dependent on im-
ports (GNI, 2016). This exposes Ireland to international gas price ‡uctuations,
more relevant in the post-Brexit scenario. On the brighter side, Irish renewable
electricity generation accounted for 27.2% of gross electricity consumption in
2016, reducing CO2 emissions by 3.1 Mt and avoided e192 million in fossil fuel
imports (Ervia, 2015). Wind provided 22% of all electricity in Ireland in 2016,
with an installed capacity of over 2800 MW. Hydro generators provided 3% of
Irish electricity needs in 2016, and will continue to play their part in achieving
the 2020 target (Eirgrid & SONI, 2016). This outlines the bene…cial hedging
e¤ect of renewable energy sources. Ideally, Ireland should structure its energy
portfolio to seek little volatility, stable price, low production cost, and providing
hedging e¤ect to mainstream electricity consumption. However, SEAI (2017)
predicts that in absence of any further support measures, Ireland would fail
to meet its 2020 target. According its report, between 300 MW and 350 MW
of additional wind capacity must be installed every year and supply of approx
320 million litres of biofuels must be secured for blending with fossil fuels for
transport, doubling the existing supply and increasing biofuel penetration to
8% (SEAI, 2017).
2

3. Figure 1: Energy mix of Ireland in 2016 (SEAI, 2017)
3 Modern Portfolio Theory and key concepts
The foundation for Modern Portfolio Theory (MPT) was established in 1952
by Harry Markowitz. MPT is an investment framework for the selection and
construction of investment portfolios based on the maximization of expected
returns of the portfolio and the simultaneous minimization of investment risk
(variance). In 1958, economist James Tobin in his essay, “Liquidity Prefer-
ence as Behavior Toward Risk” derived the ‘E¢ cient Frontier’ and ‘Capital
Market Line’ concepts based on Markowitz’ works. Independently developed
by William Sharpe, John Lintner, and Jan Mossin, another important capi-
tal markets theory evolved as an outgrowth of Markowitz’and Tobin’s earlier
works— The Capital Asset Pricing Model (CAPM) (Mangram, 2013). Techni-
cally, Markowitz portfolio selection theory and CAPM together led to deduction
of MPT.
Prior to Markowitz’s work, security-selection models focused primarily on
the returns generated by investment opportunities. Standard investment advice
was to identify those securities that o¤ered the best opportunities for gain with
the least risk and then construct a portfolio from these. The Markowitz theory
retained the emphasis on return; but he elevated risk to a coequal level of
importance, and the concept of portfolio risk was born. Whereas risk has been
considered an important factor and variance an accepted way of measuring risk,
Markowitz was the …rst to clearly and rigorously show how the variance of
a portfolio can be reduced through the impact of diversi…cation, he proposed
that investors focus on selecting portfolios based on their overall risk-reward
characteristics instead of merely compiling portfolios from securities that each
individually have attractive risk-reward characteristics (Chen et al, 2010).
3

4. 3.1 Calculation of asset return
In order to predict future returns (expected return) for a security or portfolio,
the historical performance of returns are often examined. Expected return can
be de…ned as “the average of a probability distribution of possible returns”
(Expected Return, n.d.). Calculation of the expected return is the …rst step in
Markowitz’portfolio selection model. Expected return, also commonly referred
to as the mean or average return, can simply be viewed as the historic average
of a stock’s return over a given period of time (Benniga, 2006). The return
computation …nds the weighted average return of the securities included in the
portfolio. CAPM will also be used to calculate a return based on risky and risk-
free components in the following sub-section. Given any set of risky assets and
a set of weights that describe how the portfolio investment is split, the general
formulas of expected return for n assets is (Chen et al, 2010):
E(RP ) =
nX
i=1
wiE(Ri) (1)
Where,Pn
i=1 wi = 1.0;
n = the number of securities;
wi = the proportion of the funds invested in security i;
Ri; RP = the return on ith security and portfolio p; and
E() = the expectation of the variable in the parentheses.
3.2 Calculation of risk
There are various ways to determine the volatility (risk) of a particular secu-
rity’s return. The most common measures are variance and standard deviation.
Variance is a “measure of the squared deviations of a stock’s return from its
expected return”— the average squared di¤erence between the actual returns
and the average return (Bradford, J. & Miller, T., 2009). The variance of a
single security is the expected value of the sum of the squared deviations from
the mean, and the standard deviation is the square root of the variance. The
variance of a portfolio combination of securities is equal to the weighted average
covariance of the returns on its individual securities (Chen et al, 2010).
V ar(RP ) = 2
P =
nX
i=1
nX
j=1
wiwjCov(Ri; Rj) (2)
Covariance can also be expressed in terms of the correlation coe¢ cient as
follows:
Cov(Ri; Rj) = ij i j = ij (3)
where
ij= correlation coe¢ cient between the rates of returns Ri and Rj,
4

