Damages in Energy and Natural Resources Arbitrations
The importance of energy and natural resources matters in arbitration
According to the 2016 ICSID caseload statistics report, 26 per cent of currently registered cases are related to disputes in the oil, gas and mining sectors.Similarly, a look at the ICC caseload data reveals that the energy sector made up the largest segment of arbitrations in 2014, comprising 18.6 per cent of the entire ICC caseload in that year. It is no coincidence that about one-quarter of total treaty and commercial arbitration cases are related to energy and natural resources. These sectors share at least two key economic attributes that make them susceptible to disputes: their output prices are subject to substantial volatility and their investments soon become sunk (i.e., cannot be easily moved to alternative uses). These features make energy and natural resources assets particularly vulnerable to opportunism, where the parties with an economic stake in their generation of profits (private or public) are likely to seek to change terms to their favour.
When market prices of natural resources change dramatically, parties that are involved in long-term contracts might have strong incentives to renegotiate – and when renegotiation is not viable or feasible, disputes arise. The increased volatility in commodity prices that started in 2003, for example, illustrates why so many crude oil, natural gas and gold mining arrangements agreed upon prior to this point in time are ending up in renegotiation, mediation, arbitration or litigation.
Price evolution on key natural resource prices (Brent Crude oil and gold)
|Average annual price|
|Year||Brent Crude oil|
(US$ per barrel)
(US$ per troy ounce)
The likelihood for price renegotiation and changes in the regulatory regime is high in energy and natural resource projects given the high capital investment necessary to develop reserves and unleash production. Once the exploration risks have been overcome and the associated investment costs have been sunk, governments may be tempted to act opportunistically, knowing that investors cannot move their sunk assets to alternative uses.Under these circumstances, sovereigns may attempt to increase their ‘government take’ on natural resources, either through increasing taxation, royalties, fees, rights and duties by altering the pre-existing profit-sharing or revenue-sharing agreements with the private sector, or by demanding that private companies relinquish shareholdings in their companies to the state or to a state-owned oil company. Similarly, private parties may renege to their obligations if deemed to have become too onerous. Disputes among shareholders will equally become more likely given that the volatility of prices may alter the initial allocation of risks between partners in ways that were unforeseen or unexpected.
Key valuation issues affecting damages methodologies in extractive resources matters
Estimating damages compensation in international arbitration disputes in extractive resources industries poses several challenges from the perspective of a damages valuation expert. A valuation expert must ask the following basic questions:
- What is the size and quality of reserves that are economically extractable?
- At what price can these reserves be sold and what is the exposure to price volatility?
- What is the nature of the contractual rights to exploit the resource (i.e., how long is the term of the contract, and what type of exposure to regulatory and country risk exists)?
- What is the underlying legal theory of the case and how does such theory determine the date of valuation?
The size and nature of economically extractable reserves
Assets in energy and natural resources markets derive a significant portion of their value from their potential to extract estimated resources at some future date. As a result, the amount of economically extractable reserves plays a significant role in value determination for any energy or natural resources asset.
Reserves estimates are largely a function of the current and future expected price of that resource in the market. As market prices rise, a greater portion of the resource in the ground becomes economically viable for extraction. The opposite is also true. In fact, the decline in crude oil prices that began in the second half of 2015 and continued into 2016 caused many large oil companies, such as BP, Shell, Total and Exxon Mobil to cut back billions in investment, affecting the size of their future reserves.Similarly, in the Canadian oil sands, where producers have some of the highest break-even costs globally, the price of crude oil plays a significant role in the decision to extract. In August 2015, for example, it was estimated that as a result of low crude oil prices, more than three-quarters of Canada’s 2.2 million barrels per day of oil sands production was no longer economically recoverable.
Economically extractable reserves can be categorised into proven developed (PD) reserves and proved undeveloped (PUD) reserves, a distinction that can provide useful insight when calculating damages in energy and natural resources disputes. PD reserves are those that can be produced with existing wells, or from additional reservoirs where minimal additional investment is required. PUD reserves, on the other hand, require additional capital investment, such as the drilling of new wells, to extract the resource from the ground.
In oil and gas industries, proven reserves are referred to as 1P, denoting a ‘reasonable certainty’, or high degree of confidence, of being recovered.Valuation experts, however, may also consider the inclusion of unproven reserves weighted (or ‘risked’) by their probability of extraction, since unproven reserves have a lower level of technical certainty of recovery. Unproven reserves are classified as probable (together with proven reserves, referred to as 2P) and possible (together with proven and probable reserves, referred to as 3P).
