NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Variance Analysis of Wind and 

Natural Gas Generation under

Different Market Structures: 

Some Observations

Brian Bush, Thomas Jenkin, David Lipowicz, 

and Douglas J. Arent 

National Renewable Energy Laboratory

Roger Cooke

Resources for the Future

Technical Report

NREL/TP-6A20-52790

January 2012
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

National Renewable Energy Laboratory

1617 Cole Boulevard

Golden, Colorado 80401

303-275-3000 • www.nrel.gov

Contract No. DE-AC36-08GO28308

Variance Analysis of Wind and 

Natural Gas Generation under 

Different Market Structures: 

Some Observations

Brian Bush, Thomas Jenkin, David Lipowicz, 

and Douglas J. Arent 

National Renewable Energy Laboratory

Roger Cooke

Resources for the Future

Prepared under Task No. 6A50.1020

Technical Report

NREL/TP-6A20-52790

January 2012
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iii

Acknowledgments

The authors would like to thank a number of individuals who were kind enough to provide 

suggestions on earlier drafts or to discuss some of the ideas related to the contents of the report. 

These individuals include Sam Baldwin and Darrell Beschen from the Office of Energy 

Efficiency and Renewable Energy, James Milford and Gian Porro from the National Renewable 

Energy Laboratory, Nils Melquist from Deutsche Bank Climate Change Advisors, and John 

Parsons from Massachusetts Institute of Technology. We would also like to thank the 

Department of Energy for partially funding the work contained in this report. 
iv

List of Acronyms

ARRA American Recovery and Reinvestment Act

CCGT combined-cycle gas turbine 

CT combustion turbine 

DRM downside risk measure 

EBITDA earnings before interest taxes depreciation and 

amortization

ERCOT Electric Reliability Council of Texas 

kW kilowatt

kWh kilowatt-hour 

LCOE levelized cost of energy

LMP locational marginal price

MVPA mean-variance portfolio analysis 

MW megawatt 

MWh megawatt-hour 

NYMEX New York Mercantile Exchange

O&M operation and maintenance

PJM Pennsylvania-New Jersey-Maryland 

Interconnection 

PTC production tax credit 

RTO regional transmission organization 

RoR rate of return

RE renewable energy

U economic utility 
v 

Executive Summary

An important area of current research is whether large-scale penetration of variable renewable 

generation such as wind and solar power pose economic and operational burdens on the 

electricity system. In such scenarios, this issue has also raised considerable interest in the 

potential role and value of electricity storage as a method of mitigating variability in generation 

associated with the inherently variable nature of these forms of generation. At the same time, a 

number of studies have pointed to the potential benefits of renewable generation as a hedge 

against the volatility and potential escalation of fossil fuel prices. Prior research and this work 

suggest that the lack of correlation of renewable energy costs with fossil fuel prices means that 

adding large amounts of wind or solar generation may also reduce the volatility of system-wide 

electricity costs.1

The analysis in this report recognizes that the potential value of risk mitigation associated with 

wind generation and natural gas generation may depend on whether one considers the 

consumer’s perspective or the investor’s perspective and whether the market is regulated or 

deregulated. We analyze the risk and return trade-offs for wind and natural gas generation for 

deregulated markets based on hourly prices and load over a 10-year period using historical data 

in the PJM Interconnection (PJM)

 Such variance reduction in overall system costs may be of significant value to 

consumers due to risk aversion. In contrast to this observation, other studies have focused on 

returns in restructured markets and noted that, in deregulated markets, baseload natural gas 

power generation may be relatively more attractive to investors because—unlike wind 

generation—peak power prices are often strongly correlated to natural gas prices.

2

In a deregulated market such as PJM,

 from 1999 to 2008. Similar analysis is then simulated and 

evaluated for regulated markets under certain assumptions. Estimating the absolute value, as 

opposed to the relative value, of variance reduction will also depend on assumptions about risk 

aversion and other consumer preferences, such as loss aversion, and this is discussed. Some key 

observations include: 

• Returns for natural gas generation are partially hedged because power prices are often 

set by natural gas generation, though with significant seasonal variations. 

• Returns for wind generation are better hedged than natural gas generation because 

wind often operates in off-peak hours, where power prices are much less volatile and 

less correlated with natural gas prices, whereas natural gas generation operation is 

focused more heavily during peak hours.3

• The impact of incremental net revenue from tax credits, such as production tax credits 

(PTCs) or other sources of revenue, can have a significant impact on the risk return 

relationship. In PJM over this period with credits, wind was found to be dominant in 

 

 

1 Although the impact of potentially off-setting effects due to operational intermittency resulting from natural 

variations in wind or solar output over a variety of timescales needs to be carefully considered. 2

 PJM Interconnection is a regional transmission organization (RTO) that coordinates the movement of wholesale 

electricity in all or parts of 13 states and the District of Columbia (www.pjm.com).

3 For wind and natural gas technologies with the cost and performance assumptions used in this analysis.
vi 

terms of risk and reward; that is, it had both greatest returns and the lowest risk, as 

measured by standard deviation of returns. 

• More generally, without PTCs investors may benefit from investing in both wind and 

natural gas generation, with the optimal mixture depending on the investor’s risk 

aversion (and perhaps also loss aversion) preferences due to well-known lack of 

correlation effects. 

• While the opportunity for investors to diversify in broader markets may reduce some 

of the variance reduction benefits of investing in different electric technologies, it is 

unlikely to completely eliminate these benefits in the electric sector where power 

prices are often very volatile and positively skewed, which has implications for 

financial distress. 

• Consumers, especially smaller commercial and residential consumers, may benefit 

from reductions in the variance of electricity prices due to risk aversion and loss 

aversion effects.4

• The levelized cost of energy (LCOE) of different technologies is not directly 

comparable if they operate in different hours because the value of electricity differs 

significantly throughout each day. This variation reflects the daily load profile, with 

hourly load and hourly power prices also showing strong seasonal effects. This effect 

can be seen in our analysis of PJM data when comparing the difference in the average 

annualized hourly price of variable wind generation and dispatchable natural gas 

generation.

 

In a regulated market: 

• The inherent nature of regulated markets means that producers earn, with some 

caveats, a utility-designated rate of return. A consequence of this is that the risk 

associated with fuel costs is passed on to the consumer. The “cost-plus” nature of 

regulation means that consumers also bear some increased risk associated with poor 

investment decisions. Consumers are partly compensated for this because the 

producer may be willing to accept a lower expected rate of return compared to 

deregulated markets.

• For consumers, who are generally risk averse, the reduced variation in electricity 

prices (and hence consumer costs) because of wind’s lack of correlation with other 

system costs should have value (as has been suggested by others). Loss aversion also 

may place a value on variance reduction of electricity prices and consumer costs. 

• Simplified mean variance cost optimization techniques using annualized LCOEs for 

the power sector often fail because the assets within the portfolio are too dissimilar 

(e.g., baseload versus peaking or either of these versus a variable or non-dispatchable 

resources such as wind or solar). 

• A variance reduction-based technique could, however, be used more broadly under 

more sophisticated representation of system costs where the hourly operation of the 

 

4

 This could also hold true for large consumers such as utilities if they or regulators realized they could quantify the 

value of such variance reduction to consumers and get paid by consumers some fraction of this value to do so.
vii 

technologies is modeled more explicitly. Specifically for a regulated electric system, 

the concept of lowest-cost planning could be refined to have an array of “least-cost 

planning” solutions corresponding to different variances, where the values of the 

expected annualized system cost and the standard deviation of the annualized system 

cost are physical properties of the electric system that are completely independent of 

any risk or loss aversion preferences. The value of variance reduction could then 

reflect both risk aversion and loss aversion. We discuss explicitly how to estimate the 

difference in the economic utility between alternative system-based, expected costcost variance choices, including the impact of the distribution being positively 

skewed toward higher costs. 

In conclusion, we should point out that while some of the observations and findings may be 

generally applicable, others are empirical observations for a specific location and a specific time 

period under specific technology cost and performance assumptions.5 

 

5 For example, within PJM over the same time period, different assumptions about technology performance and cost 

for wind and natural gas could lead to different risk-return relationships. Similarly, the risk-return relationships may 

vary outside of PJM, or over different time periods within PJM, because of differences in hourly electricity prices. 
viii

Table of Contents

Acknowledgments ........................................................................................................................ iii

List of Acronyms .......................................................................................................................... iv

Executive Summary ...................................................................................................................... v

Table of Contents ....................................................................................................................... viii

List of Figures ............................................................................................................................... ix

List of Tables ................................................................................................................................. x

1 Introduction ............................................................................................................................. 1

1.1 Structure of this Report .................................................................................................. 1

1.2 Background .................................................................................................................... 2

1.3 Variance Reduction of Portfolio Due to Lack of Correlation of Costs or Returns ........ 6

2 Wind and Natural Gas Generation ..................................................................................... 10

2.1 Background .................................................................................................................. 10

2.2 Methodology ................................................................................................................ 12

3 Wind and Natural Gas Generation in a Deregulated Market .......................................... 15

3.1 Producer Returns over 10-Year Period (1999–2008) ................................................... 15

3.2 Producer Prices and Consumer Costs in a Deregulated Market ................................... 17

3.3 Some Cost, Value, and Portfolio Optimization Considerations ................................... 18

4 Wind and Natural Gas Generation in a Regulated Market and in Comparison with 

Deregulated Markets ............................................................................................................ 22

4.1 Comparison of Annualized and Monthly Returns in Regulated and Deregulated 

Markets ......................................................................................................................... 23

4.2 Comparison of Consumer Costs and Variance in Regulated and Deregulated 

Markets ......................................................................................................................... 25

4.3 Some Comments on Investment Decisions and Risk and Uncertainty in the Electric 

Sector ............................................................................................................................ 28

4.3.1 Investment Decisions Under Risk Aversion and Loss Aversion ........................... 28

4.3.2 Using System Models to Estimate the Economic Value of Alternative Electricity 

System Cost-Cost Variance Combinations ............................................................ 32

5 Summary and Conclusions................................................................................................... 35

References .................................................................................................................................... 38
ix

List of Figures

Figure 1-1. Daily price variation of natural gas, oil, and electricity prices (1999 to 2008) ........... 3

Figure 1-2. Distribution of energy prices separated into two 5-year blocks (1999 to 2008) ......... 5

Figure 1-3. Risk and return relationship for mixes of two assets under different correlation 

assumptions ................................................................................................................. 6

Figure 2-1. Growth in natural gas and wind generation in the United States (1999-2008) ......... 10

Figure 2-2. Spread between real-time electricity prices (PJM 2009) and the cost of natural gas 

for a combined-cycle gas turbine (under 40% efficiency assumption) (1999-2008) 11

Figure 3-1. Annual and monthly returns for wind and natural gas generation in PJM (deregulated 

market example) (1999-2008) ................................................................................... 15

Figure 3-2. Annual utilization and average price received for wind and natural gas technology 

over 24-hour period ................................................................................................... 18

Figure 3-3. Risk-return relationship for wind and natural gas without subsidies ........................ 20

Figure 4-1. Risk versus reward using standard measures (top row) and robust measures (bottom 

row) from the perspective of a producer ................................................................... 24

Figure 4-2. Average monthly price ($/MWh) of wind and natural gas generation in deregulated 

market (PJM) and simulated regulated market (1999 to 2008) ................................. 26

Figure 4-3. Consumer cost versus risk relationships for wind and natural gas generation in 

deregulated market (PJM) and simulated regulated market ...................................... 28

Figure 4-4. Expected return and standard deviation of return for wind and natural gas generation 

(without PTC or capacity payment) .......................................................................... 29

Figure 4.5. Optimal asset mix as a function of risk and loss aversion (illustrative) .................... 32
x 

List of Tables

Table 1-1. Correlation of Daily Energy Prices ............................................................................... 5

Table 2-1. Contract Variables and Price Assumptions ................................................................. 14

Table 2-2. Price Formulas for the Four Contracts ........................................................................ 14

Table 4-1. Price and Measures of Risk for Wind and Natural Gas Generation in Deregulated and 

Regulated Markets ........................................................................................................................ 27
1 

1 Introduction

1.1 Structure of this Report

An important area of current research is whether large-scale penetration of variable renewable 

generation, such as wind and solar power, pose economic and operational burdens on the 

electricity system. In such scenarios, this issue has also raised considerable interest in the 

potential role and value of electricity storage as a method of mitigating variability in generation 

associated with the inherently variable nature of these forms of generation. At the same time, a 

number of studies have pointed to the potential benefits of renewable generation as a hedge 

against the volatility and potential escalation of fossil fuel prices (Bolinger et al. 2002). Prior 

research and our analysis suggest that the lack of correlation of renewable energy costs with 

fossil fuel prices also means that adding large amounts of wind (or similarly solar) generation 

may lead to a reduction in the volatility of the system-wide electricity costs (Awerbuch and 

Berger 2003). Risk aversion has been investigated in relation to traditional financial markets, in 

relation to individual versus societal discount rates (Portney and Weyant 1999), and also in 

relation to technology choices (Roques et al. 2008), but less analysis has been done that 

compares and contrasts the impact of renewable energy under different market conditions. In this 

initial report, we consider possible variance-related benefits (and costs) by comparing wind and 

natural gas generation investments from both a producer and consumer perspective (using 

annualized returns and monthly and annualized consumer costs respectively) and examine how 

these outcomes depend on whether these technologies operate in a deregulated or regulated 

market.