5. Figure 2: Concepts of Modern Portfolio Theory
i and j = standard deviations of Ri and Rrj respectively. Therefore,
equation 2 can be written as:
V ar(RP ) =
nX
i=1
nX
j=1
wiwj ij i j (4)
From equation 2, we deduce that high covariance signi…es increase in one
stock’s return is likely to correspond to an increase in the other. Therefore,
low covariance corresponds to return rates are relatively independent. Negative
covariance means increase in one stock’s return is likely to correspond to a
decrease in the other. Also, from equation 4, if ij = 1, then there is perfect
positive correlation and diversi…cation is not e¤ective. On the other hand, if
ij < 1, then there is bene…t from diversi…cation. An investor can reduce
portfolio risk simply by holding instruments which are not perfectly correlated,
i.e. diverse portfolio.
E¢ cient asset allocation can be explored by using two risky assets for ex-
ample. The …gure 2(a) shows a two-asset scenario, where AB is the correlation
coe¢ cient between the returns of technologies A and B. An investor can reduce
portfolio risk simply by holding instruments which are not perfectly correlated.
E¢ cient portfolios may contain any number of asset combinations. The …g-
ure 2(a) shows the opportunity set with perfect positive correlation - a straight
5

6. line through the component assets ( = 1). No portfolio can be discarded as
ine¢ cient in this case, and the choice among portfolios depends only on risk
preference. Diversi…cation in the case of perfect positive correlation is not ef-
fective. If < 1, then there is bene…t from diversi…cation.
3.3 Capital Asset Pricing Model for asset diversi…cation
CAPM simpli…ed MPT by introducing the idea of speci…c and systematic risk.
In 1958, John Tobin explained how the introduction of risk-free investments into
Markowitz’theory further reduces the risk of a portfolio. According to Tobin,
the Capital Market Line (CML) de…nes a new "e¢ cient frontier" of investments
for all investors. Applied to project appraisal, Markowitz theory reveals that
an individual project’s risk is not as important as its e¤ect on the portfolio’s
overall risk. So, whenever management evaluate a risky project they must cor-
relate the individual project risk with that for the existing portfolio it will join
to assess its suitability. Without the bene…t of today’s computer technology,
the mathematical complexity of the Markowitz model arising from its covari-
ance calculations prompted other theorists to develop alternative approaches to
e¢ cient portfolio diversi…cation. In the early 1960s by common consensus, the
CAPM emerged as a means whereby investors in …nancial securities were able
to reduce their total risk by constructing portfolios that discriminate between
systematic (market risk) and unsystematic (speci…c) risk (Ebrary, 2017). This
is graphically represented in …gure 2(b). CAPM can be represented below:
E(RP ) = RF + P [E(RM ) RF ] (5)
P = measure of market risk
P = 1; is the beta for the market M
P > 1 returns in excess of market returns
P < 1 returns lower than market returns
P = 0 is zero market risk = risk-free return
E(RM ) RF = market risk premium
3.4 Sharpe Ratio
The Sharpe Ratio is used to calculate the performance of an investment by
adjusting for its risk (Sharpe, 1975). The higher the ratio, the greater the
return of portfolio relative to the risk taken, and thus the better the investment.
Conventionally, Sharpe ratio < 1 is bad, 1 –1.99 is adequate/ good, 2 –2.99 is
great and >3 is excellent. It is calculated by the following equation:
Sharpe_Ratio = [E(RP ) RF ]= RP
(6)
3.5 E¢ cient Frontier
The concept of E¢ cient Frontier was introduced by Markowitz. Every possible
asset combination can be plotted in risk-return space, and the collection of all
6