In mining industries, reserves are simply the part of an identified resource that could be economically extracted or produced at the time of determination.Additionally, in mining, particular attention is paid to the cut-off grade, which is used as the level of mineral in an ore, below which it may not be economically feasible to mine – an important distinction when measuring reserves for use in the valuation of assets.
Valuation experts would typically rely on technical assessments from reserve experts or outfits that certify the size of extractable reserves at any given point in time. Given that output prices are volatile, it is important that the reserve certification be contemporaneous to the date of valuation, as otherwise the size of economically extractable reserves might be overestimated or underestimated.
Impact of price forecasts and volatility on value
Forecasting output prices involves making decisions about future values that might be too volatile and difficult to predict. Valuation experts can seek to mitigate these features by using price forecasts based on either market-based data or by resorting to specialised outfits that model supply and demand so as to obtain expected model equilibrium prices.
Market-based data on price forecasts can be derived by looking at futures contractsand spot prices. Futures contracts are useful in that they provide forecasters with market evidence of contractual agreements between the buyers and sellers of a particular commodity, and therefore might serve as a benchmark for future price levels. Spot prices, on the other hand, provide forecasters with a current view of the market, but could have the shortcoming of not anticipating changes in supply and demand conditions that are expected in the marketplace. Given the wide array of price forecasts that are present in the market for most commodities, valuation experts can derive an opinion of expected output prices based on both existing market information and the myriad forecasts established by specialised outfits.
By using all available information, possibly discarding projections that are considered extreme or outliers to the sample, and adopting a path that is consistent with the majority of forecasts and information from futures contracts, valuation experts can make informed and comprehensive decisions about price expectations in the future.
Contractual terms and adjustment for proper regulatory and country risk exposure
While typically challenging to quantify, contractual, regulatory and country-specific risks play an equally important role in calculating damages in energy and natural resources disputes. Contractual terms and regulatory conditions can significantly impact the risk inherent in the valuation of any asset, and therefore adjustments are required to account for the risk exposure of the specific asset being valued.
Contract length, for one, can have a direct impact on the estimate of reserves at a particular site. Shorter production contract terms imply a lower economically extractable reserves estimate, given the time constraint inherent in the contract itself. For that same reason, contract renewal provisions play an important role in the valuation of natural resources assets, particularly in the calculation of their terminal value.
Similarly, the location of an asset matters, as the associated risks of operating the asset from a particular jurisdiction depend on whether the asset is located in a country with a predictable economy and strong institutions, such as the United States and Germany. The term ‘exposure to country risk’, therefore, is used to capture incremental risks such as:
- the additional volatility of domestic demand, which may be more prone to recessions and booms as compared to a more developed economy;
- the infrastructure of a developing economy, which may expose the asset to supply risks as services, logistics and suppliers may be unreliable;
- governmental actions and macroeconomic policy affecting businesses, which may be unstable, thereby affecting volatility and thus increasing the overall risks of doing business; and
- exposure to changes in taxation, royalties and other forms of ‘government take’.
A distinction must be made between general country risk and the specific exposure that any particular asset might have to this risk. General country risk measures the incremental risk that an average investor faces from investing in a particular country. The specific exposure of country risk, by contrast, is the incremental risk that an investor in the target asset faces taking into account the particular protections and safeguards that such asset might have, which may differ from that of an average investor with assets in any other industry.
Because energy and natural resources assets involve sunk investments and are particularly prone to government opportunism, they typically exhibit characteristics that shield them, at least in part, from the full extent of the general country risk associated with the assets’ location. Most notably, significant portions of revenue from these assets are isolated from country-specific demand risk, given that their products (i.e., commodities) are traded worldwide.In addition, from a regulatory perspective, many contracts include explicit protections against egregious tax measures and the size of the ‘government take’, or simply provide tax stabilisation clauses.
As a result, it is important that valuation experts take into account the specific exposure of the project to country risk, and not simply apply a standardised measure of country risk to the asset, without any adjustment. In fact, in the Gold Reserve v. Venezuela award, the tribunal rejected the discount rate proposed by one of the parties’ experts, noting that it ‘was based on both full and “generic” country risk for an investment in Venezuela’, and therefore did not adjust for the risk that was specific to the assets in question.