In this analysis, we recognize that the potential value of risk mitigation associated with wind 

generation and natural gas generation may depend on whether one considers the consumer’s 

perspective or the investor’s perspective and whether or not the market is regulated or 

deregulated. We analyze the risk and return trade-offs for wind and natural gas generation for 

deregulated markets based on hourly prices (and load) over a 10-year period using historical data 

in PJM Interconnection (PJM) from 1999 to 2008. PJM is a regional transmission organization

(RTO) serving 51 million people in the eastern United States. Similar analysis is then simulated 

and evaluated for regulated market under certain assumptions. Estimating the absolute, as 

opposed to the relative, value of variance reduction will also depend on assumptions about risk 

aversion and other consumer preferences, such as loss aversion, and this is discussed. Though 

much of our analysis is focused on discrete wind and natural gas generation investments, we also 

discuss some of the implications of our analysis on system-wide optimization techniques used in 

the electric sector that place a value on the variance reduction in addition to cost minimization 

(or profit maximization) on an expected basis. 

Section 1 presents the daily average historical prices and price volatility of fossil fuel and power 

prices in PJM between 1999 and 2008 and reviews some prior work that has looked at the impact 

of renewable energy on variance reduction of consumer costs and producer returns. Section 2 

provides some relevant background material to investment decisions made for wind and natural 

gas between 1999 and 2008. The report describes a method for estimating producer net cash 

flows and returns and consumer costs in both deregulated markets and regulated markets. Section 

3 presents results for natural gas and wind generation selling into a deregulated market. Section 4 

carries out similar analysis assuming the market is regulated, and then compares differences 

observed between regulated and deregulated markets. Section 4 also discusses the value of 
2 

variance reduction more generally from both the producer and consumer perspective due to both 

risk aversion and other factors, such as loss aversion; this includes some consideration of how 

the difference in overall economic utility between alternative electricity system cost distributions 

can be evaluated. Section 5 summarizes some of the main findings and conclusions. 

1.2 Background

Consumers are often considered to be risk averse.6

 In the context of their heating oil or 

electricity bills, this would mean that consumers generally prefer a fixed price bill (for given 

energy usage) to a variable bill with the same expected value on an annualized basis. Because of 

this, consumers would be expected to be willing to pay a premium for less uncertainty or 

variance of their fuel or electricity bills. Similarly, producers often place a value on greater 

certainty of future net cash flows.7 This assumption lies at the foundation of using discounting in 

conventional financial valuation techniques such as net present value.8 Generally speaking, the 

more uncertain the future net cash flows generated by a physical asset or financial investment, 

the higher the required expected return to make such an investment attractive. This is one of the 

reasons why regulated assets such as electric transmission and distribution assets generally earn 

lower allowed rates of return and why these lower rates of return are acceptable to investors (i.e., 

the riskiness or uncertainty of the future net cash flows is lower, and this has inherent value to a 

risk-averse investor).9

 Similar reasons are behind why investors anticipate bonds providing 

lower expected rates of return than stocks: bond holders have first (though limited) claim on 

returns generated by a firm and are senior to equity in the capital structure in the event of a firm 

liquidation or default.10

 

6 For example, a study by Guiso and Paiella (2005) that measured risk aversion based on the willingness to pay for a 

risky asset found that “the vast majority of the participants are risk averse... (while) a small proportion (4%) are 

either risk-neutral or risk seeking” (p. 8). Guiso and Paiella also noted even among the risk-averse there is a lot of 

heterogeneity in the degree of risk aversion, which shows that preferences do differ significantly across individuals.

 Risky private sector investments are not, of course, without benefits and 

are believed to drive innovation and encourage improvements to operational efficiency, so 

eliminating or reducing risk is not always desirable. Rather, investors would be expected to want 

to be (or at least anticipate being) compensated on average for taking greater risks. 

7 For example, many oil producer companies hedge some of their future production output, though the proportion 

can vary significantly by company. In some cases, such hedging can be a requirement to satisfy their loan covenants. 

On the other hand, some companies with large annual net cash flows, such as ExxonMobil, do not sell forward in 

this manner and in fact view their strong debt rating as a competitive advantage. For example, ExxonMobil’s (2009) 

10-K notes that “the Corporation’s size, strong capital structure, geographic diversity and the complementary nature 

of the Upstream, Downstream and Chemical businesses reduce the Corporation’s enterprise-wide risk from changes 

in interest rates, currency rates and commodity prices. As a result, the Corporation makes limited use of derivative 

instruments to mitigate the impact of such change....[The Corporation’s] limited derivative activities pose no 

material credit or market risks to ExxonMobil’s operations, financial condition or liquidity” (p. 55). This suggests 

that ExxonMobil values the fact that its net cash flows, and hence returns, are naturally hedged to significant 

degrees. Whether or not the firm values what some might consider a diversifiable risk is covered in more detail in 

Section 3.3.

8 There are other factors beyond the uncertainty of future cash flows for requiring a premium. Specifically, there has 

historically been a premium to defer consumption from today to “tomorrow.” This risk-free rate is often 

approximated by U.S. Treasury bills (T-bills), which are often considered to be risk-free because they are backed by 

the U.S. government.

9 This is partly because some of the risk has been passed to the consumer. 10 The actualized (as opposed to ex ante anticipated) stock returns of the S&P 500 over the last decade 

notwithstanding.
3 

In the electric sector, deregulation was driven in part by anticipated improvements in efficiency 

of investments and their operation, though there has been significant skepticism of both the 

inherent benefits of and practical problems to capture such benefits, and this is a subject of ongoing debate.11 In the electric sector, changes in fossil fuel prices, especially for natural gas, can 

directly influence electricity prices, given that natural-gas-powered generation often sets the 

hourly dispatch price (i.e., is “on the margin”). 

Figure 1-1. Daily price variation of natural gas, oil, and electricity prices (1999 to 2008) 

Sources: NYMEX (2009); EIA (2009); PJM (2009)

Figure 1-1 shows the variations in daily natural gas, oil, and electricity prices over a 10-year 

period, 1999–2008 in three primary U.S. energy markets. The fossil fuel prices and power prices 

show significant price volatility and are also strongly correlated to each other, which is not 

unexpected, though on a daily basis there are significant seasonal effects because the hourly 

price of power, even if set by natural gas generation units, will also be affected by demand (see 

Table 1-1 and Figure 1-1).12

 

11 For a more detailed discussion of electric restructuring issues that cover a range of views, see for example,

Blumsack et al. (2006), Joskow (2008), and Wolak (2003). 

 For example, increases (or decreases) in daily natural gas prices 

tend to lead to increases (or decreases) in the daily average of hourly power prices because 

natural gas generation is often on the margin during peak periods. The correlation and magnitude 

of this relationship will depend on demand, which in turn is set by many other factors (see, e.g., 

12 Measures of volatility (as well as the associated expected price) clearly depend on what timescale is chosen (e.g., 

there may be significant hourly power price volatility during any given day, and significant volatility in the monthly 

average of hourly prices between months due seasonal effects, and yet such observations might also be consistent

with little or no volatility on an annualized basis). How investors and consumers react to volatility will also depend 

on the timescales chosen.
4 

Karakatsani and Bunn 2008). In general, the daily average of hourly electric power prices has 

greater volatility than natural gas prices, though this volatility is not likely to be constant 

throughout the year. Volatility in daily average or hourly peak electricity prices can be expected 

to be greater during summer months when peak demand is likely to be higher compared to winter 

months (see Figure 1-1). Further, price volatility depends strongly on what timescale is chosen 

(e.g., daily, monthly, or yearly), and both the producers’ and consumers’ attitudes to volatility 

will depend on the timescale considered. For example, consumers might be expected to be 

relatively indifferent to monthly fluctuations in their electricity bills that correspond to seasonal 

differences in demand and price. In contrast, they may be far more concerned with volatility in 

overall annualized costs or changes in marginal costs (on $/MWh) between two similar 

periods.13

Figure 1-2 shows the multi-year distributions of the absolute and relative volatility of daily 

natural gas, oil, and power prices. These price distributions are not “normal” but positively 

skewed toward higher prices. On an annualized basis (as well as shorter timescales), the 

distribution of power prices and related potential cost drivers to consumers are asymmetric in a 

way that may adversely affect consumers and society because the “benefit” of lower costs is 

inherently limited or capped (i.e., prices cannot generally, except in limited special cases, drop 

below zero). By contrast, higher future fossil fuel and power prices (and hence costs to 

consumers)—which might be driven, for example by growth of less industrialized nations—are 

essentially uncapped. Moreover, while the relative volatility of daily prices between each of the 

different energy commodities is similar, the absolute values and their variance show significant 

variation over the two 5-year time periods. This supports the view that predicting future prices 

based on historical information is extremely difficult. 

Risk aversion assumes that deviations from an expected value are treated equally whether they 

correspond to gains or losses. Work pioneered by Tversky and Kahneman (Tversky and 

Kahneman 1981, Kahneman and Tversky 1979) and many others has shown that people often 

feel losses more than equivalent gains. This concept is known as “loss aversion,” and Kahneman 

et al. (1991) have observed that the relative difference in value for small or moderate gains and 

losses of money is often about two to one, though many factors will affect this. Such a view 

requires that the economic utility associated with either side of the distribution has a different 

weighting, whereas in the simple application of risk aversion this is not the case. Which side of 

the distribution corresponds to gain or a loss will depend on what the distribution represents; for 

example, for a consumer a loss might refer to the right-hand side of the distribution 

corresponding to a higher than expected dollar per megawatt-hour cost of electricity. In this case, 

the asymmetric impact of loss aversion to a consumer would reflect the fact that the marginal 

“benefit” to consumers of lower electricity bills (on a $/MWh basis) is likely to be worth less to a 

typical consumer than the “loss” associated with a comparable increase in dollar per megawatthour cost (relative to some expected cost). We shall apply ideas from both risk aversion and loss 

aversion in Section 4. 

