How to justify green power without apologizing for the price.

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Policymakers have shown considerable interest in the concept of a renewable portfolio standard (RPS), and how it might affect the cost of energy.

The RPS would require electricity providers to include a small amount of renewables-based power - typically less than 3 percent or 4 percent - in their resource mix. Several recent analyses estimate the costs associated with RPS requirements[Fn.1] and draw similar conclusions: They find that any additional costs incurred in attaining the desired levels of renewable energy are "minimal"[Fn.2] as compared to an all-fossil portfolio. This finding is then used to justify portfolio standards as a reasonable means of accelerating the diffusion of renewables, which is seen as a socially desirable, national objective. The message reads like an apology. With "hat in hand," these advocates tell the policy-makers, in effect, "Promoting renewables is a good idea, which will not cost too much."

In reality, however, that message gets it wrong - it sells renewables short. The prediction that renewables will raise overall generating costs flies squarely in the face of portfolio theory, a well-established part of modern finance.

Indeed, the standard RPS cost analysis arrives at this result by focusing on the direct cost of investing in renewables while ignoring the other important aspect - the favorable effect on portfolio risk that results because the costs incurred for renewable generation are generally fixed over time. In effect, we can think of renewable energy as essentially riskless,[Fn.3] which allows us to consider more properly the RPS concept using a finance-oriented analysis that weighs fuel price risk as well as the overall weighted-average generating cost.

If renewables in fact do raise portfolio costs, as previous studies show, then it would make little sense to mandate portfolio strategies in the name of altruism and nationalism, even if the percentage cost increases were small. Given the magnitude of our national outlays for electricity, even small percentage increases have a way of translating into serious dollar amounts. When we examine the RPS idea using finance theory, however, it turns out that renewables have a very favorable impact. Indeed they serve to reduce overall generating cost at a given level of risk; or, in the alternative, they reduce overall risk at a given cost. It is this reduction in risk and/or cost, rather than altruism or vaguely derived "green targets," that should provide a sound basis for RPS in our national policy.

How can renewables accomplish the neat trick of reducing portfolio cost? Don't they cost more than fossil alternatives? The short answer is, yes, they do cost more on a stand-alone busbar basis. But renewable technologies such as photovoltaics (PV) or wind are different - they are "passive" in the sense that they have no state of "on" or "off."[Fn.4] When included in an all-fossil portfolio, such renewables will reduce electricity costs, or risk, or both. This counter-intuitive result, which makes it seem that the economist's proverbial "free lunch" actually may exist, stems from the unique characteristic of such passive technologies: They are devoid of systematic (as opposed to random) risk. To be precise, they have the attributes of a zero-beta technology.

For our purposes, we can think of the term "riskless" as implying that year-to-year generating costs are largely fixed and that any fluctuations are not correlated to movements in fossil fuel prices. It is not necessary that renewables be entirely free of risk, just that their risk properties be reasonably close to those of "riskless" Treasury obligations, which also are not really risk-free as discussed in subsequent sections. Renewable technologies may exhibit random risks - a component may fail or the wind may not blow on any particular day - but these random risks are diversifiable and do not affect portfolio analysis. Thus, in the overall sense, these riskless renewables are entirely analogous to the key role played by U.S. Treasury bills in a diversified financial investment portfolio. It is well known that when added to a diversified portfolio of risky stocks, Treasuries improve efficiency. They raise expected returns at any given level of risk, even though their own expected return is lower.

The important point is that (systematically) riskless renewables affect the resource mix along two axes - cost and risk. When added to the fossil mix, renewables might raise cost, but they will also lower risk. That means that we cannot make a meaningful evaluation by examining only cost (while ignoring risk) as previous studies have done. Any RPS "cost" assessment must be based on underlying theory, which shows how to estimate expected portfolio costs at various levels of risk. Indeed meaningful, apples-to-apples comparisons of portfolio costs "before" and "after" renewables can be made only by holding the risk constant. Portfolio theory tells us that when properly constructed, such a comparison will show that the addition of riskless renewables serves to lower overall generating costs.[Fn.5]

Of course, renewable energy is not entirely free of risk, and neither are U.S. Treasury obligations. Nevertheless, the arguments for including Treasury bills in a financial portfolio, and the implications they hold for renewables in the generating resource mix, are compelling:

* T-Bills Are Expensive. U.S. Treasury obligations are the most expensive investment generally available. Consider a hypothetical T-bill yielding 5 percent and a risky stock with an expected yield of 20 percent. To generate an expected income stream of $100 per year requires an investment of $500 in the stock, but a much larger investment of $2,000 in T-bills. The T-bills are "more costly" and yield less. This feature, plus their "riskless" character, makes renewables and T-bills virtually identical in the financial sense.

