Environ. Sci. Technol. 2010, 44, 9134–9142
Future Sustainability Forecasting by Exchange Markets: Basic Theory and an Application NATALIYA MALYSHKINA* AND DEB NIEMEIER* University of California, Davis, The Department of Civil and Environmental Engineering, One Shields Avenue, Davis, California 95616, United States
Received March 5, 2010. Revised manuscript received August 26, 2010. Accepted October 8, 2010.
Setting sustainability targets and evaluating systems progress are of great importance nowadays due to threats to the human society, to economic development and to ecosystems, posed by unsustainable human activities. This research establishes a probabilistic theoretical approach based on market expectations reflected in prices of publicly traded securities to estimate the time horizon until the appearance of new technologies related to replacement of nonrenewable resources, for example, crude oil and oil products. To assess time T when technological innovations are likely to appear, we apply advanced pricing equations, based on a stochastic discount factor to those traded securities whose future cash flows critically depend on appearance of such innovations. In a simple approximation of the proposed approach applied to replacement of crude oil and oil products, we obtain oil alt oil alt T ≈ (Poil 0 /C0) · ln (∆ · P0 /P0 ), where P0 and P0 are the current aggregate market capitalizations of oil and alternativeenergy companies, C0 is the annual aggregate dividends that oil companies pay to their shareholders at the present, and ∆ is the fraction of the oil (oil products) replaced at time T. This formula gives T ≈ 131 years for replacement of gasoline and diesel. The proposed market-expectations approach may allow policymakers to effectively develop policies and plan for longterm changes.
Introduction Perhaps the most commonly recognized definition of sustainability is that recommended by The World Commission on Environment and Development: “[sustainable development that] meets the needs of the present without compromising the ability of future generations to meet their own needs”. Putting this definition into practice, however, has proven to be problematic primarily because it is very difficult to predict the needs of future generations, which would require at the minimum forecasting the availability of future technological innovations (new effective technologies). In fact, we argue that this problem of forecasting the availability of new technology for practicable industrial activities (as opposed to purely scientific discoveries) is of the utmost importance, because it directly impacts our ability to assess current levels of sustainability. In this paper, we describe a general theoretical framework for a proposed marketexpectations-based approach to estimation of the time * Address correspondence to either author. E-mail: nmalyshk@ gmail.com (N.M.);
[email protected]. 9134
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horizon T until the appearance and adoption of new technologies related to important sustainability problems. Our framework can be used to extend many recently developed quantitative measures of sustainability (1, 2). For example, the Graedel and Klee’s sustainable emissions and resource usage model involves comparison of the maximum sustainable rate to the current annual consumption rate of a resource (3). One critical (and debatable) assumption in this comparison is that the number of years T that the resource is expected to last before an alternative means of fulfilling that consumption is available, is equal to the time period of roughly two human reproductive generations, or 50 years. Our proposed method provides a means for directly estimating T in Graedel and Klee’s model using market expectations. There are other application examples: T could be used to adjust the relative weights for the Environmental Performance Index indicators, or to define the stability of sustainability for specific systems (4), or to estimate long-term financial, social, and environmental impacts in company performance (5). Even estimating the number of Earths in constructing ecological footprints requires some assessment of the introduction of new technology (6): the number of Earths needed to indefinitely support the current rate of consumption of a nonrenewable resource would formally be equal to infinity, unless a replacement of this resource is taken into account and time T is estimated. Finally, throughout much of the life cycle analysis applications (e.g., see ref 7), the various determinations of environmental impacts due to production, transportation and consumption of a product/service crucially depends on time T until the appearance of new technologies for the product/ service manufacture and disposal. It is clear that for both the theory and the practice of setting sustainability targets and evaluating system progress at any scale, a theoretical framework for estimating the time T until appearance of new technologies is critically important. But estimating T is difficult because it must be based on an unknown future (8). Prior studies that considered forecasting and effects of future technologies, mainly in the energy and transportation sectors (9-13), and many of them based on (socio)economic and/or system dynamics models (9, 11-13), required that a number of (questionable) assumptions about future demand, supply, production and innovation functions be made. Other studies primarily rely on polling of futurists, forecasters and technical experts (e.g., ref 10), with the possibility of biased results being a disadvantage. We propose instead an approach that utilizes market expectations to estimate T. That is, we use the prices of market traded securities to forecast the time T until the appearance and adoption of new technologies. The theoretical basis for this approach is grounded in the fact that average prices of market-traded securities must, and do reflect the current expectations of investors about probabilities and timing of potential technological innovations because in the future these innovations will lead to significant changes and redistributions in cash flows paid to investors. Sophisticated investors tend to put considerable effort into collecting, processing and understanding information relevant to the future cash flows paid by securities, and as result, market forecasts of future events tend to be relatively accurate (14-16). For example, in the past marketexpectations-based forecasts have been successfully used for predicting the probabilities of future events not only in finance and business (17), but also in politics (18) and sports (19). Another important advantage of market predictions is that, being consensus predictions by a large number of investors, they are politically and ideologically unbiased (20). 10.1021/es100730q
2010 American Chemical Society
Published on Web 11/08/2010