 

13 Throughout this text we will be discussing prices and costs, and we have tried not to use the terms in an 

interchangeable manner. On the other hand, one person’s costs can often be another person’s prices (e.g., the cost of 

natural gas to a natural gas generator will depend on the price paid for it) as well as at times being ambiguous (e.g., 

if electricity prices go up, and the end-user consumer’s bill increases has the cost or the price of energy, or both, 

gone up from the consumers’ perspective).
5 

Table 1-1. Correlation of Daily Energy Prices

Henry-Hub Natural Gas Spot Price PJM Day-Ahead Locational 

Marginal Price (LMP) (daily 

average)

0.66

Henry-Hub Natural Gas Spot Price NYMEX Light Sweet Crude Oil 

Closing Price

0.71

NYMEX Light Sweet Crude Oil 

Closing Price

PJM Day-Ahead LMP Price (daily 

average)

0.61

Figure 1-2. Distribution of energy prices separated into two 5-year blocks (1999–2008) 

Sources: NYMEX (2009); EIA (2009); PJM (2009)

For society, or at least the risk-averse consumers and producers who make up a large part of it, it 

would seem that—all else being equal—power generation technologies that can provide 

electricity without price risk ought to be worth something more than technologies with price risk. 

Some renewable energy technologies that have this zero-cost fuel characteristic, including wind 

and solar, are not without revenue risk because output is dependent on when the wind blows or 

the sun shines. This intermittency may lead to increases in both operational costs and volume, 

and hence revenue risk, and thus present different risk/benefit profiles to consumers and 

producers. It may also limit the ability of such renewable energy sources to provide firm 
6 

capacity.14 Geographical diversity can mitigate supply variance to some extent because the 

generation of variable renewable energy in different locations will not be perfectly correlated. 

Geothermal energy is generally considered a dispatchable renewable resource with low fuel 

costs.15

1.3 Variance Reduction of Portfolio Due to Lack of Correlation of Costs or 

Returns

The idea that adding wind to an electric system leads to potential benefits through the reduced 

variance in the system costs was pioneered by the late Shimon Awerbuch (see, e.g., Awerbuch 

and Berger 2003) through the application of ideas from mean-variance portfolio analysis 

(MVPA) to electric generation portfolios. MVPA is often used for financial markets to select 

“efficient” portfolios of stocks and bonds that maximize the expected return for a given risk 

(usually measured as the standard deviation of the return or a similar metric) or vice versa. For a 

portfolio with N assets, the range of efficient outcomes lies on a curve on the risk-return diagram 

known as the “efficient frontier.” The degree of curvature of the efficient frontier toward lower 

return for a given risk reflects the correlation of the returns. With perfect correlation, mixes of 

assets lie on a straight line with no back curvature (the blue line); with no correlation, the mixes 

are curved backwards (the red curve); and with perfect anti-correlation, the mixes go back 

linearly. Figure 1-3 shows the return obtained by mixing different combinations of two assets 

with different returns and variance for different correlations. 

Figure 1-3. Risk and return relationship for mixes of two assets under different correlation 

assumptions

 

14 Dispatchable plants are not without volume-based revenue risk in that they will not dispatch if the electricity price 

is too low to overcome the variable cost of generating power.

15 Though over the longer term there may be significant resource risk in terms of the overall amount of usable 

energy.

Return versus Risk

0%

2%

4%

6%

8%

10%

12%

14%

16%

0% 1% 2% 3% 4% 5% 6%

Standard Deviation (%)

Return (%)

Perfectly Correlated Perfectly Uncorrelated Perfectly Negatively Correlated
7 

The back curvature generated by the lack of correlation of returns of the two assets is attractive 

to risk-averse investors because it reduces the variance for a given return (compared to the 

perfectly correlated case). While MVPA theory gives a range of alternative efficient risk-return 

portfolios corresponding to the combinations of assets that fall on the “efficient frontier,” it does 

not provide any information on which of these portfolios is better. The portfolio preferred by a 

particular investor will vary depending on the level of risk aversion and other factors, and this is 

discussed further in Section 4.3.16

Awerbuch’s essential insight was to see a parallel between a portfolio of stocks and bonds and a 

portfolio of generation assets (see e.g., Awerbuch and Berger 2003) Specifically, he argued that 

adding significant amounts of wind generation to an existing electricity system would reduce the 

variance of the system’s annualized electricity costs because the levelized cost of wind is a 

constant (since the variable cost of wind is zero), and its contribution to the overall system costs 

are therefore uncorrelated with the rest of the system’s fossil fuel costs. This variance reduction, 

Awerbuch reasoned, should be worth something given that consumers (and many producers) 

tend to be risk averse. While Awerbuch observed the directional impact of adding wind 

generation to a generation portfolio with a significant amount of fossil generation, he was aware 

of and noted the limitations of using such an approach to optimize the overall portfolio because 

of operational differences of the different technologies. 

 

• For example, a natural gas combustion turbine (CT) is designed to operate for short 

periods during the more expensive peak hours, while nuclear and coal thermal generation 

plants tend to operate in a baseload manner around the clock. Therefore, CTs and 

baseload plants are not providing the same service and would not be expected to have the 

comparable levelized costs. More generally, the levelized cost of generation depends on 

utilization, and thus the assumption that utilizations of different dispatchable generation 

technologies are fixed under different portfolio mixes is unlikely to be valid unless such 

analysis is restricted to baseload units.17

• Relatedly, wind generation suffers from intermittency issues, so that (as we shall show in 

Section 3.1 and Figure 3-2) the average marginal price (and hence value) of wind 

generated in any specific hour throughout the year will be different from any form of 

dispatchable generation. 

 

Overall, this lack of equivalency between the average value of an hour of generation provided by 

a gas turbine and a baseload plant over the entire year, and either of these types of generation and 

wind generation, is why applying MVPA will not in general be successful in terms of portfolio 

optimization using a simple levelized cost of energy (LCOE) approach.18

 

16 Other factors that may be important include the investors’ reference point (e.g., the degree to which they can 

afford to take the risk). An individual with $1 million in the bank might behave quite differently if his or her cash 

assets were reduced to $1,000 or less. A preference for gains over losses may also be a factor that depends on the 

person’s reference point. The topic of “loss aversion” will be revisited in Sections 4.3 and 5.

As a result, more 

17 Such baseload analysis was done recently by Roques et al. (2008).

18 A useful way to understand this is to test the accuracy of the simple LCOE algorithm under the assumption that 

there is no cost uncertainty. This type of simplified optimization would suggest—wrongly—that 100% of the load

would be met by a baseload technology with the lowest LCOE. This misses the point that peaking units will also be 

needed to meet demand during some parts of the day and that building a baseload unit to meet peaking demand is 
8 

recent work on portfolio optimization has often restricted comparisons to baseload units, though 

this approach is still not without some issues (see, e.g., Roques et al. 2008). 

Awerbuch’s (see e.g., Awerbuch and Berger 2003) approach focused on considering the variance 

associated with least-cost investment decisions. While this restricts the direct application of the 

approach to regulated cost-plus markets, this is less of a drawback than might first be imagined 

because such markets still represent a significant proportion of electric generation capacity in 

operation in the United States.19 Deregulated wholesale power markets, on the other hand, in the 

United States or Europe, such as PJM and ERCOT20

Peak hourly electricity prices in PJM (and many other markets) are often set by the marginal 

natural gas generation unit. Because of this, while the daily price of natural gas is often quite 

volatile, it is less obvious ex ante that in such a market, a producer’s net revenue from natural gas 

generation will be more volatile than the net revenue from a wind producer selling into the 

market.

 in the United States and the United 

Kingdom, respectively, differ in that all generation units bidding into the wholesale power 

market and then being called on to provide power in a given hour get paid the price of the 

marginal generation unit for that hour. Hourly price generally varies significantly over a 24-hour 

period, peaking during the day, and also often exhibits significant weekend versus weekday and 

seasonal variation. 

21 In contrast, consumers buying directly from the hourly spot market will experience the 

full volatility of the hourly power prices unless they have taken measures to mitigate such 

risks.

22

 

likely to be very expensive (i.e., if the capacity factor is lowered, the levelized cost will go up). As a result there is 

no single levelized dollar per megawatt-hour solution. Moreover, for any given region, an array of baseload plants 

might be desirable when real factors such as resource availability and coal transportation costs are considered. Such 

disadvantages can be reduced if one moves to more realistic electricity system models. From a purely statistical 

perspective, to the degree the risk-free version of the model (e.g., a production cost model) provides a reasonable 

portfolio solution, adding a variance-based constraint would seem appropriate. That is, a higher system cost might 

be preferable—to some lower cost solutions—if the variance of distribution is reduced sufficiently. This is discussed 

further in Section 4.3. 

 The limitation of the original approach to least-cost planning to account for these 

market-structure-based differences was recognized by Roques et al. (2008), who applied mean 

variance portfolio analysis to investment returns (rather than electricity costs) in what they term 

“liberalized” markets for three types of baseload generation (natural gas, coal, and nuclear). As 

suggested above, Roques et al. (2008) found the correlation between natural gas prices and 

19 It also represents how some electricity systems model capacity expansion across the entire United States 

regardless of whether the market is regulated or deregulated.

20 The Electric Reliability Council of Texas (ERCOT) manages the flow of electric power to 23 million Texas 

customers—representing 85% of the state's electric load and 75% of the Texas land area (see e.g., www.ercot.com

for more details). 21 In fact, as we show later, rather counter-intuitively, in PJM the monthly and annual net return for natural gas 

generation is still more volatile than for wind, even though natural gas often sets the on-peak marginal price. This is 

because natural gas generation in our analysis dispatches at peak hours where prices are more volatile than during 

off-peak hours, whereas this effect is cushioned for wind because it operates across the entire 24-hour period, 

including the less volatile hours during off-peak periods. Note: For common hours of operation, natural gas net 

revenue would indeed be partially hedged relative to wind.

22 Customers with a direct bilateral contract to buy wind power would, on the other hand, experience much lower 

(zero, in fact) price volatility for that fraction of the load that could be met through such a contract. Depending on 

the structure of the contract, they may experience volume and ultimately cost risk to meet their demand 

requirements.
9 

power prices reduced a gas generation owner’s return-based risks relative to other baseload 

generation such as coal and nuclear. In Section 3, we shall show that in PJM over the period 

considered, the volatility of monthly and annualized returns for wind generation is lower than for 

a combined-cycle gas turbine (CCGT) because of the different hours in which the two 

technologies operate. This finding is based in part on our technology assumptions about 

conversion efficiency that resulted in the natural gas generation operating mainly during peak 

hours.23

Volatility of returns for specific investments, or a portfolio of diverse power generation 

technologies, needs to be viewed within the larger context of risk mitigation and risk tolerance. 

For example, sophisticated producers or large consumers may worry less about the variance 

reduction benefits due to the use of renewable energy, owing to their ability to diversify away 

much of this risk though investments in the market, or in a portfolio of power generation 

technologies. For average consumers, on the other hand, such mechanisms are rarely available, 

and many consumers in the commercial or the residential sectors are likely to be significantly 

exposed to these risks in practice. Furthermore, even for large producers or consumers where 

energy costs or revenues are a large part of their business (e.g., the steel industry, chemical 

companies, or an electric utility), actions taken to reduce the variance of net cash flows add value 

if they reduce the chance of financial distress. This is especially true in the electric sector where, 

as Bessembinder and Lemmon (2002) have noted, the volatility of electricity prices is much 

higher than the volatility observed for the stock market, and the distribution of price outcomes is 

not normal but skewed toward higher prices (see also Figure 1-2). More generally, it might be 

argued that adding large amounts of renewable energy to the electric sector might lead to 

fundamental structural changes that alter the underlying risk-return outlook for investors or riskcost outlook for consumers. While potentially beneficial at a plant and portfolio level, under 

today’s market structure, large quantities of zero marginal cost wind power may be detrimental 

to overall power sector economics, as exemplified by recent incidences of negative marginal 

pricing, which in part reflects generators being paid $20/MWh simply for running (Yang 2008). 

New market structure and rules will likely have to evolve to enable the power markets to adapt to 

greater quantities of variable generation while maintaining appropriate investment incentives. In 

Sections 4 and 5, we will return to some of these and related ideas. 

 

23 This finding reflects the specific technology assumptions we made. Of particular relevance, the relatively high 

heat rate for CCGT compared to today means that the utilization for the gas generation was low (about 30%), and 

therefore very different from Roque’s baseload assumption (Roques et al 2008).
10 

2 Wind and Natural Gas Generation

2.1 Background 

Figure 2-1. Growth in natural gas and wind generation in the United States (1999–2008) 

Note: The 10-year period reflects the period of analysis. 