* Yet T-Bills Boost Performance. Textbook portfolio theory tells us that every optimal portfolio must contain riskless T-bills. Why? Because even though their yield is lower, their inclusion serves to increase the expected portfolio return at virtually any given level of risk.[Fn.6]

* Renewables Can Do the Same. Wind, PV and similar passive renewable resources can improve the performance of the generating portfolio in the same manner T-bills enhance financial portfolios. Photovoltaics and other passive renewables are systematically riskless, for all practical purposes. Their addition to a fossil fuel portfolio can serve to lower the risk and/or cost of electricity produced.

For policymakers, the message should be clear. These portfolio-enhancing properties of renewables - risk and cost reduction - provide a sound basis for pursuing the RPS idea in electric restructuring.[Fn.7]

Portfolio Theory: The Basic Ideas

Figure 1 shows the risk-reward tradeoff for a financial portfolio of two risky assets, A and B, which can be two common stocks (or groups of common stocks), or two groups of generating assets. Risk is defined as the standard deviation of the periodic (i.e., year-to-year or month-to-month) returns to the portfolio.[Fn.8] [Note: Figures/graphics not included. See print copy.] Stock A (top right) is riskier; it has an expected return of 17 percent, coupled with a standard deviation of 0.41. Stock B offers lower return coupled with less risk; its expected return is just over 7 percent and its standard deviation is 0.27.

From a risk-reward perspective, it makes little sense to own only Stock B (or analogously, generating technology B), since there exist combinations of A and B that will produce superior results. In general, it makes no sense to own any portfolio combination that lies below portfolio V. For example, Portfolio R (consisting of 48 percent A plus 52 percent B) has the same standard deviation as Portfolio P (18 percent A plus 82 percent B) but produces a higher expected return. Investors seeking returns greater than those provided by V and R must accept greater risk by incorporating more Stock A into their mix. This choice moves them along the risk-reward curve to portfolios like S.

Given the two risky assets A and B, it is not possible to prescribe a single optimal portfolio combination, only the range of efficient choices, i.e., those that lie on the risk-return curve above V. Investors will choose a risk-return combination based on their own preferences and risk aversion. More risk-averse investors would be inclined to own relatively conservative portfolios such as V, while less risk-averse individuals will operate at S or A.

The Riskless Asset:

Diversification and Leverage

Adding a riskless asset to the A-B mix produces interesting and counterintuitive results. In financial portfolios, riskless assets generally consist of U.S. Treasury bills. The term "riskless" actually is misleading since even short-term T-bills bear some risk; e.g., their market value will fluctuate in response to changing interest rates. For this reason, T-bills are more properly called zero-beta assets, to distinguish that they are not truly free of risk, but are riskless when the returns are expressed in a particular manner.[Fn.9] This section describes the remarkable effect that so-called "riskless" Treasuries have on the financial portfolio.

Figure 2 illustrates the effects of adding riskless T-bills (that yield 5 percent) to the previous mix of risky stocks A and B. The risk-reward curve for various combinations of A and B remains unchanged from Figure 1. The new element in Figure 2 is the straight line, which represents the risk-return combinations for portfolios consisting of risky and riskless assets.[Fn.10] Point M, the tangency point between the line and the curve, now becomes the optimal mix of risky assets (M consists of 60 percent A plus 40 percent B). The solid portion of the straight line gives the risk-return combinations for portfolios consisting of the mix M plus T-bills. For example, Portfolio H consists of 50 percent T-bills plus 50 percent of the portfolio M (i.e., 50 percent T-bills, 30 percent A and 20 percent B). As more T-bills are added, the risk/ return point moves down the line (each tick mark represents a 25 percent change) until the portfolio consists of 100 percent T-bills and 0 percent M. At this point, its risk and return are 0.0 and 5 percent respectively, as shown in Figure 2.

Diversification. We now can more closely examine the powerful (and counterintuitive) impact that T-bills have on the portfolio. For example, portfolio H, which includes T-bills, has the same expected return as P (which does not), but is considerably less risky. This example (Figure 2) illustrates that by including lower-yielding but riskless assets, we can create a portfolio that produces the same expected return - 9 percent - but cuts risk nearly in half! Similarly, T-bills make it possible to move from portfolio V up to K, a move that raises return to 12 percent (from about 10.4 percent) without increasing risk.