In short, in spite of considerable day-to-day volatility of market conditions, the advantages of long-term market forecasts are substantial. Long-term investors are both cognizant of and savvy to different adaptations to markets that involve new research and technology. In this paper, we outline a theoretical approach for estimating time T until appearance of sustainability-related technological innovations using market pricing data, which reflects all (or nearly all) of the currently available information on progress in development of the innovations and all other relevant factors (such as government regulations, policies, and taxes, and the currently estimated likelihoods of their future changes). As both a matter of practical importance as well as providing an interesting application, we use the replacement of crude oil and oil products by viable substitute(s) to demonstrate our theoretical framework. Crude oil is a widely used nonrenewable fuel and energy source and a vital component in the chemical industry. The current global reserves of crude oil are estimated to be at about 1.3 trillion barrels, whereas annual oil consumption is around 31 billion barrels (21). There is near universal agreement that in the future crude oil will need to be replaced by substitutes (22, 23), which makes the estimation of the time until such substitution might occur due to development of new technologies of clear importance for policymakers and scientists. In making inference on market expectations about time T until appearance of an oil substitute, we consider stock shares of oil companies and alternative-energy companies. Future cash flows of these companies directly depend on the arrival of the oil substitute and their current market prices reflect investor sentiment about the timing of such an event. General Theoretical Framework. Markets are strongly influenced by the laws of supply and demand, and, over the long-term, market forecasts are effective in pricing traded securities (14, 17, 24). The time-zero (today’s) price P0n of security n that is a claim to a stream of future cash flows Cnt , paid at time periods t ) 1,2,3, ..., can be generally expressed as (17, 25), ∞
Pn0 )
∑ E[S C |I ] n t t 0
(1)
t)1
Here St > 0 is the stochastic discount factor for the cash flow paid at a future time t, and the expectation is conditional on the information set I0, which includes all the information available to investors at time zero (today). The future cash flows Cnt are usually random variables, which are unknown at the present time and become revealed only at future time t (for example, future dividends depend on performance of companies in the future). The stochastic discount factor St is taken to be also random, with the purpose of accounting for investment risk associated with uncertainty of the future cash flows. It is important that St is the same for any security freely traded in an efficient market (i.e., St does not depend on the security index n), and also S0 ) 1 (present cash flows are as good as cash). Note that the current price Pn0 is observed from the market trading data and is known today (at time t ) 0). A practical application of eq 1 has to include a specification for the stochastic discount factor St. The conceptual framework behind our market-expectations-based approach is straightforward: we apply the pricing eq 1 to those traded securities whose future cash flows depend on appearance of technological innovations related to important sustainability issues. Our goal is to use this equation and the pricing data to expose current market beliefs about when these innovations are likely to appear. We follow three steps in the market-expectations-based estimation of time T until an appearance of a technological innovation: I. Identify traded securities, whose future cash flows strongly depend on the appearance of a new technology of
interest (e.g., a viable replacement of crude oil, or a technology for reducing CO2 emissions). II. Specify a model for pricing these securities using eq 1. The model design must include specifications for the stochastic discount factor and for the future cash flows paid by the securities. The dependence of the future cash flows on time T should be accounted for by the model design (T is one of the model’s free estimable parameters). III. Collect historical and current market data on the securities (e.g., share prices, number of shares outstanding, dividends paid, etc.). Using these data, estimate the values of all estimable parameters of the pricing model, including time T until the appearance of the new technology. The estimated time will reflect the current expectations and beliefs of market investors. The pricing formulation given in eq 1 is very general and can be used for most market-traded securities and contracts (provided the market “frictions”, such as transaction costs and lack of liquidity are negligible). Since, one way or another, almost any innovation will considerably influence future payoffs by some market-traded securities and contracts, the proposed three-step market-expectations-based approach can be used for a wide scope of applications that are underpinned by the estimation of time until appearance of many important sustainability-related technological innovations. Data Description. To estimate our model, we take advantage of market data on major oil and oil-refining companies, as well as on major alternative-energy companies that carry out research on oil and oil product substitutes and can potentially discover new technologies to replace oil and oil products in the future. We used publicly traded securities whose cash flows directly depend on appearance of an oil substitute. These are stock shares of oil/oil-refining companies and alternative-energy companies. The oil/oil-refining companies are in the business of oil extraction, refinement, and supply, therefore, their business crucially depends on demand for oil and oil products. The alternative-energy companies develop substitutes for oil and oil products, and are considered by the market to directly benefit from appearance of these substitutes. To collect data, we relied on major financial information and news sources including the U.S. Securities and Exchange Commission database (www.sec.gov), Google Finance (www. google.com/finance), and Yahoo Finance (www.finance. yahoo.com). We limited our analysis to including only those major companies publicly traded on U.S., European and Australian stock exchanges (NYSE, NASDAQ, AMEX, LON, BIT, ASX, etc.). We chose 17 oil and 8 oil-refining companies with market capitalization (the total dollar value of all outstanding shares) above 10 billion dollars for oil companies and above 1 billion dollars for oil-refining companies, these companies are listed in Table 1. While we do not include several large oil companies that are not traded on U.S./European/Australian exchanges, such as Saudi Aramco (Saudi Arabia), Statoil ASA (Norway), and Rosneft (Russia), we show that our results are not sensitive to such omissions. For the alternative-energy companies, we chose only those companies pursuing development of new technologies intended to substitute for oil and/or oil products (such as gasoline and diesel) and for which current earnings are relatively small. Specifically, we chose companies that work in the areas of production of ethanol, biodiesel, biofuel, hydrogen, and development of fuel cells, batteries, and propulsion systems for “clean” vehicles. In each of these areas, we considered the largest alternative-energy companies, which together occupy about 99% of the market share in the respective area. In total, we collected data for 44 alternative-energy companies, which are listed in Table 1. We do not consider alternative-energy companies working in the areas of geothermal, wind, and solar energy, because their research is mostly VOL. 44, NO. 23, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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oil oil oil oil oil oil oil oil oil oil oil oil oil oil oil oil-ref. oil oil oil-ref. oil-ref. oil-ref. oil-ref. oil-ref. oil-ref. oil-ref.