Source: EIA (2009)

From Figure 2-1, we see that wind capacity increased rapidly over this 10-year period, from 

about 2 GW in 1999 to just over 25 GW at the end of 2008, in part stimulated by the availability 

of production tax credits (PTCs); wind capacity has since grown to 40 GW by the end of 2010. 

In fact, investments in wind generation have shown a strong stop-start correlation between 

investments and the ending and extension of these credits.24 These credits, which were recently 

extended again to 2012 as part of the 2009 American Recovery and Reinvestment Act (ARRA), 

are currently worth about $20/MWh.25 Most of these wind investments, especially in the early 

years, were for bilateral fixed-price contracts. This often made sense to both the purchaser of the 

power consumer (often a utility) and the producer because they reduce variance in cost of energy 

to the utility (and their customers) and returns for the producer. More recently, possibly because 

of increases in electricity prices and price volatility, more wind investments have been made on a 

merchant basis where the producer is either partially or fully exposed to market prices.26

In contrast, the growth of natural gas generation was much more rapid early on, corresponding to 

an explosion of interest in gas-fired generation. The absolute scale of growth was nearly an order 

of magnitude greater for natural gas than for wind. Figure 2-1 shows that natural gas generation 

 

 

24 The strong stop-start correlation between tax credits and investment does not necessarily imply such credits are 

necessary because if a developer believes tax credits will be available the following year, the investor may choose to 

wait. 

25 For the first 10 years of operation.

26 A variety of derivatives can mitigate exposure to price fluctuations to some degree, though not without a cost for 

floors and caps, or by giving up some of the potential upside through the use of collars. 
11 

grew from about 150 to 300 GW over the 10-year period, with almost all of this growth coming 

from the merchant model, where owners sell into a daily spot market for power. After the natural 

gas generation market crash in the early 2000s, growth has been far more limited and the thenstandard business model has been largely abandoned because, as we shall show, the risk-return 

characteristics were unattractive to the investor. A detailed description of the history of the 

natural gas boom and bust period is outside the scope of the report and has been covered 

elsewhere (see, e.g., Rigby 2004). For natural gas generation, the decision to dispatch in any 

given hour will depend on whether the hourly price of power exceeds the cost of the natural gas 

needed to generate that power (the “spark spread”), plus associated variable operations and 

maintenance (O&M) costs is positive. One major driver behind the difficulties faced by gas 

generators was the collapse of the “spark spread,” which can occur if the price of natural gas 

changes faster than the price of electricity. This effect can be seen in Figure 2-2, which shows 

natural gas prices, power peak prices, and average peak period spark spread between 1999 and 

2008. Though peak power prices tended to be positively correlated to changes in natural gas 

prices (0.66), the change in power prices was often muted. Moreover, there are clearly seasonal 

effects at play that impact electricity prices and natural gas prices differently. 

Figure 2-2. Spread between real-time electricity prices and the cost of natural gas for a combinedcycle gas turbine (under 40% efficiency assumption) (1999–2008)

Sources: NYMEX (2009); PJM (2009)
12 

2.2 Methodology

In this study, we first analyze and compare the value and uncertainty of selling electricity 

generated by wind and natural gas in regulated and deregulated markets from both producer and 

consumer perspective over a variety of timescales. We assume in all cases the owner operates the 

generation asset to maximize profits. For wind generation, which has no fuel costs and is 

variable, this simply means selling whatever it can generate (within cut-in and cut-off wind 

speeds). In contrast, for natural gas generation, the decision to dispatch in any given hour will 

depend on whether the hourly price of power ($/MWh) exceeds the cost of the natural gas and 

variable O&M needed to produce it.

There are two broad classes of natural gas generation: (1) CTs and (ii) CCGTs. CTs are by 

design relatively cheap to build but inefficient due to the once-through non-cyclical nature of 

their combustion process, which leads to a lot of waste heat being discarded by the turbine. 

CCGTs are basically comprised of a CT, but where the waste heat from running a CT is then 

used to generate steam to drive a conventional thermal electric generator (which uses the heat to 

boil water at high pressure and this dry steam drives the turbine). The “twice-through” nature of 

the CCGT leads to a significant increase in efficiency in converting the energy released by 

burning natural gas to electric power. CTs are often called peaking units to reflect their more 

limited use. In this study, we focus on CCGTs. 

Analytically, this leads to four types of variable-volume energy contracts:

• Deregulated Wind—a contract to supply wind-generated electric power at the realtime PJM hourly electricity price. The owner operates for 100% of the time, though 

the output will be variable (including no power output from a particular wind turbine 

if wind speeds are too low or too high) and the hourly price received variable.

• Deregulated Natural Gas (CCGT)—a contract to supply natural-gas-generated 

electric power at the real-time hourly PJM electricity price. The price or cost of 

natural gas is assumed to be the spot market price delivered to an “average” delivery 

point in PJM.27

• Regulated Wind—a contract to supply wind-generated electric power at a fixed price 

that is set annually based on actual utilization so that the owner recoups a defined 

fraction of initial capital costs, including a return on capital. The owner operates for 

100% of the time, though the output will be variable. For both wind and natural gas 

cases, we examined two scenarios corresponding to an 8% and 10% real return. 

Given that the historical rate of inflation over the period averaged 2.5%, this 

corresponds to a nominal rate of return of 10.5% and 12.5%, respectively.

 The owner operates the CCGT only when it is economical to do so, 

that is, when the “spark spread” is positive and at least greater than the variable O&M

costs.

• Regulated Natural Gas (CCGT)—a contract to supply natural-gas-generated 

electric power at a fixed price that is set annually so that the owner recoups a defined 

fraction of initial capital costs, including a return on capital. The natural gas used is 

 

27 We follow PJM market analysis in using Transco Zone 6 Non-New York as a proxy for the cost of natural gas. 

This price is often $0.50–$2.00/MMBtu or more greater than the price of natural gas at Henry Hub. 
13 

assumed to be purchased at spot market price for natural gas delivered to PJM. The 

owner operates the CCGT only when it is economical to do so. We approximate a 

regulated market by assuming that the hourly operation of the CCGT is the same as in 

the deregulated case, though the owner no longer receives the deregulated hourly 

prices. 

Table 2-1 lists the variables used in formulating these contracts and the numerical values 

assumed for cost parameters. Table 2-2 summarizes how costs were computed. In each case, the 

producer and consumer revenues are given by: 

ܴ௧

ሺPሻ ൌ ܲ௧ܳ௧ െ ߙܱܥ െ ܨܳ௧ െ ܸܳ௧

and 

ܴ௧

ሺCሻ ൌ െܲ௧ܳ௧

Additionally, the producer’s annual return on capital is calculated as the ratio of their revenue 

minus overnight capital to their overnight capital cost. Although the regulated contracts have 

prices set so that yearly revenue exactly balances, the defined annual return on capital, revenue 

over different time periods (weekly or monthly), does not exactly equal that defined annual 

return, depending on either the available wind resource or the spark spread. In general, we 

compute monthly and annual cash flows. The monthly values are of interest because settlement 

typically occurs over that timeframe and annual values are of interest because the regulated 

prices in this analysis vary year by year. 
14 

Table 2-1. Contract Variables and Price Assumptions28

Quantity Variable Notes 

Contract Price ܲ௧

Contract Power ܳ௧

Electricity Spot Price ܧ௧

Wind Power Output ܹ௧

Natural Gas Power Output ܥ

Natural Gas Spot price ܰ௧

Natural Gas Efficiency ߝ ൎ 0.42697

Producer Revenue ܴ௧

(P) When this is zero, the producer has 

covered his fixed, variable, and fuel 

costs plus ߙ of his overnight capital 

cost. 

Producer Return on Capital ݎ௧

(P)

Consumer Revenue ܴ௧

(C)

Annual Fraction of Overnight 

Capital Cost Required for 

Producers 

ߙ ൌ 0.10/yr 

Overnight Capital Cost 

(1997$) for Wind 

ܱ ൌ $1,109,000/MW installed 

Overnight Capital Cost 

(1997$) for Natural Gas 

ܱ ൌ $445,000/MW installed 

Fixed O&M Cost (1997$) for 

Wind 

ܨ ൌ $25,920/MW installed/yr 

Fixed O&M Cost (1997$) for 

Natural Gas 

ܨ ൌ $15,350/MW installed/yr 

Variable O&M Cost (1997$) 

for Wind 

ܸൌ0

Variable O&M Cost (1997$) 

for Natural Gas 

ܸ ൌ $0.51/MW/hr 

Table 2-2. Price Formulas for the Four Contracts 

Contract Price Formula 

Deregulated Wind ܲ௧ ൌ ܧ௧

ܳ௧ ൌ ܹ௧

Deregulated Natural Gas ܲ௧ ൌ ܧ௧

ܳ௧ ൌ ቄܥ for ܧ௧ ൒ ܰ௧/ߝ ൅ ܸ

0 otherwise

Regulated Wind ܲ௧ ൌ ∑ ሾሺߙܱ ൅ ܨሻܥ ൅ ܸܹ௧ሿ year

∑year ܹ௧

ܳ௧ ൌ ܹ௧

Regulated Natural Gas ܲ௧ ൌ ∑ ሾሺߙܱ ൅ ܨሻܥ ൅ ܸܳ௧ሿ year

∑yearܳ௧

ܳ௧ ൌ ቄܥ for ܧ௧ ൒ ܰ௧/ߝ ൅ ܸ

0 otherwise

 

28 1997 capital cost and operation and maintenance assumptions come from an EIA report (1998) and are considered 

reasonable proxies for investment costs and performance parameters for investments made in 1998. 
15 

3 Wind and Natural Gas Generation in a Deregulated Market 

3.1 Producer Returns over 10-Year Period (1999–2008) 

Figure 3-1. Annual and monthly returns for wind and natural gas generation in PJM (deregulated 

market example) (1999–2008) 

Figure 3-1 shows the annualized and monthly returns for CCGT and wind generation both with 

and without production tax or capacity credits (“credits” in the Figure 3-1 labels) calculated in 

accordance with the methodology outlined in Section 2.2.29 For both technologies, when 

operated in any given hour, the technologies are assumed to receive the hourly PJM real-time 

price. For wind, this corresponds to any hour the wind turbines are generating, 30 whereas for 

natural gas it corresponds to hours when the sum of spark spread and the variable O&M cost is 

positive. For wind, the credit corresponds to a PTC of $20/MWh, while for CCGT the credits 

correspond to a variable monthly capacity payment. Figure 3-1 shows that the wind annualized 

return with a PTC included has increased from about 10% to nearly 15% in more recent years. In 

contrast, the annualized return for natural gas CCGT generation is significantly lower despite the 

 

29 To separate out the potential effect of financing considerations, we estimate returns based on simple unadjusted 

net cash flow of earnings before interest, taxes, and depreciation and amortization (EBITDA). This simplification 

should be recognized when considering additional payments due to tax or capacity credits. 

30 We use the 10-minute wind-power output from a representative site in the Eastern Wind Integration & 

Transmission study (NREL 2009). The results in Sections 3 and 4 all use this site, and though the details are 

dependent on the site, the general characteristics and trends are common among representative sites. 

No Credits With Credits

2000 2003 2006 

Month

2000 2003 2006 

Month

Aggregation by Month

No Credits With Credits

2000 2003 2006

Year

2000 2003 2006

Year

Natural Gas Wind

0%

10%

20%

30%

Rate of Capital 

Recovery [1/yr]

0%

10%

20%

30%

Rate of Capital 

Recovery [1/yr]

Aggregation by Year
16 

much lower assumed capital costs. Over the 10-year period, the average annual returns without 

and with a capacity payment are 9% and 11.5%, with the value remaining flat or declining over 

time. Capacity payments can lift the return for natural gas generation owners, but these are also 

highly uncertain and generally low over this period. Figure 3-1 also shows that volatility in 

returns for natural gas generation is much higher than wind, both on an annual and a monthly 

basis. Without credits, the annual volatility for wind and natural gas generation was 2.5% and 

3.5% respectively. In contrast, the monthly volatility of wind and natural gas generation was 

3.5% and 11.0%, respectively. The higher volatility of monthly returns is largely to be expected, 

and much of it reflects seasonal variations in demand. 