(The gain from such moves can be even more sizeable depending on the relative risks of A and B and the risk-free rate of return. That these moves are possible illustrates why M is the optimal mix of A and B.)

With riskless assets, investors seeking risk-return combinations below M can construct portfolios such as K and H (which use a mix of M plus T-bills) that are superior to mixes that include only risky assets. That means that by adding a mixture of, for example, risky Internet stocks and T-bills, the investor can improve the annual return from Portfolio V without increasing its volatility. This powerful result, which holds in spite of the fact that T-bills yield less than either blue-chips or Internet high-flyers, has significant implications for generating portfolios, where the inclusion of riskless renewables similarly can reduce risk and/or cost.

Leverage. The dotted portion of the straight line in Figure 2 represents the additional risk-return combinations available when margin borrowing is permitted.[Fn.11] Recall that in Figure 1, the only option for raising return above M was to add more high-flyers to the mix, moving along the curve to points like S. Now, however, if an investor should want returns greater than M, she can borrow funds and use them to buy more of M, which would move her to points like N (consisting of 150 percent of M coupled with 50 percent margin borrowing).[Fn.12] Clearly margin borrowing is the better way to go: Note that N is superior to S. The implication for generating portfolios is as follows: Contractual fixed-price arrangements that are the financial equivalent of margin borrowing will improve overall performance.

To summarize, investors will adjust their risk return point to suit their preferences by adding riskless assets in Portfolio M or by using leverage. That means that all investors, independent of their risk preferences, will hold Portfolio M. This result has significant implications for national energy planning since it clearly implies that in the presence of riskless renewable resources, there exists a unique optimal mix of risky (fossil-based) alternatives that is independent of individual preferences and risk aversions.

Renewables:

The Riskless Alternative

The financial risks associated with PV, wind and other passive, capital-intensive renewables are very similar to those of "riskless" U.S. Treasuries. Such technologies are essentially riskless in the sense that their year-to-year costs are virtually unchanged. To be sure, they can never eliminate all uncertainty. For example, the value of renewable-based generating assets may rise and fall with the market price of electricity just as the value of U.S. Treasuries changes with inflation. But year-to-year market valuations are not relevant since PV installations presumably are intended to be a "going concern" for the life of the modules. That makes their risk entirely analogous to U.S. Treasuries, which are "riskless" on a nominal basis only if held to maturity.

There are other risks: Some arrays may fail prematurely. But even if not covered by manufacturer's warranties, the risks of failure are random and unsystematic (i.e., uncorrelated to overall economic cycles or to fossil fuel prices) and hence easily diversifiable. For example, in any large installation it might be reasonable to expect a certain number of modules to fail each year. These costs can be planned for - like the furniture reserve in a hotel - and hence are not "risky." The important point is that these failures are random and therefore uncorrelated with the systematic movement of fossil prices over time.[Fn.13] Random costs always are diversifiable and thus not relevant to portfolio analysis.

In short, PV and wind come about as close as real assets can to mimicking the zero-beta properties of T-bills. PV-based generation has an essentially fixed or "zero-beta" cost, which - like the nominal T-bill interest payment - is virtually certain and hence "riskless" for all practical purposes.[Fn.14]

Evaluating Generating Portfolios:

An Illustration

This section uses historic data to develop cost-risk results for a fossil portfolio consisting of gas and coal, then shows the effects of including riskless renewables, such as PV or wind.[Fn.15] The analysis is offered as illustrative only - not so much to form firm policy recommendations as to call attention to the value of portfolio theory in attacking the problem. It shows that resource alternatives should not be evaluated solely on the basis of their stand-alone costs, but on the basis of their contribution to the overall cost and risk of the portfolio of generating alternatives.

The analysis is based on annual coal and gas fuel price data for the period 1975 to 1999,[Fn.16] and on the following levelized generating costs: coal - $0.08 per kilowatt-hour, gas - $0.05 per kilowatt-hour, PV/wind - $0.12 per kilowatt-hour. These are not current costs, but represent the levelized total cost, going forward, over the life of the assets. Although the analysis can be performed using these kilowatt-hour costs directly, transforming them into measures of return yields more useful graphical results that closely resemble the standard textbook presentation of portfolio theory. Annual return measures an output (yield) divided by an input (cost). A useful return measure for our purposes is kilowatt-hour per $0.01 - the simple inverse of the familiar busbar cost. The resulting portfolio risk measure thus remains essentially one of cash-flow variance.