The fit to the legal theory and the choice of date of valuation
In addition to the intrinsic value of the asset in question, the valuation expert must take into account the underlying legal theory, which in turn can influence the choice of date of valuation. In international arbitration, the standard concerning remedies for damages arising from an illegal act is the judgment of the Permanent Court of International Justice in the Chorzów case.Under this judgment, restitution in kind is the primary remedy; payment of compensation is to take its place if restitution is not possible. There is some consensus that the Chorzów judgment requires tribunals to award the highest of (1) the value on the date of expropriation (plus interest) or (2) the current value as at the date of the award (plus historical lost profits). Subsequent tribunals have applied this ‘highest of’ standard in cases where the legal theory fits with a principle of restitution (typically related to a finding of an expropriation being unlawful).
The selection of valuation dates and to what extent the damage expert should use the benefits of hindsight information in performing a valuation is of considerable importance, given the volatility of commodity prices.Whereas in cases of lawful expropriation it might be important to value the asset using expectations as of the time of the taking (also known as an ex ante valuation exercise), it is equally important to use hindsight information in cases in which the date of valuation is set as the date of award (also known as an ex post valuation exercise).
In ex ante valuations particularly, the selection of a pre-judgment interest rate plays a central role in the amount of compensation awarded as at a current date. The wrong interest rate could result in a monetary award that does not fully restore the position of the damaged party in the absence of the measures.While the use of either ex post or ex ante information is valid in determining damages in energy and natural resource arbitrations, each is likely to yield a different damages result, mostly due to price volatility over the relevant period.
Unfortunately, there is no established academic consensus as to the selection of the pre-judgment interest rate and this is true not only for international arbitration but also for US litigation cases. This lack of consensus is predictably reflected in tribunals’ decisions, which have granted pre-judgment interest rates using a variety of different criteria, or even granted no interest at all. Notable criteria for a pre-judgment interest rate include interest based on the borrowing rate of the respondent, as proposed by Professors Patell, Weil and Wolfson,use of a risk-free interest rate, as proposed by Professor Fisher, or interest based on the opportunity cost of the lost investment, as advocated by John and Robin Keir.
Methodologies to assess damages in energy and natural resources cases
There are several approaches to value assets in energy and natural resources disputes. In this chapter, I briefly review the most common valuation methodologies used by practitioners.
Income-based approaches, such as the discounted cash flow (DCF) method, are quite suitable to value energy and natural resources assets because they provide a direct way to measure expected revenues (and their corresponding cash flows) into the future. In fact, the DCF method is the most common methodology used in valuation analyses involving assets in the energy and natural resources industries (as well as most other industries).First, it is widely supported by professional literature, and its workings are well understood. Indeed, most investors rely on a DCF analysis to determine whether or not to undertake a particular project. Second, the DCF approach is a widely accepted method to estimate damages and fair market valuations in international disputes; in many energy and mining cases panels have adopted the DCF method without hesitation.
In practice, the DCF method calculates future cash flows for the particular asset to be valued, and discounts them back to the agreed-upon valuation date. The method therefore requires several key inputs, such as revenues, extraction, investment, retirement and cleaning costs, discount rate, and terminal value, in addition to any other project-specific assumptions.
While the DCF method is widely used, some tribunals have been reluctant to adopt it unless the business in question was a going concern at the date of valuation.Imposing this limitation on natural resources assets, however, is counterintuitive from an economic perspective, since once the exploration stage is surpassed and the reserves are certified, there should be little doubt that reserves can be monetised into future cash flows. Operational risks would still exist, but such risks can be modelled through a discounted cash flow analysis, even if the asset is not yet operational.
Relative multiples approaches
A relative multiple is simply an expression of the market value of an asset relative to a key statistic that is assumed to relate to that value. Expressing market value in terms of a specific key statistic such as EBITDA, revenues, asset value or size of reserves standardises the value of the asset and thus allows for comparison across assets of varying absolute value. Generally, multiples can be derived from information about comparable assets or companies that trade in public markets (trading multiples) or from information about recent transactions of comparable assets or companies (transaction multiples).