The observation that the returns for wind generation have a lower variance than the returns for 

natural gas generation is consistent with a wind generation owner being better hedged than an 

owner of natural gas generation. This is less intuitive than it might seem because, in a 

deregulated market, the peak price of electric power is often set by natural gas generation 

(correlation of 0.66), which might be expected to act as some sort of natural hedge for net 

revenue variability. For example, in a comparison by Roques et al. (2008) of the simulated 

dispatch of generation assets in the United Kingdom, it was found that the owner of a natural gas 

generation plant may be better naturally hedged than coal and nuclear facilities because of the 

correlation between peak power prices and natural gas prices. As discussed by Roques et al. 

(2008): “...the correlation between electricity, gas and carbon markets [in the U.K.] make[s] 

‘pure’ portfolios of gas plants more attractive than diversified portfolios as gas plants’ cash flows 

are self-hedged” (p. 1832). Roques et al. (2008), however, were considering different types of 

baseload power generation only (coal, natural gas, and nuclear) and did not consider wind. For 

wind, our analysis shows the returns were better hedged than natural gas in PJM over this period 

(given our technology assumptions about wind power output and natural gas generator’s heat 

rate). Three factors that contribute to this are:

• Although positively correlated, peak power prices often “move” much less than the 

underlying natural gas prices. This can lead to the “spark-spread” for natural gas 

being squeezed and can impact both operation and net profitability.

31

• For our technology assumptions in PJM, the natural gas generation is operating in 

more of the higher and more volatile peak price hours and less of the lower demand, 

low price hours than wind. Specifically, unlike wind, natural gas is not operating as a 

baseload plant across all hours as was assumed in the Roques et al. (2008) analysis. 

 

• While wind generates intermittently, its operation is more evenly spread across both 

peak and off-peak hours than natural gas generation units. As a result, compared to 

natural gas generation, wind often operates at lower price off-peak hours where the 

hourly power price is not driven by natural gas and is less volatile. 

The effect of these factors can be seen by looking at two related parameters: (1) the annualized 

average hourly price received for natural gas and wind generation for hours 1 through 24 and (2) 

the fraction of the time the technology generates in any given hour during the year. This effect 

can be seen in Figure 3-2 and is discussed in Section 3.2. 

 

31 However, similar behavior might be expected to be observed in the United Kingdom study. 
17 

3.2 Producer Prices and Consumer Costs in a Deregulated Market

The previous section analyzed risk and return from a producer perspective. How does the 

consumer fare under wind or natural gas generation in a deregulated market? Figure 3-2 (top 

row) shows the annual average price to producers (2009$/MWh) of power received in a 

deregulated market for wind and natural gas generation, respectively between 1999 and 2008, 

and we see that the average annual hourly price of power from natural gas generation is 

approximately $20–$30/MWh higher from wind than power. It would be wrong, however, to 

think (at least for small amounts of added wind) that wind power in any given hour during these 

periods was any cheaper than natural-gas-fired generation in a deregulated market. In a 

deregulated market, buyers of wholesale power, such as utilities, see only one price in any given 

hour, and this price is set by the marginal price of the last generation unit to meet demand in that 

hour.32

While not examined in any detail in this report, large-scale renewable penetration in deregulated 

markets can be expected to add value to consumers through variance reduction when wind or 

solar penetration is so great that these technologies are setting the marginal price of power

 Thus, whether the power is supplied by wind or natural gas, it is supplied at the same 

market price in any given hour. Overall, it is true that the price of natural-gas-generated power is 

both higher and more volatile than the price of power supplied by wind on average during any 

given year, but this is because they are operating in different hours. This can be clearly seen from 

Figure 3-2 (lower two rows), which shows distributions of the annual average hourly generation 

utilization (or dispatch fraction) for these two technologies across the day. Wind is used to 

generate power intermittently across the whole 24-hour period. The variability corresponds to an

annual average capacity factor of 39%, which is reasonably similar across all hours though with 

somewhat higher utilization at night than during the day (see third row in Figure 3-2). In 

contrast, natural gas generation is dispatchable but restricted to more volatile and higher-priced 

peak hours when the spark spread is positive. The CCGT was assumed to have gas-to-power

conversion efficiency of 43%, which led to an average capacity factor of 30% (though with 

significant variation between the years, as seen in the second row in Figure 3-2). The costs paid 

by large consumers and smaller end users are likely to reflect the load-weighted average price of 

power (whether purchased directly from the wholesale market or passed through by the utility) 

and therefore is only indirectly linked to the actual running costs of most wind- and natural-gasgenerating units.

33, 

though this effect may be somewhat off-set by production effects due to the impact of variability. 

As mentioned earlier, given that the marginal cost of wind is close to zero (and prices below zero 

have been observed due to PTCs), market structure rules for capacity payments and other 

incentives may need to be revisited in such cases to encourage investments in wind that properly 

reflect societal benefits. 

 

32 Strictly speaking in PJM there are two separated (though interrelated) markets for day-ahead and real-time power, 

which will have somewhat different prices in any given hour.

33 Even when not setting the marginal price of power, large amounts of wind could reduce the hourly price by 

adding low cost power to the supply curve, especially during peak periods if less efficient, higher-priced peaking 

natural gas units are no longer needed to meet demand
18 

Figure 3-2. Annual average price received for wind and natural gas technology and annual 

utilization for these technologies over 24-hour period 

3.3 Some Cost, Value, and Portfolio Optimization Considerations 

Figure 3-2 demonstrates the limitation of using mean variance portfolio theory to determine the 

optimal generation supply mix based on the simple use of annualized LCOE. While applying 

mean variance theory may be reasonable when the assets are equivalent (or nearly so), wind and 

natural gas generation are not equivalent because the two technologies have different utilizations 

and more generally operate in significantly different hours; this latter distinction is important 

since even if wind and natural generation had by coincidence the same utilization, they would 

still operate in very different hours. 

Year

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

0.0 0.5 1.0

Dispatch 

Fraction

0.0 0.5 1.0

Dispatch 

Fraction

0.0 0.5 1.0

Dispatch 

Fraction

0.0 0.5 1.0

Dispatch 

Fraction

0.0 0.5 1.0

Dispatch 

Fraction

0.0 0.5 1.0

Dispatch 

Fraction

0.0 0.5 1.0

Dispatch 

Fraction

0.0 0.5 1.0

Dispatch 

Fraction

0.0 0.5 1.0

Dispatch 

Fraction

0.0 0.5 1.0

Dispatch 

Fraction

Natural Gas Wind

0

5

10

15

20

25

Hour of Day

0

5

10

15

20

25

Hour of Day

Dispatch by Hour

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Natural 

Gas

Wind

Natural 

Gas

Wind

Natural 

Gas

Wind

Natural 

Gas

Wind

Natural 

Gas

Wind

Natural 

Gas

Wind

Natural 

Gas

Wind

Natural 

Gas

Wind

Natural 

Gas

Wind

Natural 

Gas

Wind

0

20

40

60

80

100

Price [$/MWh]

Annual Prices
19 

The problems associated with directly comparing LCOEs for different technologies have been 

recently discussed by Joskow (2010), and a number of our observations are consistent with his 

findings. For example, in the 10-year timeframe of PJM data analyzed, we observe that natural 

gas units, while utilized less overall than wind (average capacity factors of 30% and 39% for 

natural gas and wind, respectively), operated in very different hours, with an emphasis on higher 

priced peak hours. The differences in hours of operation for natural gas generation lead to an 

average annual hourly output capacity weighted price premium of $20–$30/MWh more for each 

hour of operation compared to wind (see first row in Figure 3-2). It should be noted that the size 

of any premium will depend on specific technology assumptions and market conditions and will 

be location specific. Similar considerations apply when comparing solar energy (whether 

photovoltaic or concentrated solar thermal power) and wind, with solar potentially having a 

considerably higher average annual marginal value based on the hours it generates because of the 

strong temporal relationship between solar radiation and peak load periods. 

The average annual hourly price differences and the distribution in average annual utilization 

over a 24-hour period (shown in Figure 3-2) support the use of models that explicitly use or 

simulate hourly data over the entire year in valuing generation assets.34 While the average annual 

dollar per megawatt-hour value differential between two technologies will depend on many 

factors, including the specific choices made for the utilization and efficiency, it does not tell you 

anything about the rate of return (RoR) for these technologies since that will also depend on the 

technologies’ capital costs and operating costs, including any fuel costs. An analysis of RoR for 

the two technologies is discussed below and in Section 4.2. We find the RoRs without credits 

quite similar (though with somewhat different risk profiles) despite having very different average 

revenue per megawatt-hours generated; this in part reflects the fact that natural gas generation 

needs to cover the cost of natural gas when generating, whereas wind is economic whenever the 

wind blows.35

More generally, because the lowest LCOE solution does not correctly predict the technology 

portfolio in the risk-free case (in part because it will only predict one baseload technology), it 

cannot be expected to work when expanded to include uncertainty and correlation effects using 

mean variance portfolio theory. On the other hand, a private sector financier investing in both 

wind and natural gas generation will gain a lower variance for a given return because the returns 

of the wind (or solar) and gas technologies are not perfectly correlated. With no credit for wind 

or natural gas generation, we see from Figure 3-3 that the natural gas provides a return (the open 

circle) that is slightly greater than wind (the star) and has a corresponding higher variance. In 

such circumstances, an investor can reduce their variance for a given return by investing in both 

types of assets. This is shown in Figure 3-3 where the variance associated with a return in the 

range of 8.5% to 9.0% can be reduced by about 40% (e.g., from 3% to 2%). 

 

 

34 See, for example, the System Advisor Model https://www.nrel.gov/analysis/sam/ for full description and 

download option. 

35 Again it should be emphasized that our observations depend on the specific assumptions made. For example, the 

relatively low utilization for natural gas generation used in this analysis reflected quite a conservative heat rate 

(corresponding to 43% conversion efficiency in 1998). Significantly higher conversion efficiencies would have been 

available over much of the period between 1999 and 2008, and this would be expected to lead to changes in 

observed average price premiums, net revenues, and risk-return relationships.
20 

Figure 3-3. Risk-return relationship for wind and natural gas without subsidies

If an investor had no risk aversion (and was risk neutral), then the investor will go for the 

greatest expected return regardless of any variance. More generally, where an investor chooses to 

be on the efficient frontier will depend both on the shape of the curve and their risk aversion (see

Section 4.3). Figure 3-3 shows how fiscal instruments, such as PTCs or capacity payments, can 

affect the risk-reward relationship and encourage investment in new generation assets in a 

market with price caps. The impact of PTCs for wind generation is effectively to keep the risk 

(i.e., the variance of the returns) the same for a significantly greater expected return since, under 

PTC, every megawatt-hour generated effectively gets a $20/MWh credit. When both wind and 

natural gas generation are given PTCs and capacity credits, respectively, investment in wind is 

dominant over natural gas because wind has both a higher return and a lower risk than CCGT. 

The difference in risk-return of wind versus natural gas power would be even more pronounced 

if wind received the PTC or equivalent support and natural gas generation did not receive a 

capacity credit. In contrast, with no wind subsidy but with a natural gas generation capacity 

credit available, the risk-return efficient frontier changes substantially in favor of greater 

proportionate investment in natural gas generation for any given risk-aversion profile. 