ethanol biodiesel batteries biofuel batteries fuel cell batteries batteries fuel cell clean vehicle biofuel biofuel fuel cell fuel cell batteries ethanol ethanol biodiesel
Alternative-Energy Companies Cosan Ltd. (CZZ) Gushan Environmental Energy Ltd. (GU) Exide Technologies (XIDE) AE Biofuels Inc. (AEBF) Ener1 (HEV) FuelCell Energy Inc. (FCEL) Saft Groupe SA (SAFT) Valence Technology Inc. (VLNC) Ballard Power Systems Inc. (BLDP) Westport Innovations Inc. (WPT) GreenHunter Energy Inc. (GRH) Rentech Inc. (RTK) Medis Technologies Ltd. (MDTL) Plug power Inc. (PLUG) Altair Nanotechnologies Inc. (ALTI) Verenium Corp. (VRNM) Pacific Ethanol Inc. (PEIX) Nova Biosource Fuels Inc. (NBFAQ)
area
Oil and Oil-Refining Companies Exxon Mobil Corp. (XOM) PetroChina Company Ltd. (PTR)a Petroleo Brasileiro SA (PBR)a Royal Dutch Shell plc (RDS.A)a BP plc (BP)a Chevron (CVX) Total S.A (TOT)a ENI (E)a ConocoPhillips (COP) Occidental Petrolum (OXY) Repsol YPF SA (REP)a Suncor Energy Inc. (SU) Imperial Oil Limited (IMO) Marathon Oil Corp. (MRO) Hess corp. (HES) Valero Energy Corp. (VLO) Petro-Canada (PCZ) YPF- SA (YPF)a Sunoco, Inc. (SUN) Polski Koncern Naftowy (PSKZF) Caltex Australia Ltd. (CTX) Tesoro Corporation (TSO) Sinopec Shanghai Petrochemical Company Ltd. (SHI) Frontier Oil Corporation (FTO) ERG SpA (ERG)
company name (ticker symbol)
1773 758 728 553 536 471 467 341 321 306 304 224 218 208 195 147 145 138
425 766 223 088 214 071 209 462 188 702 172 853 157 996 115 141 110 626 58 788 43 447 42 856 41 580 30 590 29 111 20 547 20 172 17 759 5255 4614 3299 3084 2438 2369 1803
market cap, 106 $
TABLE 1. Financial Data for Major Oil and Alternative-Energy Companies (2008 Only)
174 893 145 166 831 943 69 284 000 84 641 642 103 382 000 68 571 000 18 471 782 111 593 000 85 763 207 88 087 882 20 216 032 165 480 000 40 693 544 89 383 000 85 903 712 64 134 000 50 147 000 110 199 966
5 149 000 000 183 020 977 818 8 774 076 740 6 171 489 652 18 963 000 000 2 037 000 000 2 246 700 000 3 639 000 000 1 480 240 553 817 635 000 1 220 863 463 935 524 213 882 604 000 713 000 000 325 800 000 524 000 000 484 597 467 393 312 793 117 100 000 427 709 061 270 000 000 139 200 000 7 200 000 000 103 904 472 148 308 882
number of shares
10.14 4.55 10.51 6.53 5.19 6.87 25.27 3.06 3.75 3.47 15.05 1.35 5.37 2.33 2.27 2.29 2.90 1.25
82.69 1.22 24.40 33.94 9.95 84.86 70.32 31.64 74.73 71.90 35.59 45.81 47.11 42.90 89.35 39.21 41.63 45.15 44.88 10.79 12.22 22.16 0.34 22.80 12.16
share price, $
0.00 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1.55 0.02 0.47 1.60 0.55 2.53 2.53 1.91 1.88 1.21 1.27 0.20 0.38 0.96 1.20 0.57 0.66 7.42 1.18 0.00 0.33 0.40 0.00 0.23 0.59
dividends per share, $ 7981 4153 4124 9874 10 439 5154 5684 6954 2783 989 1544 187 335 684 391 299 320 2920 138 0 89 56 0 24 87
dividends, 106 $
77.04
99.12 20.67
37.03 55.39
53.35 53.72 51.91 21.21 18.08 33.54 27.80 16.56 39.75 59.42 28.13 229.05 123.98 44.69 74.46 68.79 63.07 6.08 38.20
P/D ratio
0.09 0.23 0.46 -0.19 -0.42 -1.41 2.79 -0.18 -0.40 -0.12 -4.08 -0.38 -3.75 -1.36 -0.34 -2.89 -3.02 -0.38
8.69 0.09 2.15 4.26 1.12 11.67 9.11 3.57 -11.60 8.35 3.28 2.26 4.36 4.95 7.24 -2.16 6.43 2.91 6.63 -1.45 0.13 2.00 0.12 0.77 6.41
net income per share, $
44 745 16 352 18 864 26 291 21 155 23 772 20 467 12 999 -17 171 6827 4005 2114 3848 3529 2359 -1132 3116 1144 776 -619 35 278 888 80 950
net income, 106 $
112.65 19.62 22.84 -34.38 -12.35 -4.87 9.05 -16.98 -9.37 -28.48 -3.69 -3.55 -1.43 -1.71 -6.68 -0.79 -0.96 -3.30
9.52 13.64 11.35 7.97 8.92 7.27 7.72 8.86 -6.44 8.61 10.85 20.27 10.81 8.67 12.34 -18.15 6.47 15.52 6.77 -7.45 93.99 11.08 2.74 29.61 1.90
P/E ratio
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biofuel fuel cell fuel cell clean vehicle ethanol biofuel ethanol biofuel fuel cell clean vehicle fuel cell batteries clean vehicle hydrogen biodiesel ethanol batteries ethanol biofuel batteries hydrogen biofuel clean vehicles ethanol fuel cell fuel cell
Beacon Energy Holdings Inc. (BCOE) Ceramic Fuel Cells Limited (CFU) Hoku Scientific Inc. (HOKU) Quantum Fuel Systems Technologies (QTWW) Green Plains Renewable Energy Inc. (GPRE) DynaMotive Energy Systems (DYMTF) Bluefire Ethanol Fuels Inc. (BFRE) New Generation Biofuels Holdings, Inc. (NGBF) Hydrogenics Corp. (HYGS) Azure Dynamics Corp. (AZD) Enova Systems Inc. (ENA) Lithium Technology Corp. (LTHU) UQM Technologies Inc. (UQM) ITM Power Plc. (ITM) BDI - BioDiesel International AG (D7I) ADA-ES (ADES) Hong Kong Highpower Tech. Inc. (HPJ) BioFuel Energy Corp. (BIOF) D1 Oils plc. (DOO) Axion Power International (AXPW) Hy-Drive Technologies Ltd. (HGS) Renegy Holdings, Inc. (RGYH) Ecotality, Inc. (ETLY) Dyadic International Inc. (DYAI) AFC Energy plc. (AFC) Power Air Corp. (PWAC)
131 120 110 100 87 86 83 79 75 69 59 58 55 53 50 49 48 45 43 38 29 20 17 10 9 9
market cap, 106 $ 30 556 011 314 717 091 16 656 000 76 791 000 12 366 000 210 987 688 28 064 572 18 725 312 92 406 666 313 802 407 19 660 000 1 593 027 896 26 196 278 102 079 609 3 800 000 6 100 000 13 233 353 15 419 000 108 840 317 22 826 187 61 244 815 6 208 000 125 673 412 29 940 000 105 545 868 66 453 675
number of shares 4.27 0.38 6.61 1.30 7.08 0.41 2.96 4.24 0.81 0.22 2.99 0.04 2.09 0.51 13.08 8.00 3.59 2.92 0.39 1.64 0.47 3.20 0.13 0.32 0.09 0.13
share price, $
-2.42 -6.56
P/E ratio
-0.04 -0.02
net income, 106 $
0.00 0.00
net income per share, $
-12.95 -5.07 -25.42 -1.17 -12.64 -13.63 -5.79 -4.61 -40.38 -1.82 -4.53 -9.03 -11.61 -8.98 7.30 -11.95 23.95 -1.10 -0.86 -3.58 -4.68 -1.63 -2.19
P/D ratio
-0.33 -0.08 -0.26 -1.11 -0.56 -0.03 -0.51 -0.92 -0.02 -0.12 -0.66 -0.00 -0.18 -0.06 1.79 -0.67 0.15 -2.65 -0.45 -0.46 -0.10 -1.97 -0.06