7. such possible portfolios de…nes a region in this space. The line along the upper
edge of this region is known as the e¢ cient frontier. Combinations along this
line represent portfolios (explicitly excluding the risk-free alternative) for which
there is lowest risk for a given level of return. The …gure ?? shows a hyperbola
representing all the outcomes for various portfolio combinations of risky assets,
where standard deviation is plotted on the X-axis and return is plotted on the
Y-axis.
MPT suggests that combining an investment portfolio which sits on the e¢ -
ciency frontier with a risk free investment can actually increase returns beyond
the e¢ ciency frontier for a given risk. When a risk free investment possibility
is introduced into the mix, the tangential line shown in …gure 2(c) becomes the
new e¢ ciency frontier, and is called the Capital Allocation Line (CAL). It is
tangential to the old e¢ ciency frontier at the risky portfolio point with the high-
est Sharpe Ratio. In …gure 2(c), the y-axis intercept of the CAL represents a
risk free investment portfolio, i.e. de…ned as ‘no variability’in return. The point
of tangency with the hyperbola represents the portfolio with the most desirable
risk-return pro…le in relation to the available …xed-return investment. Points in
between these two options along the CAL represent the best possible combina-
tions of investments (including risk free ones) for each risk level (Gaydon et al.,
2012, Merton, 1972).
4 MPT for energy mix: Case studies
Following the above discussion on how the asset managers take into account
the risk for diversifying the asset, the energy planners need to abandon their
reliance on traditional, “least-cost”stand-alone kWh generating cost measures
and instead evaluate conventional and renewable energy sources on the basis of
their portfolio cost i.e. their cost contribution relative to their risk contribution
to a mix of generating assets (Awerbuch, 2006). Renewable technologies, which
tend to have greater levelized costs than non-renewable options, can help to
decrease portfolio risk for a given level of portfolio cost, due to their zero corre-
lation with fossil fuel prices following equations 3 and 4. MPT can help reduce
the decision set of technologies, and determine their shares in portfolios to an
examination of the small subset of the total of such portfolios which are e¢ cient
in terms of their risk-return characteristics. MPT can also measure the impact
of additional technologies in terms of their contribution to portfolio costs and
risks. An e¢ cient portfolio is one in which the cost is lowest for any given level
of risk. In the following paragraphs, some key studies have been discussed with
their resulting e¢ cient frontier diagrams.
One key feature in the application of MPT to energy portfolios is the comple-
mentarity among the various technologies in the mix. Awerbuch (2006) discusses
portfolio case studies from EU and USA in the energy sector. The representa-
tion of energy portfolio of EU in 2000 and 2010 and US in 2002 has been shown
in …gure 3. In …gure 3(a), portfolio risk is measured in the traditional manner as
the standard deviation of historic annual outlays for fuel, operation and main-
7