Figure 3 illustrates the results, using the historic fossil prices and their correlation. The 100 percent coal portfolio (Point B) "yields" 12.5 percent, (1 kWh at $0.08). Adding some gas to the mix helps; it reduces risk while simultaneously raising return (up to Point V; this result is driven by the historic covariance of the fuel prices so that altering the levelized costs for A and B does not change this outcome). As a nation, however, we have pretty much exploited these gains over the past decade by expanding our gas-based generation from its 1990 levels.

The minimum variance of the fossil portfolio (0.21) occurs at V, which represents a coal-gas mix of approximately 80 percent-20 percent. (Each tick mark represents a 5 percent change in mix on the fossil portfolio.) After this point, further gas additions increase both risk and return until a 100 percent gas portfolio is obtained (Figure 3 is truncated at 60 percent gas-40 percent coal for illustration purposes).

As in Figure 2, the straight-line segment in Figure 3 represents portfolios consisting of the mix M combined with a riskless resource. At F (lower left), the portfolio consists of 100 percent riskless renewables. (Each tick mark along the line segment represents a 25 percent addition of the fossil mix M.) Finally, at M, the portfolio consists entirely of the fossil mix. Portfolios along the dashed line above M consist of M plus the riskless (i.e., fixed-price) sale of power at $0.12 per kilowatt-hour, which is directly analogous to the previous section's results using margin borrowing. Such portfolios may have important implications for private power marketers, although their public policy ramifications do not seem clear at this time.

The Optimal Mix:

Coal vs. Gas vs. Renewables

What does portfolio theory teach us about the optimal mix of coal- and gas-fired generation?

The optimal coal-gas mix is entirely analogous to the optimal mix of risky financial assets in the last section. In the presence of the $0.12 per kilowatt-hour riskless renewable, it turns out that the optimal mix is 72 percent coal-28 percent gas (Figure 3, Point M). By comparison, the 1998 U.S. coal-gas generation mix (utility and non-utility power plants) already is at 77 percent coal-23 percent gas (Figure 3, Point U).[Fn.17] The results of Figure 3 therefore clearly imply that we must reconsider our policy of significantly higher gas usage. From a risk-reward perspective, gas usage should be expanded by only 22 percent to reach M (seven percentage points, from 23 percent to 28 percent of the mix).[Fn.18] Further increases push the mix past this optimum into an undesirable region where the risk of the fossil portfolio increases rapidly but returns rise very slowly.[Fn.19]

Should we require generators to add more PV or wind resources?

Recall that in Figure 2, by adding T-bills an investor could improve portfolio performance (from V to K in Figure 2) without increasing risk. Similarly, increasing the deployment of PV/wind at $0.12 per kilowatt-hour reduces the risk and/or cost of the generating portfolio from its present values. This important result is not recognized widely; here is how it happens. Wind and solar sources represent 0.2 percent of 1998 U.S. capacity and 0.1 percent of the generation, according to data from the Energy Information Administration. Increasing the generation of these resources to about 3 percent, for example (Figure 3-Detail, Point L), reduces cost (i.e., raises return) as compared to U without increasing risk! (The actual cost reduction is around 1.5 percent.) This result stands in stark contrast to the estimates produced by the previously cited RPS analyses, which consistently find that renewables raise overall costs.

On the other hand, renewables can be used entirely to reduce portfolio risk: The renewables proportion can be increased to about 6 percent (Point K), which produces the same yield (i.e., cost) as U but cuts risk by about 10 percent. In short, given our underlying cost assumptions, any operating point between K and L, i.e., 3 percent-6 percent renewables, improves the current U.S. generation mix.

Moving from our current operating point U to points such as K or L involves two strategies, which could be implemented simultaneously:

a. Increase gas to the optimal mix M (28 percent of gas-coal),[Fn.20] and

b. Increase renewables to the range of 3 percent-6 percent of total generation.

The capacity proportions for coal, gas and renewables under this strategy now can be derived as follows. At K, the portfolio contains 94 percent of mix M (72 percent-28 percent coal-gas) plus 6 percent renewables. The capacity proportions for coal, gas and renewables therefore would be 0.94 x 28 percent gas + 0.94 x 72 percent coal + 6 percent PV/wind = 26 percent gas + 68 percent coal + 6 percent PV/wind. At point L, by comparison, the portfolio consists of roughly 27 percent gas, 70 percent coal and 3 percent PV/wind.

Why not simply operate at M with no renewables?