dividends, 106 $
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dividends per share, $
a American Depositary Receipt (ADR), a negotiable certificate issued by a U.S. bank representing a specified number of shares (or one share) in a foreign stock that is traded on a U.S. exchange.
area
company name (ticker symbol)
TABLE 1. Continued
TABLE 2. Aggregated Financial Data for Oil and Alternative-Energy Companies (T and T2009 are Calculated from Eq 7 for ∆ = 0.634) (1999-2008) year
total market capitalization of oil companies P0oil, 106 $
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
662 881 748 000 750 723 684 351 701 544 1 099 666 1 521 193 1 920 055 2 250 523 2 145 416
total market capitalization of alternative-energy companies P0alt, 106 $ 4116 14 026 7399 4474 3707 5362 5456 8748 10 137 9362 average value median value standard deviation
related to base-load electricity production and cannot replace fuels and oil-related chemical products. For each of the oil and alternative-energy companies chosen, we collect fundamental financial data including the market capitalization (in millions of dollars), number of shares outstanding, company average annual share price, annual dividends paid per share, total annual dividends paid (in millions of dollars), P/D ratio (price-to-dividends ratio is equal to the ratio of the share price and the dividends paid per share), company’s annual net income per share, total annual net income (in millions of dollars), and P/E ratio (price-toearnings ratio is equal to the ratio of the share price and the net income per share). The number of shares outstanding, the net income per share and the dividends per share were collected from annual fillings that companies submit to the U.S. Securities and Exchange Commission in forms K-10, 20-F, 40-F, and 10KSB. The share price was averaged over daily (or, in some cases, weekly) historical prices obtained from the Google Finance and Yahoo Finance electronic resources. Note that while oil companies generally have considerable annual incomes and usually pay significant dividends, the alternative-energy companies typically lose money and pay no dividends. For example, the aggregate P/E and P/D ratios, averaged over years 1999-2008, are about 9.82 and 29.9 for oil companies and about -10.7 and 674 for alternative-energy companies. The oil companies belong to the “value stocks” category; that is, investors buy their shares because oil companies currently make profits and pay dividends. In contrast, alternative-energy companies belong to the “growth stocks” category, investors buy their stock only because they believe that these companies can potentially make money in the future (after discovery of technological innovations). Even though many oil companies also conduct research on alternative-energy technologies, we can neglect this because share prices of the oil companies are determined mostly by their current earnings. It is worth acknowledging that markets are volatile and investors can be either too optimistic or too pessimistic. In order to reduce uncertainty and increase the reliability of our analysis, we collect and use financial data aggregated over individual companies, to eliminate idiosyncratic volatility, and we average our results over a 10-year period 1999-2008, to smooth over time variations of investor sentiment within a business cycle, which is about 8-10 years (according to the International Monetary Fund). Note that only 2008 data for individual companies is given in Table 1. The aggregate data (summed over the companies) on market capitalization and dividends paid is provided in Table 2. Time until Appearance of a Viable Substitute. To specify the pricing models for the oil and alternative-energy company 9138
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total dividends paid by oil companies C0, 106 $
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18 019 24 409 28 985 27 802 33 637 45 464 52 841 58 277 62 573 65 210
γ
T
T2009
0.974 0.969 0.963 0.961 0.954 0.960 0.967 0.971 0.973 0.971 0.966 0.968 0.006
170 108 108 113 100 118 149 163 178 164 137 133 30
160 99 100 106 94 113 145 160 176 163 131 129 32
stock shares, we apply eq 1 to price aggregate stock shares. To do this, we make a few simplifying assumptions, similar to the Gordon growth model (24, 26). We use annual time periods, thus t ) 0 is the current year and t ) 1,2,3, ... are the future years in eq 1. We assume that the aggregate cash flows paid by the oil companies to investors are deterministic and grow with a constant risk-adjusted annual rate G > 1 until year T when a viable oil substitute appears. This is a good approximation because an exponential fit to the aggregate dividends paid by the oil companies has high coefficient of determination R2 ) 0.96. We further assume that starting at year T + 1, due to appearance of the oil substitute, the oil business will lose a fraction, ∆, of their market niche, while the alternative-energy companies will gain this market fraction. In reality, market diffusion takes time, and oil will be gradually substituted. In the next section we account for this effect and show that it normally does not significantly change the answer for T. Thus, starting at year T + 1, the oil and alternative-energy companies will respectively pay investors 1 - ∆ and ∆ fractions of the cash flows that the oil companies would pay if the substitution did not happen. In other words, the cash alt flows Coil t and Ct of oil and alternative-energy companies are t Coil t ) C0G ·
{
1, t ) 1, 2, ..., T 1 - ∆, t ) T + 1, T + 2, ... 0, t ) 1, 2, ..., T t Calt t ) C0G · ∆, t ) T + 1, T + 2, ...