8. tenance (O&M) and construction period costs. Portfolio return is expressed as
kWh/US-Cent –the inverse of generating costs. Higher returns in …gure 3(a)
represent lower costs. An in…nite number of portfolio mixes exist at di¤erent
risk-return locations, each with a di¤erent mix of technologies. For US, in …gure
3(b), the move to Mix-N from the US-2002 Mix reduces risk by 23% (from 8.5
to 6.6%) without changing cost. Mix-S, by comparison, lowers generating cost
by 12% relative to the US-2002 Mix, and leaves risk unchanged. Figure 3(b),
also illustrates that the US policy of continued gas expansion raises risk rapidly
while yielding only small cost reductions. A move from Mix S to a mix of 100%
gas, increases risk by 35% (from 8.5 to about 11.5%) but reduces cost by less
than 9% (.27/.295).
Roques et al. (2010) came up with an e¢ cient frontier for EU future energy
mix by including all the technological constraints of wind energy. Figure 4(a)
represents the constrained and unconstrained e¢ cient frontier for optimising
wind power output. Potential gains from actual and projected portfolio to
e¢ cient frontier range from 4% to 7% (lower than for theoretical unconstrained
portfolios for which the potential gains range from 7% to 9%). Figure 4(b)
represents the constrained and unconstrained e¢ ciency frontiers to maximise
wind power contribution to system reliability during peak-hours. Even if the
constrained e¢ cient frontier is considerably lowered compared to the theoretical
unconstrained portfolios, the projected portfolio for 2020 is still far from the
constrained e¢ ciency frontier. These results highlight the need for more cross-
border interconnection capacity, for greater coordination of European renewable
support policies, and for renewable support mechanisms and electricity market
designs providing locational incentives.
Zhu and Fan (2010) applied MPT to evaluate China’s 2020-medium-term
plans for generating technologies and they considered externalities caused by
CO2-emission. They came up with 4 di¤erent scenarios with their separate cost-
risk curves and e¢ cient frontiers as shown in the …gure 5. They concluded that
in the CO2-emission-constrained scenarios, the generating-cost risk of China’s
planned 2020 portfolio is even greater than that of the 2005 portfolio, but in-
creasing the proportion of nuclear power in the generating portfolio could reduce
the cost risk e¤ectively. For renewable-power generation, because of relatively
high generating costs, it would be necessary to obtain stronger policy support
to promote renewable-power development.
Awerbuch and Yang (2007) studied the optimization of the European Union’s
2020 electricity plan against the background of global climate change. Their
research pointed out that optimization of the European Union’s 2020 electricity
plan will be restricted by shortages of o¤shore wind power and nuclear power.
They came up with two e¢ cient frontiers depending on whether CO2-emission
is being priced or not, as shown in …gure
Many other studies have also been undertaken around the world applying
MPT for determining energy mix. Krey and Zweifel (2006) re…ned the econo-
metric evidence for Swiss and US power generation e¢ cient frontiers, by im-
plementing seemingly unrelated regression estimation (SURE) to obtain rea-
sonably time-invariant covariance matrices as an input to the determination of
8

9. Figure 3: (a) Cost and risk of EU generating mixes from Awerbuch and Berger
(2003); (b) Risk-return for 3-Technology US generating mix from Awerbuch et
al. (2005)
9

10. Figure 4: Constrained and unconstrained e¢ cient frontiers for (a) Optimising
wind power output and (b) maximising reliability
e¢ cient electricity-generating portfolios. Roques, Newbery, and Nuttall (2008)
introduced Monte Carlo simulations of gas, coal and nuclear plant investment
returns as inputs of a Mean-Variance Portfolio optimization to identify opti-
mal base load generation portfolios for large electricity generators in liberalized
electricity markets.
In most of the studies except few, the externalities and social costs have
not been dealt with in depth. CO2-emission has been taken as only externality
which may not represent the whole extent of social cost. In the next section
of conclusion, a clear roadmap to conduct an MPT analysis will be represented
using some key articles (Marrero et al., 2015; Allan, et al., 2010).
5 Conclusion
5.1 Way forward: How to implement MPT?
In order to apply MPT in energy mix studies, certain steps need to be followed in
order to plot the technologies in risk-cost space and obtain the e¢ cient frontier.
These steps are discussed below:
10

11. Figure 5: Portfolios and e¢ cient frontier under 4 scenarios in China (compiled
from Zhu and Fan, 2010)
Figure 6: E¢ cient frontiers (e0/t CO2 and e35/t CO2) for EU 2020 electric-
ity generation mix (Values in parentheses next to the mixes show annual CO2
emissions in million tonnes. The 2020 EU-BAU emits 1,273 million-tonnes per
year) (Awerbuch and Yang, 2007)
11