In the energy and natural resources industries, specifically, multiples are typically based on cash measures, such as EBITDA or net profits, or on a market-specific metric, such as the amount of 1P reserves in the oil and gas industry or to proven and probable equivalent reserves in mining.There are, however, a number of criticisms against the use of multiples as a tool for valuing damages in energy and natural resources disputes. For one, multiples are relatively simplistic and static – that is, they distil a great deal of information into a single number that represents a snapshot of the value of an asset at a particular point in time, and thus do not capture the dynamic and ever-changing nature of energy and natural resources markets. Similarly, multiples are based on historic data or near-term forecasts, which therefore may fail to capture differences in projected growth, expected life term of the reservoir, and performance over the longer term. Additionally, damages valuations based on relative multiples approaches must be adjusted to account for, among other considerations, large or small sample size issues, and control premiums.
Stock market capitalisation
Generically, the market capitalisation approach refers to techniques that use either the stock market price of the underlying asset (or that of its parent company) or stock market indices of benchmark companies, as a tool to evaluate and assess damages.
Computing damages in investment arbitration under the market capitalisation approach is recommended when the equity shares of the target asset under analysis are publicly traded. In addition, when the shares of the parent company of the target asset are traded and the target asset represents a significant part of its portfolio, it is also feasible to identify changes in value of the parent company attributable to changes in the value of the underlying target asset.
Under this approach, one can distinguish at least two techniques that can be used to construct a counterfactual scenario that excludes the effects of the actions by the wrongdoer. These are event studies and market trends of benchmark companies.
An event study is a statistical tool that analyses the response of a stock price to certain market announcements (i.e., events related to expropriation threats, or unfair treatment of investments), controlling for other factors producing stock price movements, such as general market and industry trends, or other company-specific announcements.The assumption behind an event study is that the effect of an event is reflected immediately in the price of the company shares, making it possible to statistically isolate and quantify the impact of the wrongful actions.
The market capitalisation approach that looks at the trends of stock prices from benchmark companies consists of building a but-for scenario in which the stock price of the target company that existed (or would have existed) in the absence of the wrongful actions is adjusted until the date of valuation following the evolution of an index (or a basket of indices) of publicly traded benchmark companies. Using an index of benchmark companies to mimic the but-for scenario of the target asset allows the valuation expert to incorporate two of the major factors affecting stock prices: (1) the movements reflecting economy-wide information; and (2) movements reflecting industry-related information. This method is particularly well-suited for investment disputes involving full expropriation of traded assets, provided that the expert can properly establish the latest clean date before any threats or actions of expropriation, and a set of benchmark companies that are also traded and whose evolution and trends prior to the measures are comparable to the target company.
Various other valuation methodologies exist. Asset-based approaches, utilising either replacement values or book values of assets, and liquidation value can be advocated but are not likely to be very useful in determining damages in energy and natural resources cases because they would typically depart from market values. Such methods provide an historical account of past investments and thus will not represent the value that shareholders can extract from future cash flows, thus failing to account for the true value (and risks) related to the activity.
Liquidation value, in particular, assumes the assets are no longer a going concern and thus assigns value based on prices at which physical assets, such as real estate, fixtures, equipment and inventory could be sold, typically at a discount to market value. Book values, in turn, will incorporate accounting rules and principles that typically fail to track the market value of the assets. In addition, in emerging countries, accounting legislation might not even require companies to attempt to price their assets in the books according to market values. Thus, discrepancies between market values and book values are likely to be common and relevant, in particular given the volatility of commodity prices, which directly affect the market value of natural resource companies.
Cost-based approaches are not likely to be useful either, as they value assets based on the cost of the land and construction, less any depreciation, and would most likely fail to represent the value that shareholders could extract from future cash flows. The only instance in which cost-based valuation approaches may be appropriate would be for valuing energy or natural resources assets that are in an exploration stage, at which point in time the value of the asset may be restricted to its cost given that there would not yet be any reasonable expectations of future cash flows.
 This chapter was written by Manuel A Abdala, with contributions from economist Rob Mulcahy, who provided valuable support and insights. Manuel A Abdala is executive vice president at Compass Lexecon in Washington, DC. The opinions expressed here are exclusively his own.
 The ICSID Caseload Statistics (Issue 2016-1), available at: https://icsid.worldbank.org/apps/ICSIDWEB/resources/Documents/ICSID%20Web%20Stats%202016-1%20(English)%20final.pdf.
 International Chamber of Commerce (ICC), Arbitration of Oil and Gas Disputes, www.iccwbo.org/Training-and-Events/All-events/Events/2015/Arbitration-of-oil-and-gas-disputes/.