{
(2)
Here we neglect cash flows generated by the alternativeenergy companies before year T + 1, which is a reasonable assumption because alternative-energy companies are categorized as growth stocks and have little current earnings. Cash flow C0 is equal to the aggregate amount paid by the oil companies to investors at the current year t ) 0. Substituting eqs 2 into eq 1, we find formulas for the aggregate market capitalizations P0oil and P0alt of the oil and alternativeenergy companies ∞
Poil 0 )
∑
T
Coil t E[St |I0] )
t)1
∑
C0
t)1
Gt + (Rt)t
∞
t
∑ (1 - ∆)C (RG ) 0
t)T+1
C0 ∞
Palt 0 )
∑C t)1
∞
alt t E[St |I0]
)
t
∑ ∆C (RG ) 0
t)T+1
t
t
)
t T+1
t
γ - ∆γ 1-γ
) C0
∆γT+1 1-γ
(3)
(4)
Here we introduce the annual gross interest rates Rt ) E[St|I0]-1/t > 1, for simplicity, assume a flat term structure of
interest rates, Rt ) R ) const >1, and define a nonstochastic discount factor γ ≡ G/R. The assumption Rt ) const is reasonable because the values of long-term interest rates are typically similar, and, when the ratio G/R < 1 is close to unity (which holds), the sums in eqs 1, 3 and 4 are dominated by long-term cash flows (which are paid at t ≈ (1 - G/R)-1 > > 1). Substituting γT+1 from eq 4, we can easily solve eq 3 for γ, alt oil alt γ ) (Poil 0 + P0 )/(P0 + P0 + C0)
(5)
Next, substituting this result into eq 4, we obtain T) ≈
alt alt ln[∆ · (Poil 0 + P0 )/P0 ]
ln[(Poil 0 + Poil + Palt 0 0 C0
oil alt Palt 0 + C0)/(P0 + P0 )] alt · ln[∆ · (1 + Poil 0 /P0 )]
(6)
where, to obtain the final expression, we apply the Taylor expansion for the logarithmic function (ln [1 + x] ≈ x when x < < 1), and we use condition C0 < < (P0oil + P0alt), which is easily satisfied in practice. That is, the cash flow is going to generally be much less than the total market capitalization. If we assume condition P0alt < < P0oil, which is also normally satisfied (again, that the market capitalization of alternative energy companies is much less than the capitalization of the oil companies), we can further simplify eq 6 to oil alt T ≈ (Poil 0 /C0) · ln(∆ · P0 /P0 )
(7)
Equation 7 is a straightforward formula for applying the market-expectations-based approach to estimating time T (in years) until the appearance of an oil substitute. Note also that C0/P0oil is the current annual aggregate dividend yield (dividend-price ratio) for the oil companies, and, therefore its value is not sensitive to omissions of oil companies from our data sample as long as the companies that we include into the sample are representative of the whole oil industry. In addition, factor ln (∆ · P0oil/P0alt) is not sensitive to the aggregate market capitalization values P0oil and P0alt and to the value of ∆ because normally ∆ · P0oil/P0alt . 1 and ln (x) is a slow varying function of x when x . 1. Thus, our estimation result for T is not sensitive to incompleteness of the data sample and to the value of ∆. Of course, if ∆ is very small, this is not particularly interesting from a sustainability point of view because only a small fraction of oil would be replaced. The last step in our method involves collecting sufficient market data on the oil and alternative-energy companies to find the values of P0oil, P0alt and C0, and then using these data, to estimate T from eq 7. In Table 2, the total market capitalization of oil companies, P0oil, (or alternative-energy companies, P0alt) for a given year is equal to the sum of market capitalizations of individual oil (or alternative-energy) companies for that year. Similarly, the total annual cash flow C0 paid to investors by all oil companies is the sum of annual dividends paid by individual oil companies. From Table 2 we see that conditions C0 < < (P0oil + P0alt) and P0alt , P0oil are well satisfied. Focusing on the replacement of oil used for motor fuels, we take ∆ ) 0.634, equal to the fraction of oil used for gasoline and diesel (according to the U.S. Energy Information Administration, 63.4% of oil is used for gasoline and diesel, 8.6% for jet fuel, about 19.7% for chemical industry feedstock, and 8.3% is mostly used as heating oil). Using eqs 5 and 7, we compute the values of γ and T, which have been reported in Table 2. Note that here, T is the estimated number of years beginning with the year given in the far left column. To normalize the results to the same year, T2009 has been benchmarked at 2009 (last column, Table 2). We estimate that the average time period between 2009 and the time when
an effective oil-replacement technology may appear, based on market expectations, to be approximately 131 years (computed from eq 6, T2009 ≈ 135 years, which is close, as we would expect). We postpone a discussion of these results until the last section. Effects of Market Diffusion. In the previous section we assumed that an oil substitute discovered in year T will replace the fraction of market share, ∆, of oil (oil products) starting the very next year T + 1. In reality, the replacement is not likely to instantaneously happen because the process of adopting of a new technology or a product by the market, that is, market diffusion, takes some time. In this section, we examine the effects of including market diffusion in the estimation of time T. Under conditions of gradual market diffusion, the cash alt flows Coil t and Ct of the oil and alternative-energy companies t t oil oil are Ct ) C0G and Calt t ) 0 until year T, and Ct ) C0G · (1 t - ∆ · mt) and Calt t ) C0G · ∆ · mt starting at year T + 1 (compare to eqs 2). Here ∆ · mt is the fraction of the oil (oil products) market niche that is occupied by the alternative companies after year T; this market fraction eventually goes to ∆ when the market diffusion process is complete. Note that the oil companies will occupy 1 - ∆ · mt fraction of the market at t > T. Equations 3 and 4 now become ∞
T
Poil 0 ) C0 ·
∑γ
t
+ C0 ·
t)1
∑ (1 - ∆ · m ) · γ
t
(8)
t
t)T+1 ∞
Palt 0 ) C0 ·