12. 5.1.1 Data and factors a¤ecting future energy mix
Development of operational electricity generation capacity needs to be collected.
Capacity operational installed in each decade for each technology needs to be
found out. Also, the energy ‡ow with TPER and the sectoral requirements need
to be known from Government reports. These data will give a clear indication of
current energy mix of the country. A number of scenarios need to be determined
according to technical (network and grid constraints and developments, and
the remaining lifetimes of existing plant) and policy (requirement of EU or
other regulatory agency, environmental regulations, etc). Sometimes, various
organizations come up with future scenarios which can be included in the study,
but it also needs a central scenario around which sensitivity analysis needs to
be performed.
5.1.2 Calculating asset return and risk
The asset return and risks associated to main energy use sectors need to be
calculated separately and then integrated using equation 1. CAPM and various
other risk calculation methods can also be used for this task. The following
three …elds have been identi…ed to be considered for such calculations (Marrero
et al., 2015):
I Electricity supply options- Asset Return: unit cost for each technology
(LCOE in p/kWh); Risk: year-to-year variation in each technology’s generating
cost
I Electricity-generating technologies- Asset Return: holding-period re-
turns measuring range of change in the cost streams from one period to the
next; Risk: Std deviation of holding-period returns for cost streams for each
technology
I Road Transport- Asset Return: Average running cost for midsized car
(e/Km), CO2 emissions (gm/Km); Risk: Fluctuation in price of crude oil, sug-
arcane, corn, rapeseed, soybean oil. Energy global commodity index can be
taken as the baseline market index
In calculating the asset return (costs) and risk, the factors detailed in the
…gure 7(a) needs to be considered for each technology (renewable and non-
renewables). The external costs should include non-use values and non-human
values. At present, only CO2 emission costs are included. As the holding-
period returns measure the year-to-year ‡uctuations in the cost stream, the
standard deviation of these cost streams is expressed as a percentage. Each
cost component (e.g. construction, fuel, etc.) can, in principle, have a di¤erent
standard deviation for its holding-period return than that same cost component
for other technologies. Following calculation of these cost and risk, they are
represented in a risk-cost space for all the technologies (…gure 7(b)).
12

13. Figure 7: (a) Cost and Risks interpreted from Allan, et al. (2010), plus external
costs; (b) All electricity supply options in cost–risk space (Allan, et al., 2010)
13

14. 5.1.3 Correlation between costs
The next element required is to determine the correlation between the costs of
each of the technologies. Following the literature, the correlation between tech-
nologies’costs as being based on two elements viz. the correlation between fuel
costs, and between O&M costs are being estimated. Fuel cost correlations are
taken from published government documents (e.g. BERR’s Quarterly Energy
Prices publication). The correlation coe¢ cients will have values between -1 and
1 as explained in equation 4. A positive correlation coe¢ cient indicates that
time series’for two values tend to move in the same direction (e.g. the fuel costs
for coal and gas), while a negative coe¢ cient indicates that two values which
tend to move in di¤erent directions (e.g. the fuel costs of biomass and gas).
5.1.4 Technologies’shares in future electricity portfolios
The setting of an upper bound for each technology is driven by the energy re-
source constraint, or the extractable energy potential, in the case of renewable
energy options or the maximum attainable deployment levels for each technol-
ogy in the case of non-renewables. A “central case”results use the upper and
lower constraints on each technology need to be determined from Government
documents e.g. Vision 2020 documents.
5.1.5 Central results: Comparison of scenarios to e¢ cient portfolios
Firstly, the model to generate the e¢ cient frontier was solved to obtain the set
of portfolios which give the lowest level of portfolio risk for a given portfolio cost
and lowest portfolio cost for a given portfolio risk. Then the cost–risk pro…les
of the four scenarios can be compared to this frontier and the mean-variance
e¢ ciency of these scenarios can be discussed. An example has been shown in
…gure 8(a). Again, …gure 8(b) from Allen et al. (2010) shows the generation mix
for each of the four scenarios for Scotland in 2020, plus the 2007 mix. It also
shows the e¢ cient portfolios with the same cost but the minimum risk (MR),
or the same risk but minimum cost (MC), as the four scenarios. The next eight
columns show, in turn for each of the four 2020 scenarios, the minimum cost
and minimum risk portfolios which can be constructed with the same level of
risks and costs, respectively.
5.1.6 Sensitivity analysis using minimum and maximum values
This analysis is carried out in order to check the range of variation in e¢ cient
frontier generated by the model. Sensitivity analysis is done by repeating the
calculation of the e¢ cient frontier using higher and lower ranges of fuel cost,
externalities as well as technology constraints. Once this is done, three di¤erent
e¢ cient frontiers emerge, one each for central, minimum and maximum ranges
of values. Two outcomes will happen, …rstly, the risk measure for any given
technology mix will change and secondly, mixes along the e¢ cient frontier will
14