 See, e.g., Murphy Exploration & Production Company International v. Republic of Ecuador, Partial Final Award, UNCITRAL, PCA Case No. AA434 (6 May 2016), available at: www.italaw.com/cases/1198#sthash.7KDeLgdo.dpuf (regarding imposition of windfall levy on oil profits); Yukos Universal Limited (Isle of Man) v. The Russian Federation, Judgment of Hague District Court, UNCITRAL, PCA Case No. AA 227 (20 April 2016), available at: www.italaw.com/cases/1175#sthash.HuBDPx1p.dpuf (regarding nationalisation of oil and gas assets); Crystallex International Corporation v. Bolivarian Republic of Venezuela, Award, ICSID Case No. ARB(AF)/11/2 (4 April 2016), available at: www.italaw.com/cases/1530#sthash.Vl53ATnE.dpuf (regarding unlawful expropriation of untapped gold deposits); Gold Reserve Inc. v. Bolivarian Republic of Venezuela, Award, ICSID Case No. ARB(AF)/09/1 (22 September 2014), available at: www.italaw.com/cases/2727#sthash.fkDkRO8b.dpuf (regarding unlawful expropriation of untapped gold deposits).
 US Energy Information Administration, Europe Brent Spot Price FOB, available at: www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s=rbrte&f=D (last visited 23 August 2016); Quandl, Gold Price: London Fixing, available at www.quandl.com/data/LBMA/GOLD-Gold-Price-London-Fixing (last visited 23 August 2016).
 See Roderick Duncan, ‘Price or Politics? An Investigation of the Causes of Expropriation’, Australian Journal of Agricultural and Resource Economics, Volume 50, Issue 1, pp. 85–101 (March 2006) (explaining expropriation as opportunistic behaviour by host governments when profits of investments are high); Brian Levy & Pablo T. Spiller, Regulations, Institutions, and Commitment: Comparative Studies of Telecommunications 202, 203 (ed. 1996) (linking sunk costs and opportunism in the telecommunications industry, making that industry, like the energy industry, vulnerable to expropriation). In sectors like mining, oil and gas wells, and pipeline networks, assets are said to be ‘sunk’ since they are not moveable or easily transferable to other locations or alternative uses.
 See Ibid. 5; Venezuela Holdings B.V. and others v. Bolivarian Republic of Venezuela, Award, ICSID Case No. ARB/07/27 (9 October 2014), available at www.italaw.com/cases/713 (regarding oil and gas assets expropriated in 2007); Shell Philippines Exploration B.V. v. Republic of the Philippines, ICSID Case No. ARB/16/22 (filed 20 July 2016), available at www.iareporter.com/articles/shell-files-investment-treaty-claim-against-the-philippines/ (regarding the imposition of additional taxes by the State); ConocoPhillips Petrozuata BV, ConocoPhillips Hamaca BV and ConocoPhillips Gulf of Paria BV v. Bolivarian Republic of Venezuela, ICSID Case No. ARB/07/30 (pending), available at: www.italaw.com/cases/321#sthash.1QaYeZNl.dpuf (regarding the expropriation of heavy crude oil and upgrading assets).
 Matthew West, Just How Low Can Oil Prices Go and Who is Hardest Hit?, BBC News, 18 January 2016, www.bbc.com/news/business-35245133. Even US shale oil producers, who some thought could tolerate lower prices, were not expected to continue production below certain price thresholds, which means that their level of reserves had actually dropped due to low output prices.
 Nia Williams, At $22, Three Quarters of Oilsands Production is Underwater and Losing Up to $3 on Every Barrel, Financial Post, 17 December 2015, http://business.financialpost.com/news/energy/at-22-three-quarters-of-oilsands-producers-are-underwater-and-losing-3-on-every-barrel?__lsa=1c8a-d893.
 Proven reserves are reserves that have 90 per cent certainty of commercial extraction. See SPEE Petroleum Resources Management System Guide for Non-Technical Users, Society of Petroleum Engineers International, 2007, pp.10–11, available at: www.spe.org/industry/docs/Petroleum_Resources_Management_System_2007.pdf.
 Probable reserves have a 50 per cent certainty of commercial extraction. Possible reserves, in turn, have a 10 per cent certainty of commercial extraction. See Ibid. p. 11.