∑ ∆·m ·γ
t
(9)
t
t)T+1
Summing eqs 8 and 9, we obtain P0oil + P0alt ) C0 · ∑t∞) 1γt ) C0 · γ/(1 - γ). Here, we can see that the discount factor γ is given by eq 5 and is independent of ∆ and function mt (that is, in the present model discounting of future cash flows does not depend on how these cash flows are distributed between oil and alternative companies). From the Bass market diffusion model (27), the fraction of the market niche occupied by a new product/technology evolves according to differential equation dmt/dt )(1 - mt) · (p + q · mt), where p is the coefficient of innovation (coefficient of external influence), and q is the coefficient of imitation (coefficient of internal influence). The solution to the equation is (27) mt )
1 - e-(t-T)/τ , 1 + ξ · e-(t-T)/τ
tgT
(10)
where τ ≡ 1/(p + q) and ξ ≡ q/p. Here, 1/τ is the annual rate of market diffusion and when τ f 0, diffusion occurs instantaneously and the equations we’ve discussed thus far, reduce to the corresponding equations outlined in the previous section. Conversely, when τ is very large, market diffusion becomes very slow and it takes many years between the appearance of an oil substitute at time T and the time when this substitute is fully integrated into the market. As a result, the time of interest is not T, but the time T* when the oil alternative has penetrated the market by 50% and the alternative companies occupy ∆/2 fraction of the market niche. Setting mt ) 1/2 in eq 10, we obtain T* ) T + τ · ln(ξ + 2)
(11)
Note that T* weakly depends on parameter ξ because this dependence is logarithmic. We can solve eqs 8-10 analytically and find explicit formulas for T and T* in the special case when ξ ) 0. In this case, mt ) 1 - e-(t-T)/τ, and from eq 9 we obtain VOL. 44, NO. 23, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
9139
Palt 0 ) ∆· C0 ) ∆·
∞
∞
∑
γt - ∆ · eT/τ ·
t)T+1 T+1
∑ (γ · e
-1/τ t
)
t)T+1
γ e1/τ - 1 · 1/τ 1-γ e -γ
(12)
where γ is given by eq 5. Solving eq 12 for T, we obtain
(
T ) ln-1 1 +
[
ln
C0 alt Poil 0 + P0
alt ∆ · (Poil 0 + P0 )
Palt 0
(
)
· 1+
[
· alt C0 /(Poil 0 + P0 + C0)
e
1/τ
-1
)]
Discussion
-1
alt alt Poil ∆ · (Poil 1 0 + P0 0 + P0 ) ≈ · ln · oil alt C0 Palt 1 + τ · C /(P 0 0 0 + P0 )
]
(13)
where the final expression is obtained under condition C0 , (P0oil + P0alt), which is satisfied. Under condition P0alt , P0oil, which is also satisfied, eq 13 further simplifies to T≈
and 13; for τ ) 0, the values exactly coincide with those given by eq 6 (which are slightly higher than those given by eq 7 and reported in Table 2). Note that T *2009 weakly depends on τ and ξ, and it is approximately given by the simple model eqs 6 and 7, unless τ and ξ are large. From the numerical solution we find that the simple model gives an reasonable estimate of T *2009 when τ · ln (2 + ξ)jP0oil/C0 ≈ 30 years and underestimates T *2009 otherwise.
[
∆ · Poil Poil 1 0 0 · ln · C0 Palt 1 + τ · C0 /Poil 0 0
]
(14)
It is important to note that when τ < < (P0oil + P0alt)/C0 ≈ P0oil/C0 ≈ 30 years, eqs 13 and 14 reduce to eqs 6 and 7, respectively. In this case, (T* - T)/T )(τ/T) · ln (2) < < 1 (see eq 11 for ξ ) 0), which means T* ≈ T and, therefore, the effect of market diffusion of the oil substitute is negligible. When τ ≈(P0oil + oil Palt 0 )/C0 ≈ P0 /C0 ≈ 30 years, the market diffusion is somewhat important but not very important because again T* ≈ T. Finally, when τ > > (P0oil + P0alt)/C0 ≈ P0oil/C0 ≈ 30 years, the market diffusion becomes critical because T* ≈ T(τ ) 0) + τ · ln (2) ≈ τ · ln (2) > > T(τ ) 0), where T(τ ) 0) is given by eqs 6 and 7 (note that for very large τ time T becomes negative, which means that the oil substitute has already been discovered but takes a very long time to diffuse). From these results we find that the estimate T*JT(τ ) 0) holds for any value of τ. Therefore, eqs 6 and 7, which neglect market penetration, produce an optimistic estimate of time when oil is replaced by an alternative, and a very slow market diffusion with τ > > P0oil/C0 ≈ 30 years would make matters worse (in this case the relevant time would be T*, when the oil substitute has penetrated the market by 50%). In the case when ξ > 0, the analytical solution of eqs 8-10 cannot be expressed in terms of elementary mathematical functions. In this case we use MATLAB computing language to solve the equations numerically for different values of ∆, τ and ξ; the results for T *2009, which indicate the number of years between 2009 and 50% market penetration by an alternative, are given in Table 3. For ξ ) 0, the values of T *2009 given in Table 3 exactly coincide with those given by eqs 11
Our estimate T ≈ 131 years for the time until a replacement of gasoline and diesel (beginning at 2009) is about 2.6 times larger than the time until “the development of alternative ways of meeting the needs that are served by resource consumption” that was assumed by Graedel and Klee (3). Also our estimate is significantly longer than the 20 to 50 years previously suggested by several energy experts for the time horizon until a considerable fraction of oil is replaced (e.g., refs 10, 11, 22, 28-30). There are a number of possible reasons for the large range. For example, there are often subtle but persistent price signals embedded in long-term investment decisions and stock price fluctuations. In 2008 the International Energy Agency (IEA) reported that investment in renewable generation “fell proportionately more than that in other types of generating capacity” (31). In fact, the IEA predicted that for 2009, renewable investment could drop by as much as one-fifth. There are also examples in the past in which experts and scientists were overly optimistic about the diffusion of new technologies (8). In particular, a controlled thermonuclear fusion for energy production was initially expected within few decades from the first successful test of an H-bomb in 