15. Figure 8: (a) Cost–risk space showing e¢ cient frontier and four scenarios, plus
2007 generation mix, and minimum risk and minimum cost (e¢ cient) variants
of each scenario; (b) 2007 mix and four scenarios for Scottish mix in 2020, plus
minimum risk and minimum cost variants of each scenario (Allan et al., 2010)
15

16. change- previously ine¢ cient portfolios will now be e¢ cient and vice versa. Less
of these variations happen, more robust is the e¢ cient frontier calculation.
5.2 Externalities and social cost
While external costs and internal costs make up the social costs, the cost to
society can be obtained by adding private costs with social costs. This calcu-
lation of cost to society is important for calculating the risk associated with
a technology. Although the renewables may bear high construction cost, they
incur less cost to society and contribute towards the energy mix and becomes
competitive to the conventional fossil fuels. Full internalisation of all e¤ects not
transported through prices to guide for sustainable development can be achieved
by renewable energy.
Some studies in the past have included only CO2 emission as external costs.
Marrero, Puch, and Ramos-Real (2011) considers CO2 externalities to analyze
the projected generating mix for Europe in 2020 (EU-BAU) highlighting the
importance of complementarity between traditional and renewable energies to
reduce not only portfolio risk and average cost but also total CO2 emissions.
Roques, Hiroux, and Saguan (2010) applied the MPT to identify cross-country
portfolios that minimize the total variance of wind production for a given level of
production across Austria, Denmark, France, Germany and Spain. They found
that projected portfolios for 2020 are far from the e¢ cient frontier, suggesting
that there could be large bene…ts in a more coordinated European renewable de-
ployment policy. Marrero et al. (2015) deduced that moving from traditional to
other mix, not only implies that average cost and risk fall but also the CO2 emis-
sions. Sensitivity analysis accounts for the intermittency costs of renewables,
the decommissioning costs of nuclear plants and the costs of CO2 emissions.
Adding these costs when considering total risk implies that nuclear energy tend
to shrink in favor of CC Gas, while wind energy remains in its upper bound and
the reduction in CO2 emissions is much more limited. A negative externality
occurs when the social cost is greater than the production cost or private cost.
Thus true cost to society needs to be …nd out and brought into the equation
for calculating cost. Figure 9(a) shows the entire spectrum of values that need
to be determined, especially the non-use values and non-human values that are
not being calculated under the current studies. Various non-market valuation
methods that can be used for calculating these externalities and social costs
have been shown in …gure 9(b).
5.3 Renewables in Ireland’s future energy mix
Beyond the social bene…ts and negative externalities that renewables can bring
into the energy mix, there are some regulatory compulsion for Ireland to stress
upon the renewables. Ireland must achieve a mandatory target of 16% renew-
able contribution in overall consumption and a 10% share of renewable en-
ergy in transport consumption as set out in the Renewable Energy Directive
16

17. Figure 9: (a) Valuation methods for use and non-use values; (b) Non-market
valuation methods
(2009/28/EC) by EU. However, …gure 10 shows that at present rate of initia-
tive, the 2020 projection will only achieve 13.2% overall and 2% in transport
sector. Up to end 2015, only 9.1% of overall energy demand was derived from re-
newable sources through a range of actions. This de…ciency means that Ireland
can potentially miss its 2020 cumulative emissions reduction target by around
12 Mt CO2eq. Failure to comply with energy and emissions targets in 2020 will
result in EU …nes and could lead to a more arduous trajectory in the context of
post-2020 targets –both in terms of future deployment and potential compliance
costs (SEAI, 2017).
5.4 Recommendations
From the above discussions, the following points can be deduced:
Ireland is bound to include at least 16% renewable energy by 2020 (Re-
newable Energy Directive 2009/28/EC), failing which may be costly in the
long term. Failure is most likely unless the rate of renewable conversion
is stepped up.
Inclusion of renewables in the energy mix results in social bene…ts and
positive externalities, making the process more cost e¤ective and low risk.
Optimum mix of various non-renewable and renewable can be determined
using MPT and this will essentially lead to three bene…ts, viz. increasing
17