Figure 3-3 suggests that a risk-averse investor might be wise to invest in both technologies since 

the variance of the net cash flows (and associated returns) would be reduced. On the other hand, 

it might be argued that according to standard finance theory this would not be true (or would be 

significantly less true) if the wind and natural gas generation were owned by separate publically 

traded companies that made up part of the Standard and Poor’s 500.36

 

36 The basic idea is that merging a “Holidays in the Sun” firm with a “Holidays in the Snow” firm would not add 

value despite reducing the variance of the combined firm’s net cash-flows because investors could (and it is assumed 

already would) have eliminated that diversifiable risk by investing in both firms without them merging. This “value 

additivity” theory assumes neither firm is likely to have any financial distress that might be mitigated by such a 

merger, but that assumption seems unlikely to be always true in the electricity industry.

 This is because any 

premium associated with reduction in risk due to such diversification would have already been 

eliminated (because it assumes the investors in these two companies would be diversified already 
21 

in both these companies, as well as more broadly in the market). That no such risk premium is 

required for unique (as opposed to systematic (or market)) risk is important to consider but is not 

likely to be fully realized in the electric sector for a variety of reasons. Bessembinder and 

Lemmon (2002) note that: 

...companies in the power industry are likely to benefit from reducing the risk of 

their cash flows. [They] may have power price exposures sufficiently large that 

adverse price changes could lead to corporate default or bankruptcy (p. 1353).

This also seems to make sense when one considers the actual finance distress that many 

merchant electric-generation companies that were heavily focused on natural gas generation 

experienced in the early 2000s (see, e.g., Rigby (2004) for a more detailed discussion of some of 

the financial and market issues facing energy merchant companies in 2003).37

In the last two years, well over $100 billion of energy merchant market 

capitalization has disappeared as almost everything that could have gone wrong 

with the nascent energy merchant industry did. In the past year, three companies 

have filed for bankruptcy. Bond spreads suggest that investors expect more of the 

same (p. 37). 

 

Presumably adding wind generation their portfolio mix may have reduced the variance of their 

net cash flows, and this may in turn have reduced chance of financial distress. Lenders often 

appear more willing to lend, or lend at lower rates, to individual projects that have diversified 

some of the project-specific net cash flow risk. Projects may do this through aggregation against 

multiple wind projects due to spread of operational risk, as well as reduced variance of net cash

flows from reducing impact of wind speed variations at different locations. 

The managers of firms also often appear to value some degree of diversification in practice. For 

example, from ExxonMobil’s (2009) 10-K suggests that the company does not take steps to 

significantly hedge their net revenues using financial instruments because they believe that they 

have already substantially mitigated such risk due to the diversity of their holdings.38 That is, the 

firm values the reduction variance of net cash flows (over a spectrum of timescales) and 

associated annual returns that result from its diverse business interests and holdings and does not 

seem to presume that such risks are irrelevant because their shareholders can be invested in many 

other oil and gas companies or more broadly in the market. Similarly, smaller oil producers often 

have to hedge a substantial fraction of the future oil output to satisfy banker covenants. 

 

37 As Rigby (2004) noted in 2004 “credit ratings for 12 companies owning over 200,000 MW of generation 

worldwide (Table 1) have fallen from investment grade (in most cases) to low non-investment grade levels. Only 

AES Corp. and Calpine Corp., whose credit ratings were never investment grade, experienced less credit erosion, 

but only because they had less distance to fall” (p. 37).

38 From ExxonMobil’s 2009 10-K, “the Corporation’s size, strong capital structure, geographic diversity and the 

complementary nature of the Upstream, Downstream and Chemical businesses reduce the Corporation’s enterprisewide risk from changes in interest rates, currency rates and commodity prices. As a result, the Corporation makes 

limited use of derivative instruments to mitigate the impact of such change...[and that it’s].. limited derivative 

activities pose no material credit or market risks to ExxonMobil’s operations, financial condition or liquidity” 

(p. 55). 
22 

4 Wind and Natural Gas Generation in a Regulated Market and

in Comparison with Deregulated Markets

Whether deregulation or regulation is inherently better in electricity markets is a subject of 

heated debate and one that we will only touch briefly here. On one hand, regulation is associated 

with lower rates of return, which for “good” investments would seem to benefit the consumer 

and be “fair” to the investor. On the other hand, while in deregulated markets investors may 

require higher rates of return on an expected basis, competition is anticipated to promote 

innovation of newer and better technologies, reduce the number of bad investments, and improve 

operational inefficiencies and thus, offer lower overall prices to consumers in the long run. 

However, even if deregulated markets have the potential to be better for society in principle, in 

practice it all depends on how appropriate the market design is and its implementation, including 

regulatory oversight. The market failure observed in California between 2000 and 2001, for 

example, had many contributing factors, but poor market design and regulatory rulemaking and 

intervention (or a lack of it) played a significant role in the process (see, e.g., Joskow 2001 and 

Wolak 2003 for more detailed discussion).39

In this section, we explore the differences facing consumers and producers that are part of a 

“cost-plus” regulatory environment compared to a deregulated market. To do so, we again use 

the 1999–2008 data to enable a comparative study, and we ask what would have happened if 

PJM had been regulated over this period. We make the assumption that the wind and gas 

generation operate in the same hourly manner as in the deregulated market. What differs, of 

course, is what the owners of each of these technologies get paid to do with payments being 

adjusted under this approximation so that investors earn a constant rate of return. Because of the 

relative certainty of return to producers, we shall show that some of the risks previously taken on 

by the investor are transferred to consumers. This ability to transfer legitimate costs to 

consumers means that producers may be largely (at least currently) indifferent to reducing the 

variance of the cost of producing power. Many consumers, on the other hand, would be expected 

to value variance reduction for the annualized cost of energy (on a $/MWh basis) for both risk 

aversion and loss aversion reasons. 

 Even today in reasonably well-functioning markets 

such as PJM, aligning incentives to ensure optimal investments has been and remains 

challenging. Market structure and contract choices matter. 

In modeling a regulated environment, there is really no operational approximation involved in 

the case of wind because a wind turbine operates whenever wind conditions are favorable, which 

of course is independent of any market structure assumptions. While some regulated markets 

may use a more complex cost minimization algorithm that may include other cost components, 

 

39 For example, under the new rules, consumers in California were guaranteed the right to purchase power at lower 

prices than before, while their original suppliers were still legally obligated to provide power at this guaranteed 

lower price if asked. However, to do this, these “suppliers” were required to purchase their wholesale power from 

newly formed day-ahead, hour-ahead, and real-time markets. Such an arrangement is fundamentally flawed for a 

number of reasons, including: (1) the “success” of this model is reliant on such deregulation leading to significantly 

lower prices, and (2) it does not connect consumer demand and behavior to the price they pay for power.
23 

we assume that marginal dispatch is the main cost driver in regulated markets and is reasonable 

for the purposes of this analysis.40

4.1 Comparison of Annualized and Monthly Returns in Regulated and 

Deregulated Markets

In our analysis, we present two scenarios: one for 8% and one for 10% real returns.

41

 When considering the yearly aggregation of revenue, we observe that: 

 Regulation 

of producer rates of return has an implicit impact on how risks are transferred to consumers. 

Figure 4-1 shows the standard risk and return diagram that is often used to represent the trade-off 

between risk and return. Results differ when aggregated monthly or annually. 

• There is no risk to the producer in the regulated case, and returns are identical for 

wind and natural gas. 

• In the deregulated case, without the production tax or capacity credits, the natural 

gas-based producers see 1%–2% higher returns than wind-based producers but with a 

slightly higher risk. 

• The deviations from the assumption of normally distributed annual returns are minor. 

• When the PTC is included, the return for wind-based generation dominates (in the 

sense of higher return and lower risk) over natural-gas-based electricity production. 

 

40 For wind, the approach is straightforward. We look at the output over a 10-year period and allow the wind 

turbines to repay their capital at 10% and fixed and variable O&M. For CCGT, we need to first understand how gas 

generation would dispatch—and to do so properly would require running a large-scale production-costing model—

something outside the scope of this report. Instead, as a reasonable approximation, we assume that dispatch is 

identical to PJM market gas, but that the unit does not receive the PJM marginal price. Instead, natural gas daily fuel 

costs used are assumed to be an add-on, and again the generator is allowed to cover fuel costs and fixed and variable 

O&M costs.

41 We chose these values to reflect a reasonable range of regulated rates of return. 
24 

Figure 4-1. Risk versus reward using standard measures (top row) and robust measures (bottom 

row) from the perspective of a producer 

Note: The width in the figure is defined as half the difference between the 15.9 and 84.1 percentiles; for 

normally distributed data, the width is identical to the standard deviation. 

In the case of the monthly aggregation (perhaps more representative of actual cash flows for 

producers) we reach the following, somewhat different, observations: 

• In both regulatory cases, the monthly return risk for the natural-gas-based producer is 

markedly (about five times) greater than for a wind-based producer, even though the 

overall expected return is very nearly the same. 

0% 2% 4% 6% 8% 10% 12%

Standard Deviation of Return [1/yr]

0%

2%

4%

6%

8%

10%

12%

Mean of Return [1/yr]

Aggregation by Year

0% 2% 4% 6% 8% 10% 12%

Standard Deviation of Return [1/yr]

0%

2%

4%

6%

8%

10%

12%

Mean of Return [1/yr]

Aggregation by Month

0% 2% 4% 6% 8% 10% 12%

Width of Return [1/yr]

0%

2%

4%

6%

8%

10%

12%

Median of Return [1/yr]

Aggregation by Year

0% 2% 4% 6% 8% 10% 12%

Width of Return [1/yr]

0%

2%

4%

6%

8%

10%

12%

Median of Return [1/yr]

Aggregation by Month
25 

• The monthly return distribution for the deregulated case differs substantially from 

normal (Gaussian) because of a “fat tail” of large, non-normal losses. 

• Wind-based production dominates natural-gas-based production in the deregulated 

case if risk is measured robustly (see the lower right panel of Figure 4-1) because it 

has both higher return and lower risk. 

• Wind-based production with the PTC has higher return at lower or similar risk than 

natural-gas-based production. 

Regarding the question of the normality of the distribution of returns, we interpret the differences 

between the top and bottom rows as follows: the wind returns and regulated natural gas returns 

are close to normally distributed because their mean is nearly equal to their median and their 

width closely coincides with their standard deviation; the deregulated natural gas returns—most 

prominently when aggregated monthly—have fat tails, as evidenced by their width being smaller 

than their standard deviation, and have influentially large values of large returns, which skew the 

distribution because their mean is greater than their median. 

Why do we look at monthly returns when annualized returns are the benchmark measure to 

account for seasonal variation in revenues? One reason is that the magnitude of the volatility in 

the monthly net cash flow returns is much higher for natural gas generation than wind. In turn, 

the potential benefits of investing in both technologies to reduce or partially mitigate variability 

in monthly net cash flow might be underestimated if one simply considered an annualized riskreturn approach. 

4.2 Comparison of Consumer Costs and Variance in Regulated and Deregulated 

Markets

In Section 4.1, we compared the risk and return for wind and natural gas generation in regulated 

and deregulated markets from the producer perspective. We now examine the consumer costs 

from a similar perspective. Figure 4-2 shows the monthly consumer costs for power from 

regulated and deregulated markets for natural gas and wind. 42

In the deregulated market, we see from Figure 4-2 and Table 4-1 that the technology-specific 

consumer costs (if consumers were able to buy wind or gas separately) and volatility for natural 

gas generation is much greater than for wind generation (cost $76/MWh versus $47/MWh, 

volatility $18.5/MWh versus $11.4/MWh). As explained, however, in Section 3.2, these price 

differences reflect the operational differences of the two technologies. That is, gas generation 

electricity prices are higher due to the fact that natural gas generation operates in more hours 

with higher prices than wind. These costs are largely independent of whether a natural gas 

generator receives a capacity credit or a wind generator receives a PTC because the market price 

and hence consumer cost in each hour is set by the marginal cost of the last unit dispatched.

 

43

 

42 The monthly consumer costs are based directly on the monthly wholesale load-weighted hourly price in both the 

regulated and deregulated case. For this reason, the y-axis is label prices. The actual cost to smaller end-user 

consumers is assumed to be strongly correlated to these prices with some uplifts to reflect size of customer and 

profit margins due to distribution and other factors.