1952. However, despite more than 50 years of extensive research, no commercial fusion reactor is expected until the second half of the 21st century (32). Finally, differences in estimates of T can emerge as a result of variations in values assigned to the factors underpinning such estimates (e.g., the extent to which new technologies are expected to penetrate the market). In a recent article analyzing when renewable energy companies might occupy significant market share, it was pointed out that Exxon Mobil’s current market capitalization was 28 times that of First Solar and 26 times that of Vesta Wind Systems, both among the largest renewable companies. Even for major corporations like General Electric, with a large stake in wind power, stock prices are driven by other parts of the company. Without a price on carbon, most analysts suggest it could many decades before revenues and capitalization of alternative energy companies rival those producing traditional fossil fuels (33). Because of this, it is useful to also place our results in the context of current reserves and consumption patterns. Proven oil reserves have been estimated at approximately 1.332
TABLE 3. Number of Years Since 2009 until Time When the Oil Alternative Has Penetrated the Market by 50% (T *2009) τ)3
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
∆
9140
9
τ ) 10
τ ) 30
τ ) 100
τ)0
ξ)0
ξ ) 10
ξ ) 100
ξ)0
ξ ) 10
ξ ) 100
ξ)0
ξ ) 10
ξ ) 100
ξ)0
ξ ) 10
ξ ) 100
149 145 142 138 133 128 121 112 100 79
148 145 142 138 133 127 121 112 100 79
149 146 142 138 134 128 121 113 101 80
149 146 143 139 134 129 122 113 101 80
147 144 141 137 132 127 120 111 99 78
151 148 144 140 136 130 123 115 103 82
154 150 147 143 138 133 126 117 105 84
149 146 142 138 134 128 122 113 101 80
170 166 163 159 154 149 142 133 121 100
189 186 183 179 174 169 162 153 141 118
175 171 168 164 159 154 147 138 126 105
297 294 291 287 282 277 270 261 248 220
443 439 434 428 420 411 397 379 349 290
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 44, NO. 23, 2010
trillion barrels in 2008, and oil consumption was approximately 85.22 million barrels per day in year 2007 (21). Given a continued 1.3% annual growth of oil consumption (31), the world’s proven oil reserves will be depleted in approximately 2041. More optimistic estimates put the theoretical, nonproven worldwide supply at 2.0 trillion barrels, which for the same oil consumption growth rate of 1.3% gives us 2054 for oil depletion. The peak of oil production is estimated to occur approximately between 2010 and 2030 (9, 34). All these dates are considerably earlier than our estimate of the time until an alternative technology has entered the market, which is around 2140 (131 years from 2009). Obviously, our results suggest that there is a potential danger that crude oil will be depleted before it can be replaced by viable substitutes. We acknowledge that some of the difference between the estimates for the time until oil replacement and the time until oil depletion could be reduced in response to changes over time. That is, as fossil fuel resources diminish, we would expect both market and individual behavior to change. We would expect that new reserves of conventional and unconventional oil may become available for exploration due to geological exploration and advances in oil extraction techniques or that extraction from less feasible oil fields becomes more economically attractive. We would also expect that oil consumption would decrease due to energy-saving measures and/or due to responsiveness of demand to higher oil prices. All of these factors would change our predicted outcome. Some of these factors should be incorporated in future research. For example, our model could be improved by accounting for risks to cash flows (i.e., stochastic cash flows in eq 2) and by incorporating negative externalities of the oil companies, both of which could potentially impact the estimated value of T. We also think exploring the inclusion of privately held companies and nonprofit/government organizations (such as universities and government laboratories), which are not traded on the market but carry out an alternative-energy research, in the calculation of the alternative-energy companies market capitalization would be useful, although it is not entirely clear how the model specification would be derived. Finally, it is noteworthy that the estimate T ≈ 131 years, given by the pricing eq 1, is conditional on the current information set I0 (note that any forecast is always based on the information known in the present). If new information becomes available and this set changes in the future, then the estimate based on the updated information will also change when the new information is revealed (e.g., if policy interventions such as new major investments in the alternative-energy sector are made, then we would expect that the alternative-energy companies market capitalization would likely increase, with the net effect that the estimated value of T would decrease). This would suggest that alternative types of model specifications (e.g., extended using integrated socioeconomic and financial models) might be very useful. Our approach is resource-specific (based on market expectations about a replacement of a specific resource) and can be applied to nonrenewable resources other than crude oil if there are publically traded securities with cash flows that depend on replacement of these resources or other related innovations. As a result, the approach can be used to address many important sustainability problems. We hope that this study will provide a platform for integrating the appearance of new technologies into sustainability concepts.
Acknowledgments We thank Aaron Smith, Professor of Agricultural and Resource Economics, for fruitful discussions. We also thank the anonymous referees for useful comments and suggestions.