18. Figure 10: Renewable energy share in Ireland- overall progress and current
trajectory to 2020 (SEAI, 2017)
the diversity of the electricity mix, reducing the portfolio risk and main-
taining overall portfolio cost due to non-correlation with fossil fuel price-
all leading to robust future-proof energy security.
REFERENCES
Allan, G., Eromenko, I., McGregor, P., & Swales, K. (2011). The regional electric-
ity generation mix in Scotland: A portfolio selection approach incorporating marine
technologies. Energy Policy, 39(1), 6-22.
Awerbuch, S. (2006). Portfolio-Based Electricity Generation Planning: Policy Im-
plications For Renewables And Energy Security. Mitigation and Adaptation Strategies
for Global Change, 11(3), 693-710.
Awerbuch, S., & Yang, S. (2007). E¢ cient electricity generating portfolios for
Europe: maximising energy security and climate change mitigation. EIB papers,
12(2), 8-37.
Benninga, S. (2010). Principles of …nance with excel. OUP Catalogue.
BP. (2017). BP Statistical Review of World Energy. Retrieved from https://goo.gl/EAsFrk
Bradford, J., & Miller, T. (2009). A Brief History of Risk and Return, Fundamen-
tals of investments: New York, NY: McGraw-Hill.
CFI. (2017). Capital Asset Pricing Model (CAPM): A method for calculating the
required rate of return, discount rate or cost of capital. Retrieved from https://goo.gl/ndNdde
Chen, W.-P., Chung, H., Ho, K.-Y., & Hsu, T.-L. (2010). Portfolio optimization
models and mean–variance spanning tests Handbook of quantitative …nance and risk
management (pp. 165-184): Springer.
Doherty, R., Outhred, H., & O’Malley, M. (2005). Generation portfolio analysis
for a carbon constrained and uncertain future. Paper presented at the Future Power
Systems, 2005 International Conference on.
Ebrary. (2017). Portfolio Theory and the CAPM.
EirGrid, & SONI. (2017). All-Island Generation Capacity Statement, 2017-2026.
Retrieved from https://goo.gl/5yGPRf
18

19. Gaydon, D., Meinke, H., Rodriguez, D., & McGrath, D. (2012). Comparing wa-
ter options for irrigation farmers using Modern Portfolio Theory. Agricultural water
management, 115, 1-9.
GNI. (2016). Network Development Plan 2016: Assessing future demand and
supply position. Retrieved from www.gasnetworks.ie
IEA. (2016). International Energy Agency: Energy security. Retrieved from
https://www.iea.org/topics/energysecurity/
International Energy Agency. (2016). World Energy Outlook: Executive Sum-
mary. Retrieved from France: https://goo.gl/Ho6ghR
Krey, B., & Zweifel, P. (2006). E¢ cient electricity portfolios for Switzerland and
the United States. Retrieved from
Mangram, M. E. (2013). A simpli…ed perspective of the Markowitz portfolio the-
ory.
Markowitz, H. M. (1991). Foundations of portfolio theory. The journal of …nance,
46(2), 469-477.
Marrero, G. A., Puch, L. A., & Ramos-Real, F. J. (2015). Mean-variance portfolio
methods for energy policy risk management. International Review of Economics &
Finance, 40, 246-264.
Merton, R. C. (1972). An analytic derivation of the e¢ cient portfolio frontier.
Journal of …nancial and quantitative analysis, 7(4), 1851-1872.
Roques, F., Hiroux, C., & Saguan, M. (2010). Optimal wind power deployment in
Europe— A portfolio approach. Energy Policy, 38(7), 3245-3256.
Roques, F. A., Newbery, D. M., & Nuttall, W. J. (2008). Fuel mix diversi…ca-
tion incentives in liberalized electricity markets: A Mean–Variance Portfolio theory
approach. Energy Economics, 30(4), 1831-1849.
SEAI. (2017). Energy in Ireland 1990-2016. Retrieved from Ireland: https://goo.gl/oioRin
Sharpe, W. F. (1975). Adjusting for risk in portfolio performance measurement.
The Journal of Portfolio Management, 1(2), 29-34.
Zhu, L., & Fan, Y. (2010). Optimization of China’s generating portfolio and policy
implications based on portfolio theory. Energy, 35(3), 1391-1402.
19