 Of 

more interest are the differences observed in the regulated markets. While the price of power and 

43 This is not strictly true for production tax when wind sets the marginal price as power, which has resulted in 

observed negative prices being set so that wind generators can earn their credits.
26 

volatility from natural gas generation is actually quite similar to the deregulated case ($75/MWh 

and $19.2/MWh, respectively), the variance of the price of power for the wind technology is 

reduced to zero, a consequence of wind having no fuel costs. The benefit of reducing wind price 

volatility from $11/MWh to $0/MWh is partially offset by higher annual costs of $54/MWh. We 

see, therefore, in a regulated market that the consumer is faced with considerable volatility in gas 

prices on an annualized basis, whereas the cost associated with wind-generated power has no 

volatility.44 The lack of correlation of wind generation with fossil fuel prices leads to an 

additional reduction in the overall volatility of the system costs when large amounts of wind are 

added to the system. This attribute of wind and other forms of renewable energy, such as solar, 

could have value to many risk averse consumers, and yet markets do not currently compensate 

wind’s contribution to reducing the variance of overall system costs. How the value of such cost 

variance reduction effects could be estimated is considered next in Section 4.3. 

Figure 4-2. Average monthly price ($/MWh) of wind and natural gas generation in deregulated 

market (PJM) and simulated regulated market (1999–2008) 

 

44 This partly reflects approximation in modeling in that year-to-year changes in wind could lead to changes in 

utilization, which could impact the annualized ($/MWh) cost of energy. 
27 

Table 4-1. Price and Measures of Risk for Wind and Natural Gas Generation in Deregulated and 

Regulated Markets

Aggregation Regulatory 

Environment

Production 

Method

Metrics Price 

(2009$/MWh)

Price Volatility 

(2009$/MWh)

Yearly Deregulated Wind Mean/std dev 46.95 11.46

Median/width 45.64 13.82

Natural gas Mean/std dev 76.35 18.43

Median/width 75.19 21.81

Regulated Wind 54.11 0.00

Natural gas Mean/std dev 74.58 19.22

Median/width 78.33 20.12

Monthly Deregulated Wind Mean/std dev 47.24 16.24

Median/width 45.27 16.00

Natural gas Mean/std dev 76.82 27.23

Median/width 75.68 23.70

Regulated Wind Mean/std dev 54.11 0.00

Median/width 54.11 0.00

Natural gas Mean/std dev 74.58 19.22

Median/width 78.33 20.73
28 

0 10 20 30 40 50 60 70 80

Standard Deviation of Price [$/MWh]

0

10

20

30

40

50

60

70

80

Mean of Price [$/MWh]

Aggregation by Year

0 10 20 30 40 50 60 70 80

Standard Deviation of Price [$/MWh]

0

10

20

30

40

50

60

70

80

Mean of Price [$/MWh]

Aggregation by Month

0 10 20 30 40 50 60 70 80

Width of Price [$/MWh]

0

10

20

30

40

50

60

70

80

Median of Price [$/MWh]

Aggregation by Year

0 10 20 30 40 50 60 70 80

Width of Price [$/MWh]

0

10

20

30

40

50

60

70

80

Median of Price [$/MWh]

Aggregation by Month

Figure 4-3. Consumer cost versus risk relationships for wind and natural gas generation in 

deregulated market (PJM) and simulated regulated market 

4.3 Some Comments on Investment Decisions and Risk and Uncertainty in the 

Electric Sector 

4.3.1 Investment Decisions Under Risk Aversion and Loss Aversion 

Investors are generally assumed to make investments based on risk and return considerations. 

Finance theory assumes that investors are risk averse; that is, they prefer riskier investments only 

if compensated for greater uncertainty of outcomes by the anticipation of a greater expected 

return. We showed that the lack of correlation of returns for wind and natural gas generation 

bends the risk-return curve backwards, with the straight line in Figure 4-4 showing the change in 

risk and return with perfect correlation. It is important to realize that both curves are generated 
29 

by system characteristics and are independent of any individual risk preferences. For both 

curves, the optimal position on the curve will, however, depend on risk-aversion preferences of 

the investor. 

Figure 4-4. Expected return and standard deviation of return for wind and natural gas generation 

(without PTC or capacity payment) 

A standard formulation is that the economic utility, U, of any expected return, E[rp], is reduced 

due to variance associated with the return:45

 U = E[rp] – 1⁄2 λVar[rp] 

 

where lambda (λ) is a measure of risk aversion and rp is the return of the portfolio. The 

interpretation of this formula is straightforward. For a given expected return, the utility is 

reduced as the variance of the return increases in a simple linear fashion,46

 

45 This is the form used by Roques et al. (2008). In this section, we discuss the economic utility of consumers and 

producers. This utility will be denoted U and should not be confused with electric utilities. 

 and the risk premium 

associated with differences in variance will be given by 1⁄2 λ(Var[r1] – Var[r2]), with the special 

case that the risk premium compared to a risk neutral case will be 1⁄2 λVar[r1]. Simple 

discounted cash-flow methods that calculate the present value of an isolated investment utilize a 

simple discount rate in cash-flow analysis where the magnitude of the discount rate reflects the 

variance of future cash flows and a preference for consuming now rather than later. However, we 

use an approach based on more general economic utility that allows for explicit distributions 

46 The variance corresponds to the square of the standard deviation. 
30 

because a simple discount rate assumes a normal distribution, which does not fully account for 

prices, costs, and net revenues that may be asymmetric and positively skewed in the electric 

sector. This more general framework also allows for explicit examination of the impact of lack 

of positive correlation between returns or costs as well as for the incorporation of loss-aversion 

effects. 

In prior work, Roques et al. (2008) examined changes in optimal generation portfolios based on 

correlation considerations under a range of risk aversion (λ) assumptions. They found risk 

preferences can make a significant difference in determining the best technology asset mix 

among equivalent generation assets.47 In general, the greater the risk aversion the more the 

investor would move down the “efficient frontier” mix to the asset combinations with the lower 

returns and lower variance. The selected mix as a function of risk aversion is shown in Figure 4-

4 (subject to the caveats discussed in Section 3.3). 

While such a framework may be plausible for supposedly rational investors, such as electric 

utilities, the expected utility model has been shown to be less reliable for individual consumers. 

Prospect theory developed by Tversky and Kahneman (1981) shows that consumers often treat 

certain losses as more painful than certain but otherwise equivalent gains, and empirically this 

factor is often about two (Kahneman et al. 1991). The situation is more complicated because the 

utility of gains and losses depends on reference points, and risk preferences are not independent 

of the magnitude of the gain or loss. Nevertheless, for “small to moderate” gains and losses, 

consumers can be considered both loss averse and risk averse. In this case, the utility function 

can be given by: 

ܷሺܺሻ ൌ Eሾܺሿ െ ߣ

2 Varሾܺሿ െ DRMሾܺሿ

The variable X corresponds to the overall portfolio return (X = rp), so that E[X] and Var[X] 

correspond to the expected value and the variance of the portfolio return, respectively.48 The 

value of downside risk measure (DRM) is obtained by integrating the product of the probability 

density function by the difference in the variable term, X, and the expected value over the entire 

distribution. This product is multiplied by a constant, ߠ, that changes value on either side of the 

expected value to reflect the fact that “losses” are valued more greatly than otherwise equivalent 

gains. In this way, DRM is given by: 

DRMሾܺሿ ൌ ܧሾߠାሺܺെEሾܺሿሻା െ ߠିሺܺെEሾܺሿሻିሿ

With the notation ሺݕሻേ ൌ ቄݕ for ݕ ش 0

0 otherwise 

Typical values are ߠା ൌ െ1 and ߠି ൌ 2

 

47 Where λ was varied from 0.1 to 10.0. 

48 Similar considerations apply to portfolio costs (X = cp) though in this case utility increases for minimizing costs 

for a given variance rather than maximizing returns for a given variance (or vice versa). See also Jarrow and Zhao 

(2006).
31 

In effect, the value of DRM reflects the net difference in how outcomes to the left and right of 

the expected value are perceived as well as the width of the distribution.49 For a normal 

distribution, ܰሺߤ, ߪሻ, these more general expressions become:50

ܷሺܺሻ ൌߤെ

ߣ

ିߠ ൅ ାߠ െ ଶߪ 2

ߨ2√

ߪ

where μ and σ correspond to the expected value and standard deviation of (in this case) the 

annualized returns, assuming a normal distribution. Thus, for particular empirically observed 

combinations of risk and return resulting from different investment mixes, the optimal point on 

the efficient frontier curve will reflect the maximum utility, which will depend in turn on the 

individual’s risk-aversion and loss-aversion preferences.51 The utility (for a given expected 

return) decreases with variance due to both the risk-aversion and the loss-aversion terms (which 

are squared and linear with respect to standard deviation of returns). 

Figure 4-5 illustrates the impact the inclusion of risk aversion and loss aversion on where the 

optimal mix sits on the efficient frontier. The right-hand figure can be interpreted as follows. In 

the case without credits, assuming no risk aversion or loss aversion, the expected utility 

corresponds to the left-hand side of the upper black line. In this case, 100% natural gas 

generation is the mix with the highest utility. The impact of the risk-aversion and loss-aversion 

terms is to add a penalty for variance, which reduces the economic utility. This can be seen from 

the reduction in utility for 100% natural gas generation (asset ratio 0.0) as the impact of risk 

aversion (blue line), loss aversion (green line), and risk and loss aversion (red line) is added. 

However, because mixing wind with natural gas generation reduces the variance of the return for 

a given expected return (up to some limiting mix), the utility increases with the addition of wind 

up to some maximum utility. In this way, as shown in the left-hand figure in Figure 4-5, the 

optimal point on the return-return efficient frontier shifts downward. Similar effects are observed 

when loss aversion is considered or added. 

 

49 The evaluation of DRM is reminiscent in some ways of Value at Risk (VaR) calculations, though the latter 

usually considers only the tail of the less desirable “loss” side of the distribution. 

50 The normal distribution assumption is not essential, though any asymmetry may make the integrals more 

complicated to evaluate analytically. Certainly, the integral for the loss-aversion measure naturally takes account of 

any asymmetric effects in that values being further from the mean are weighted higher. For asymmetric returns or 

cost functions more generally that do not have analytic solutions, the probability function could be fitted empirically 

to the data and then the utility obtained using numerical integration. 51 Jarrow and Zhao (2006) found for normal distributions the solutions of the efficient frontier when both risk 

aversion and loss aversion are considered similar to those obtained solely using mean variance portfolio 

optimization under risk aversion. The effect of this is seen in Figure 4-5. 
32 

Figure 4-5. Optimal asset mix as a function of risk and loss aversion

4.3.2 Using System Models to Estimate the Economic Value of Alternative 

Electricity System Cost-Cost Variance Combinations

The foregoing discussion compared risk-return relationships rather than cost-risk relationships. 

System cost variance reduction is relevant in regulated electric-sector analysis as a potential 

refinement to traditional least-cost planning. 

Figure 4-2 suggests that in the regulated scenario, the significant annualized variation in natural 

gas prices is likely to be passed through to the consumer in terms of greater variability in the 

annualized average dollar per megawatt-hours cost of electricity. As previously discussed, 

adding a large amount of wind (or solar) to an electric system can be expected to reduce the 

variance in the electric system costs (and hence the variance of similar costs passed through to 

consumers). We have also discussed, however, why we cannot simply use the simple annualized 

LCOEs and related cost-variance information for various technologies to determine the impact of 

the overall portfolio costs from mixing these two technologies because they are not “equivalent” 

in terms of hourly electricity production. Nevertheless, Awerbuch’s idea of an optimal lowest 

cost portfolio for a given variance shows significant promise (at least for regulated markets) 

using models with a more sophisticated representation of system costs where the hourly 

operation of the technologies is modeled more explicitly (see e.g., Awerbuch and Berger 2003). 