As discussed above, the move to L or K from our present position at U (Figure 3, detail) is accomplished by first moving to M, the optimal fossil mix. There is no particular gain from this move, which simply involves accepting greater volatility in return for better yields (lower costs). It cannot be said that such a move leaves us "better off" in an economic sense. While some people prefer the risk-return combination at M, others prefer U. (The market provides both choices, which is no different than, say, being able to choose between plump vs. lower-priced but over-ripe strawberries, Cadillacs vs. Chevrolets, or, for that mater, blue-chips vs. "tech" high-flyers.) By contrast, a move to the region between L and K does leave us better off than we are now. It provides an efficiency gain in the form of more desirable risk-return combinations.[Fn.21] In addition, such a move creates strategic benefits; long term, in order to improve from M, we will have to reduce the cost of renewables.

What happens if the cost of renewable energy comes down, thus boosting the return (cost per kilowatt-hour) earned on such resources?

Recall that the optimal coal-gas mix is located at M, the tangency point between the line and the curve. As the cost of renewables drops (i.e., as their returns increase), the tangency point moves to the right so that the optimal mix contains more gas. That implies that our current gas expansion policy cannot be implemented in an economically efficient manner without a simultaneous national focus on reducing the cost of PV, wind and other riskless renewables. Such cost reductions could be accomplished through various policies including a national portfolio standard to accelerate PV production.[Fn.22]

A national policy that helps reduce the costs of renewables provides a portfolio benefit by significantly increasing the attainable risk-reward gains. If the cost of riskless renewables were to drop to say $.08 per kilowatt-hour, (a 12.5 percent return), the optimal coal-gas mix would shift up to N (Figure 4). Now deploying additional renewables would produce sizeable risk reductions accompanied by only small cost increases. For example, Portfolio H is half as risky as fossil portfolio N, yet costs less than a penny more.[Fn.23]

Spikes and Contracts:

The Physical Limits of

Financial Hedging

These findings suggest that any portfolio should contain some proportion of riskless (fixed-price) power. Even so, while private firms can attain optimal results by including riskless contracts for the purchase and sale of power,[Fn.24] these contracts need not be supported by renewable generation.

Indeed, individual firms may not be much impressed by the fixed-cost nature of PV or wind since they can readily obtain long-term power contracts at fixed prices. In addition, they can hedge positions with a variety of futures and options.

Unfortunately, we can't all continue to offer each other futures and fixed-price energy contracts based on underlying technologies whose costs fluctuate unpredictably without inviting financial disaster at some point.[Fn.25]

Building optimal physical generation portfolios that include riskless renewables is one alternative to dealing with price risk. Financial hedging strategies provide a second alternative for individual firms, but it is incorrect to presume that this is a superior or less-costly alternative. Hedging strategies are not free. Neither are they free of risk. Indeed, the firm will pay what it "should," for its hedging, which ultimately must include a premium for those agents undertaking risk. To the extent that these agents can diversify the risk, they may be able to undertake it at lower cost. Still, no perfect hedge can exist in reality - as evidenced by the multi-billion dollar collapse of Long Term Capital Management, a firm whose principals included prominent Nobel laureates who contributed to the valuation theories underlying the options and derivatives the firm employed.[Fn.26]

When many firms undertake strategies to hedge against the same risk, it seems reasonable to expect that the cost of such strategies will rise or the risk will increase. In any event, all the hedging strategies notwithstanding, somewhere in the system there will remain risk, which someone will have to absorb at some point. And ultimately, if energy prices rise precipitously, the system will collapse with declarations of force majeure - as was the case during the hot spell of 1998 to 1999. Except where risk is purely random and widely diversified, e.g., among numerous, large multi-national insurance firms, such results are to be expected. Indeed the industry's history includes the abrogation of fixed-price long-term nuclear fuel contracts by Westinghouse and others when the cost of "yellowcake" (a uranium-based feed material) rose sharply in the 1970s.

History validates the common wisdom that, when you have a fixed-price long-term contract, you have exactly that ¼ a contract. From a national policy perspective, therefore, incorporating riskless physical assets such as PV and wind may be essential for long-term energy security and reliability.

Shimon Awerbuch, Ph.D., is an independent financial economist in Nashua, N.H. He, along with Leonard Hyman, CFA, and Andrew Vesey, is the author of Unlocking the Benefits of Restructuring: A Blueprint for Transmission, Public Utilities Reports Inc., 1999. Contact Dr. Awerbuch at Awerbuch@aol.com.