 In the mining industry, reserves can be further classified into ‘marginal’ reserves, ‘sub economic resources’, and ‘undiscovered resources’. Each of these definitions has a decreasing level of certainty of economic extraction. See definitions for mineral resources and reserves at US Department of the Interior, US Geological Survey, Mineral Commodity Summaries 2001 (Washington, DC: GPO, 2001), Appendix C, available at: http://wps.prenhall.com/wps/media/objects/2513/2574258/pdfs/E10.4.pdf.
 On technical grounds, the term ‘cut-off grade’ refers to a unit of measure that represents a fixed reference point for the differentiation of two or more types of minerals. See Estimation of Mineral Resources and Mineral Reserves Best Practice Guidelines, CIM Council, 23 November 2003. See also Nyrstar 2015 Mineral Resource and Mineral Reserve Statement, Nyrstar, 27 April 2016.
 A futures contract is an agreement to buy or sell a particular commodity at a predetermined price at a specified time in the future. Futures prices typically take into account the current spot price, interest rates, time to maturity, storage costs, convenience yield, and any other relevant variables, which make them potential candidates for use in price forecasts.
 See, for example, Aswath Damodaran, ‘Measuring Company Exposure to Country Risk: Theory and Practice’, Stern School of Business, 2003.
 Of course, not all projects have access to exports and not all countries are free from trade barriers that may distort the domestic price of the commodity from that prevailing in the international market (net of transport and other fees).
 See the Gold Reserve Award, paras. 840 and 841.
 Factory at Chorzów, Indemnity, Merits, 13 September 1928, P.C.I.J., Series ANo. 17, P.47.
 Christopher Schreuer, Alternative Remedies in Investment Arbitration, The Journal of Damages in International Arbitration, Volume 3 Number 1, 2016.
 See S. Ripinsky and K. Williams, Damages in International Investment Law, BIICL (2008) at 256 and M. Abdala, P. Spiller and S. Zuccon, Chorzów’s Compensation Standard as Applied in ADC v. Hungary, Transnational Dispute Management, Volume 4, Issue No. 3, June 2007. See, for instance, Marion Unglaube v. Republic of Costa Rica, Award, ICSID Case No. ARB/08/1 (16 May 2012), available at: www.italaw.com/cases/1134#sthash.U50Z5yox.dpuf (on the application of the criteria of the ‘highest’ of valuation dates).
 I have previously discussed this topic extensively, and thus will not provide an in-depth explanation in this chapter. See Manuel A. Abdala, ‘Key Damage Compensation Issues in Oil and Gas Arbitration Cases’, American University International Law Review, Volume 24, Issue 3 (2009).
 Using hindsight information combined with a date of award valuation captures any elevated value due to improved business conditions which claimants were deprived of due to the measures by the party inflicting damages. In addition, it provides incentives for parties not to act opportunistically when business conditions are expected to improve, thus acting as a deterrent. Finally, its use provides accurate and adequate damage estimates, given that with the benefit of hindsight the damage expert can compute actual damages as time passes. The latter is critical information that panels usually welcome and are not likely to ignore.
 For further discussion on the importance of determining a reasonable pre-judgement interest rate, see Clemmie Spalton, ‘An Unexpected Interest in Interest’, Global Arbitration Review, 12 May 2015, available at: http://globalarbitrationreview.com/news/article/33795/an-unexpected-interest-interest/; see also, Dan Harris, Richard Caldwell & M. Alexis Maniatis, A Subject of Interest: Pre-Award Interest Rates in International Arbitration, The Brattle Group, 12 May 2015, available at www.brattle.com/system/publications/pdfs/000/005/173/original/A_Subject_of_Interest_-_Pre-award_Interest_Rates_in_International_Arbitration.pdf?1433164385.
 James M. Patell, Roman L. Weil & Mark A. Wolfson, ‘Accumulating Damages in Litigation: The Roles of Uncertainty and Interest Rates’, 11 J. Legal Stud. 341, 362 (1982) (instructing that the rate should reflect both the extent to which the plaintiff was forced to alter his consumption and investment plan and the possibility that the plaintiff bore risks which differed from those inherent in his undamaged position).
 See Franklin M. Fisher & R. Craig Romaine, Janis Joplin’s Yearbook and the Theory of Damages, 5 J. Acct. Auditing & Fin. 145, 146-48 (1990) (noting that compensating the plaintiff at the rate it reasonably expected to earn on the destroyed asset is flawed because the plaintiff would be entitled to interest compensating it for ‘the time value of money . . . [but not] also entitled to compensation for the risks it did not bear.’).