These types of electric-sector production costing models or other cost-based models could then 

be used to solve the question of what the least-cost build is for a given cost variance.52

 

52 The electric-system-based expected cost-cost variance solutions will map out a similar form to the return-return 

variance efficient frontier shown in Figures 4-4 and 4-5, except that the upper curve will be inverted if lower 

variance technologies, such as wind, tend to lead to increasing average expected cost of energy. The overall system 

cost and cost variance could be divided by generation to give a distribution with a dollar per megawatt-hour 

expected value and associated variance. As a first approximation, this might be for a single year. More generally, the 

dollar per megawatt-hour cost-cost variance distribution might be calculated over a much longer time horizon to 

reflect multi-year investment decisions (with appropriate discounting).

Within 
33 

this risk framework, there would not be one lowest cost answer; instead, there would be an array 

of answers with different minimized costs for difference variance constraints.53 If the electricity 

cost distributions are thought to be approximately normal, then the difference between the value 

of two annualized cost distributions with different expected values would be given by:54

ܷሺܺሻ െ ܷሺܻሻ ൌ ൫ߤ௫ െ ߤ௬൯ െ ൫ߪ௫ െ ߪ௬൯ ൬

ߣ

ିߠ ൅ ାߠ ൅ ௬൯ߪ ൅ ௫ߪ൫ 2

൰ ߨ2√

When the economic utility of two distributions is equal, we have 

൫ߤ௫ െ ߤ௬൯ ൌ ൫ߪ௫ െ ߪ௬൯ ൬

ߣ

ିߠ ൅ ାߠ ൅ ௬൯ߪ ൅ ௫ߪ൫ 2

൰ ߨ2√

which in the case of risk aversion only (and no loss aversion) reduces to 

൫ߤ௫ െ ߤ௬൯ ൌ ߣ

2 ൫ߪ௫

ଶ െ ߪ௬ଶ൯.

As before, the values of ߤ and ߪ are physical properties of the electric system that are completely 

independent of any risk- or loss-aversion preferences. Selection of “optimal” mixes could be 

explored for different risk-aversion and loss-aversion preferences using the formulas discussed 

above. This formula is an illustrative approximation because in practice the cost distribution as 

shown in Figure 1-2 is likely to be non-normal and positively skewed, which may lead to an 

increased source of value for technology portfolios that narrow this distribution (compared to the 

normal distribution approximation). More generally, the utility of different skewed electricity 

cost distributions (and hence the difference in their utility) could be estimated empirically using 

numerical integration to a fitted distribution.55 In this way for a regulated electric system, the 

concept of lowest-cost planning could be refined to have an array of least-cost planning solutions 

corresponding to different variances. The preferred solution would likely reflect both consumer 

 

53 An interesting question is that if such variance reduction is valued, surely the forward price for commodities such 

as natural gas, should be priced at a premium to the expected future price, and some authors suggest such a premium 

may exist (Bolinger et al. 2006). Leaving aside the obvious difficulty in accurately estimating future expected 

values to determine whether or not this is true, if both the producer and the consumer valued variance reduction, 

then such a premium might be competed away in some cases; the consumer’s willingness to pay a premium for a 

fixed price being mitigated by the producer’s willingness to accept a price cut in return for similar price certainty. It 

is interesting to note that even if the variance premium is competed away under this symmetric bilateral 

arrangement, it somewhat ironically does not undermine the fact that both parties valued and may have been willing 

to “pay” for variance reduction. 

54 A “loss” is assumed to mean paying a higher than expected cost for energy while a “gain” refers to paying a lower 

than expected cost for energy. The difference in the value of theta reflects an aversion for losses compared to 

equivalent gains. 

55 An empirical cost-cost variance distribution might be better fitted to such an asymmetric distribution because then 

costs will not be able to fall below zero and the upper limit is essentially uncapped. If the system cost data can be 

fitted to a lognormal distribution and general relationship between utility and risk aversion listed at the start of 

Section 4.3 remains valid, then there is an analytic solution for E[X] and Var[X]. More generally, as indicated 

earlier, numeric integration can be used to estimate the economic utility of the fitted distribution where no analytic 

solutions exist. 
34 

risk aversion and loss aversion.56 From the consumer perspective, regulators could then chose 

how much weight should be placed on such preferences, which may lead to a significant source 

of additional value for wind and other renewable energy sources with no fuel costs.57

 

56 Given system-generated values for ߤ and ߪ, evaluating the actual differences in utility between different electric 

system cost-cost variance combinations requires knowledge of λ. If λ is not known, a sensitivity analysis can be 

done over a range of values for λ. In principle, λ could be determined empirically by designing alternative choices 

and seeing how people respond. Similar considerations apply to loss aversion. 

57 There are numerous examples of how this type of analysis might be used. For example, when comparing the 

different expected annualized system costs of successively higher renewable portfolio standard (RPS) levels, any 

reduction in variance in the annualized electricity cost distribution (which could be generated using a Monte Carlo 

simulation of runs reflecting the variability in fossil fuel prices) resulting from increased renewable penetration will 

increase the utility, which in turn may offset partly or completely any differences in total expected systems costs. 
35 

5 Summary and Conclusions

This analysis recognizes that the potential value of risk mitigation associated with wind 

generation and natural gas generation may depend on whether one considers the consumer’s 

perspective or the investor’s perspective and whether the market is regulated or deregulated. We 

analyze the risk and return trade-offs for wind and natural gas generation for deregulated markets 

based on hourly prices (and load) over a 10-year period, 1999–2008, using historical data in 

PJM. Similar analysis is then simulated and evaluated for regulated markets under certain 

assumptions. Estimating the absolute value of variance reduction will depend on assumptions 

about risk aversion and other consumer preferences, such as loss aversion, and this is discussed. 

Some key observations include: 

In a deregulated market such as PJM,

• Returns for natural gas generation are partially hedged because power prices are often 

set by natural gas generation. The correlation for power prices and natural gas prices 

is still quite low, however, and this can significantly mitigate the effect of the hedge, 

as does the fact that gas generation tends to operate mainly during peak hours, which 

have more volatile prices. There are also significant seasonal effects reflecting 

changes in the demand and price of natural gas.

• Returns for wind generation are better hedged than natural gas generation58

• The impact of incremental net revenue from tax credits, such as PTCs or other 

sources of revenue such as capacity payments, can have a significant impact on the 

risk return relationship. In PJM over this period with credits, wind was found to be 

dominant in terms of risk and reward; that is, it had both greatest returns and the 

lowest risk, as measured by standard deviation of returns. 

because 

wind often operates in off-peak hours, where power prices are much less volatile and 

less correlated with natural gas prices, whereas natural gas generation operation is 

focused more heavily during peak hours. 

• More generally, investors may benefit from investing in both wind and natural gas 

generation, with the optimal mixture depending on the investor’s risk aversion (and 

perhaps also loss aversion) preferences, due to well-known lack of correlation effects 

without PTCs. 

• While the opportunity for investors to diversify in broader markets may reduce some 

of the variance-reduction benefits of investing in different electric technologies, it is 

unlikely to completely eliminate these benefits in the electric sector where power 

prices are often very volatile and positively skewed, which has implications for 

financial distress. 

 

58 For wind and natural gas technologies with the cost and performance assumptions used in this analysis.
36 

• Similarly, consumers, especially smaller commercial and residential consumers, may 

benefit from reductions in the variance of electricity prices due to risk-aversion and 

loss-aversion effects.59

• Large-scale integration of renewable energy could also be expected to add value if 

wind became the marginal generator on a frequent basis,

 

60 though this effect may be 

somewhat offset by integration effects due to the operational and economic factors 

resulting from the intermittency of wind.61

• On a monthly rather than annual timeframe, natural gas generation shows a much 

greater volatility in returns (in both relative and absolute terms) than wind generation, 

partly reflecting the predictable relationship between power prices, demand, and 

natural gas prices. While producers might be more concerned with annualized returns 

than monthly returns, the much greater volatility of monthly returns also suggests 

potential benefit of taking actions to reduce variance to mitigate potential financial 

distress. 

 

• The LCOE of different technologies is not directly comparable if they operate in 

different hours because the value of electricity differs significantly throughout each 

day. This variation reflects the daily load profile, with hourly load and hourly power 

prices also showing strong seasonal effects. This effect can be seen in our analysis of 

PJM data when comparing the difference in the average annualized hourly price of 

variable wind generation and dispatchable natural gas generation. 

• Bilateral fixed price contracts or PPAs between producer and consumer offer a way 

of almost eliminating producer price and thereby a significant amount of net revenue 

risk. Such contracts also go a long way to mitigate some but not all consumer cost 

risk (because they will still have to buy or sell missing or excess power in a given 

hour). 

In a regulated market:

• The inherent nature of regulated markets means that producers earn, with some 

caveats, a utility-designated rate of return. A consequence of this is that the risk 

associated with fuel costs is passed on to consumers. The “cost-plus” nature of 

regulation means that consumers also bear some increased risk associated with poor 

investment decisions. Consumers are partly compensated for this because the 

 

59 This could also hold true for large consumers such as utilities if they or regulators realized they could quantify the 

value of such variance reduction to consumers and get paid by consumers some fraction of this value to do so.

60 Market structure rules may need to be modified so that such wind generation units receive sufficient capacity 

payments to encourage proper investment.

61 Variations in the amount of wind power generated during a day can be reduced by dispersing wind turbines 

because wind conditions will vary geographically. For a given daily amount of wind energy, much of the hourly 

production risk within a day could be eliminated by the use of electricity-storage technologies if the incremental 

benefits of using storage were cost effective. For example, by storing wind energy during the night and discharging 

it during the day (subject to transmission constraints), wind production could both be made firm and used to displace 

expensive peak generation. Integrated wind-storage analysis would need to be done to determine the optimal 

operation of a storage device under such circumstances. 
37 

producer may be willing to accept a lower expected rate of return compared to 

deregulated markets.

• For consumers who are generally risk averse, the reduced variation in electricity 

prices (and hence consumer costs) because of wind’s lack of correlation with other 

system costs should have value (as has been suggested by others). Loss aversion also 

may place a value on variance reduction of electricity prices and consumer costs. 

• Simplified mean variance cost optimization techniques using annualized LCOEs for 

the power sector often fail because the assets within the portfolio are sufficiently 

dissimilar (e.g., baseload versus peaking or either of these versus a variable or nondispatchable resource such as wind or solar). 

• A variance reduction-based technique could, however, be used more broadly under 

more sophisticated representation of system costs where the hourly operation of the 

technologies is modeled more explicitly. Specifically for a regulated electric system, 

the concept of lowest-cost planning could be refined to have an array of “least-cost 

planning” solutions corresponding to different variances, where the values of the 

expected annualized system cost and the standard deviation of the annualized system 

cost are physical properties of the electric system that are completely independent of 

any risk- or loss-aversion preferences. The value of variance reduction could then 

reflect both risk aversion and loss aversion. We discuss explicitly how to estimate the 

difference in the economic utility between alternative system-based expected costcost variance choices, including the impact of the distribution being positively 

skewed toward higher costs. 

In conclusion, we should point out that while some of the observations and findings may be 

generally applicable, others are empirical observations for a specific location and a specific time 

period under specific technology cost and performance assumptions.62 Therefore, care should be 

taken in drawing any conclusion about the specific comparative risk-return relationship for wind 

and natural gas generation, both outside of PJM over the specified time period and within and 

outside of PJM going forward. Sorting out the implications of variance reduction for returns and 

consumer costs in regulated and deregulated markets for small- and large-scale renewable energy 

penetration is a broad and complicated topic, and we hope that some of our observations offer a 

useful contribution to this debate. 

 

62 For example, within PJM over the same time period, different assumptions about technology performance and 

cost for wind and natural gas could lead to different risk-return relationships. Similarly, the risk-return relationships 

may vary outside of PJM, or over different time periods within PJM, because of differences in hourly electricity 

prices. 
38 

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