Literature Cited (1) Khan, M. I.; Chhetri, A. B.; Islam, M. R. Analyzing sustainability of community-based energy technologies. Energy Sources, Part B 2007, 2 (4), 403–419. (2) Senge, P. M.; Lichtenstein, B. B.; Kaeufer, K., Bradbury, H.; Carroll, J. S. Collaborating for systematic change. In MIT Sloan Management Review; MIT: Cambridge, MA, 2007; www. sloanreview.mit.edu/the-magazine/files/saleable-pdfs/ 48211.pdf. (3) Graedel, T.; Klee, R. Getting serious about sustainability. Environ. Sci. Technol. 2002, 36 (4), 523–529. (4) Holmberg, J.; Robert, K.-H. Backcasting from non-overlapping sustainability principles - a framework for strategic planning. Int. J. Sustainability Dev. World Ecol. 2000, 7, 291–308. (5) Marshal, J. D.; Toffel, M. W. Framing the elusive concept of sustainability: A sustainability hierarchy. Environ. Sci. Technol. 2005, 39 (3), 673–682. (6) Holmberg, J.; Lundqvist, U.; Robert, K.-H.; Wackernagel, M. The ecological footprint from asystems perspective of sustainability. Int. J. Sustainability Dev. World Ecol. 1999, 6, 17–33. (7) Hendrickson, C. T.; Lave, L. B.; Matthews, H. S. Environmental Life Cycle Assessment of Goods and Services: An Input-Output Approach; Resources for the Future Press: Washington, DC, 2005. (8) Schnaars, S. P.; Chia, S. L.; Maloes, C. M. Five modern lessons from a 55-year-old technological forecast. J. Prod. Innovations Manag. 1993, 10, 66–74. (9) de Castro, C.; Miguel, L. J.; Mediavilla, M. The role of non conventional oil in the attenuation of peak oil. Energy Policy 2009, 37, 1825–1833. (10) Halal, W. E.; Kull, M. D.; Leffmann, A. The George Washington university forecast of emerging technologies: a continuous assessment of the technology revolution. Technol. Forecast. Social Change 1998, 59, 89–110. (11) Kruger, P. Electric power equipment for large-scale production of hydrogen fuel for the world vehicle fleet. Int. J. Hydrogen Energy 2001, 26, 1137–1147. (12) Train, K. The potential market for non-gasoline-powered automobiles. Transport. Res. A 1980, 14A, 405–414. (13) Turton, H. ECLIPSE: An integrated energy-economy model for climate policy and scenario analysis. Energy 2008, 33, 1754– 1769. (14) Malkiel, B. G. Is the stock market efficient. Science 1989, 243 (4896), 1313–1318. (15) Pennock, D. M.; Lawrence, S.; Giles, C. L.; Nielsen, F. A. The real power of artificial markets. Science 2001, 291 (5506), 987–988. (16) Servan-Schreiber, E.; Wolfers, J.; Pennock, D. M.; Galebach, B. Prediction markets: Does money matter. Electron. Markets 2004, 14 (3), 243–251. (17) Cochrane, J. H. Asset Pricing, revised ed.; Princeton University Press: Princeton, NJ, 2005. (18) Rhode, P. W.; Strumpf, K. S. Historical presidential betting markets. J. Econ. Perspect. 2004, 18 (2), 127–141. (19) Spann, M.; Skiera, B. Sports forecasting: a comparison of the forecast accuracy of predictionmarkets, betting odds and tipsters. J. Forecast. 2009, 28 (1), 55–72. (20) Information Markets: A New Way of Making Decisions; Hahn, R. W., Tetlock, P. C., Eds.; AEI Press: Washington, D.C., 2006. (21) CIA World Factbook. Available at www.cia.gov/library/publications/the-world-factbook. (22) International Energy Outlook 2009; U.S. Energy Information Administration: Washington, D.C., 2009; www.eia.doe.gov/oiaf/ ieo/oilproduction.html. (23) Strategic Petroleum Reserve Annual Report for Calendar Year 2006; U.S. Department of Energy: Washington, D.C., 2006; fossil.energy.gov/programs/reserves/publications/Pubs-SPR/ spr_annual_rpt_06.pdf. (24) Campbell, J. Y.; Lo, A. W.; MacKinlay, A. C. The Econometrics of Financial Markets; Princeton University Press: Princeton, NJ, 1997. (25) Hansen, L. P.; Richard, S. F. The role of conditioning information in deducing testable restrictions implied by dynamic asset pricing models. Econometrics 1987, 55 (3), 587–614. (26) Gordon, M. J. The Investment, Financing, and Valuation of the Corporation; Irwin: Homewood, IL, 1962. (27) Bass, F. M. A new product growth for model consumer durables. Manage. Sci., Ser. A 1969, 15, 215–277. (28) Burns, J. R. Solar energy and the national energy dilemma: a model for policy evaluation. Technol. Forecast. Social Change 1982, 21, 213–228. (29) Ball, M. Martin Wietschel. The future of hydrogensOpportunities and challenges. Int. J. Hydrogen Energy 2009, 34 (2), 615–627. VOL. 44, NO. 23, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
9141
(30) Gu ¨ l, T.; Kypreos, S.; Turton, H.; Barreto, L. An energy-economic scenario analysis of alternative fuels for personal transport using the Global Multi-regional MARKAL model (GMM). Energy 2009, 34 (10), 1423–1437. (31) World Energy Outlook; International Energy Agency: Paris, France, 2007-2009; www.worldenergyoutlook.org. (32) Moyer, M. Fusion’s false dawn. Sci. Am. 2010, 302, 50–57. (33) Kho, J. When will renewable energy companies overtake traditional energy companies? 2010; www.renewableenergyworld.com/rea/
9142
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 44, NO. 23, 2010
news/article/2010/01/when-will-renewable-energy-companiesovertake-traditional-energy-companies. (34) Kaufmann, R. K.; Shiers, L. D. Alternatives to conventional crude oil: When, how quickly, and market driven. Ecol. Econ. 2008, 67, 405–411.
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