This research was supported in part by a grant from the Interstate Renewable Energy Council (www.irecusa.org/). The author thanks Jane Weissman for her support and Richard Bower, Ronald Lehr and Adam Serchuk for their helpful comments. The views expressed do not necessarily reflect the position of IREC or the U.S. Department of Energy

The Math Fundamentals of Portfolio Theory

Portfolio theory generally is attributed to Harry Markowitz[Fn.27] who recognized that by considering the co-movement (co-variance) of returns, risky and riskless assets can be assembled in such a way as to increase expected returns with little or no additional risk. The theory was conceived in the context of financial portfolios, where it relates rp, the expected portfolio return, to sp, the total portfolio risk, which is defined as the standard deviation of those returns. The relationship is illustrated below using a portfolio of two risky assets. The expected portfolio return, rp, is the weighted average of the individual returns of the two securities:

E(rp) = x1 • E(r1) + x2 • E(r2) (1)

Where:

E(rp) is the expected portfolio return; x1, x2 are the proportions of the portfolio in assets 1 and 2; andE(r1), E(r2) are the expected returns for assets 1 and 2;[Fn.28]

The overall portfolio risk, sp, also is a weighted average of the two securities, but is tempered by the correlation coefficient between the two returns:

sp = SQRT { x12 s12 + x22 s22 + 2x1x2r1,2 s1s2 } (2)

Where:

r1,2 is the correlation coefficient between the two return streams, and s1 and s1 are the standard deviations of the periodic (e.g. ,annual) returns for asset 1 and 2 respectively.

The introduction of riskless assets (such as Treasury bills) into the portfolio reduces Equation (2) to a line. Consider a portfolio of a risky security (e.g. ,common stock) and a riskless T-bill. We begin with Equation (2):

sp = SQRT { x12 s12 + x22 s22 + 2x1x2r1,2 s1s2 }

where the subscripts 1 and 2 now reflect, respectively, the risky security and the riskless asset. In the case of riskless asset s2 = 0.0, so that Equation (2) reduces to the linear relationship

sp = SQRT { x12 s12 } = x1 s1 (3)

Equations (1), (2) and (3) are used to create Figures 1-4 in this article. These equations rely on a set of assumption that may not always hold in the case of real (i.e., non-financial) assets such as a portfolio of generating resources. The standard assumptions require the existence of perfect markets for trading assets, which generally implies low transactions costs, perfect information about all assets[Fn.29] and prices that follow a random walk - a condition that in fact seems to be empirically supported by the evidence for fuel prices.[Fn.30]

The market for the generating assets may be less than perfect and unlike financial securities, which can be readily sold, generating assets are less liquid. In addition, financial securities are almost infinitely divisible so that a portfolio can contain between 0 percent and 100 percent of a given security.[Fn.31] Generating assets are quite lumpy by comparison, which may cause discontinuities. For example, the optimal portfolio for a region may include 1.5 units of a particular resource, although such concerns diminish in the case of national energy planning where the lumpiness of individual units of capacity additions becomes relatively insignificant. Given these caveats, it is also important to note that portfolio theory commonly is applied to the valuation of tangible, non-financial assets, in spite of these limitations.[Fn.32] - S.A.

1 For example, Bernow, Steve, Bill Dougherty and Max Duckworth, "Quantifying the Impacts of a National, Tradable Renewables Portfolio Standard," Electricity Journal, Volume 10, No. 4, May 1997, 42-52. The authors estimate the costs associated with the Minimum Renewables Generation Requirement in the Schaefer Bill (H.R. 3790, 104th Congress), which calls for a renewables component of 4 percent (excluding hydro) by the year 2010. See also Berry, David and Ray Williamson, "Solar Power and Retail Electric Competition in Arizona," Solar Today, Volume 11, No. 12 March/April 1997 34-37. The authors discuss the Arizona RPS (since withdrawn), which required that providers include between 1 percent and 2 percent renewables in the resource mix.

2 Bernow, et. al. [1997, at page 50] estimate a cost increase in the range of 0.1 percent to 1.6 percent by the year 2010 [ibid. at 47], or about 0.03 cents per kilowatt-hour [ibid. at page 50]. Berry and Williamson [1997, at p. 36] find that the Arizona RPS would have increased cost by 0.13 cents per kilowatt-hour - pretty much the same story.

3 For the moment, we can define risk as the year-to-year fluctuations in overall generating costs. Such fluctuations are primarily driven by the systematic changes in fossil fuel prices. They cannot be diversified simply by adding different types of fossil fuel, since fossil prices are highly correlated. Other risks, such as the failure of a gas turbine o

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