 See John C. Keir & Robin C. Keir, ‘Opportunity Cost: A Measure of Prejudgment Interest’, 39 Bus. Law. 129, 147 (1983) (noting that the Company’s lost return reflects the opportunity cost of the deprived cash flows or monies to the damaged party).
 William C. Lieblich, ‘Determinations by International Tribunals of the Economic Value of Expropriated Enterprises’, 7 J. Int’l Arb. 37, 38 (1990) (explaining that the DCF method is the most common valuation method because it is the only method that can measure the amount of cash estimated to be earned by an entity on a day-to-day basis).
 See Carlos Trejo, Real Options: Understanding the Basic Concepts 1 (September 2000) (unpublished assistantship project, Mississippi State University), available at: www.rstc.msstate.edu/publications/99-01/rstcofr01-042a.pdf (contrasting DCF with other methodologies, illustrating its predominance in the valuation field).
 See Jarrod Hepburn, Quiborax v. Bolivia: Tribunal Majority Uses ‘Ex Post’ Data to Assess Discounted Cash-Flow Damages for Unlawful Expropriation – and Applies Country-Risk Premium Discount, IA Reporter, 22 September 2015; Clovis Trevino, ‘In-Depth: Unpacking the Damages Calculations That Led to $450,000 Arbitral Payday for Owens-Illinois’, IA Reporter, 19 March 2015; Luke Eric Peterson, ‘Another Expropriation Ruling Against Venezuela, as ICSID Arbitrators Award Tidewater $60 Million (Inclusive of Pre-Award Interest)’, IA Reporter, 15 March 2015. Examples of cases in which the DCF approach was adopted by panels in international disputes include: Gold Reserve Inc. v. Bolivarian Republic of Venezuela, Award, ICSID Case No. ARB(AF)/09/1 (22 September 2014), available at: www.italaw.com/cases/2727#sthash.fkDkRO8b.dpuf; Occidental Petroleum Corporation and Occidental Exploration and Production Company v. The Republic of Ecuador, Award, ICSID Case No. ARB/06/11 (5 October 2012), available at: www.italaw.com/cases/documents/768#sthash.ZwfDxsoi.dpuf.
 See Rusoro Mining Ltd. v. Bolivarian Republic of Venezuela, Award, para. 785, ICSID Case No. ARB(AF)/12/5 (22 August 2016), available at: www.italaw.com/cases/2048#sthash.X1DyyKnG.dpuf (in which the tribunal recognised ‘very special characteristics surrounding Rusoro which make the use of DCF approach inappropriate’, including, among other factors, the fact that ‘Rusoro lacks a proven record of financial performance’).
 In addition, and unique to the mining industry in particular, is the net asset value (NAV) multiple, which compares the price of a mineral property to the net present value of the mining company’s assets (gold, silver, etc.), which are, in turn, evaluated on the basis of its reserves and resources valued at a uniform real discount rate.
 In valuing assets based on comparables, the size of the sample with which the target asset or assets is being compared can have an impact on value. A larger sample size is more representative of the population, which limits the influence of outliers or extreme observations, and broadens the range of possible data, which forms a better picture for analysis; however, it is often hard to find an observable comparable set that fits the counterfactual scenario (i.e., that reflects the reality of the target asset in the absence of the damaging actions). Small-size samples, in turn, may introduce bias if the comparable assets are not too close to the target asset. In addition, a control premium may need to be added when valuing assets based on relative multiples derived from stock market data, as stock market capitalisation would typically reflect the value to (unprotected) minority shareholders. Relevant examples of recent arbitrations in which relative multiples valuation methodologies were adopted include: Crystallex International Corporation v. Bolivarian Republic of Venezuela, Award, ICSID Case No. ARB(AF)/11/2 (4 April 2016), available at: www.italaw.com/cases/1530#sthash.iACLVKfv.dpuf (in which the tribunal accepted both a market multiples approach and a stock market valuation approach to assessing damages); Antoine Abou Lahoud and Leila Bounafeh-Abou Lahoud v. Democratic Republic of the Congo, Award, ICSID Case No. ARB/10/4 (7 February 2014), available at: www.italaw.com/cases/2391#sthash.YaHsIZp6.dpuf (in which the tribunal considered the market comparables approach as one of two damages methodologies that factored into the computation of damages).
 See Rosa M. Abrantes-Metz, Santiago Dellepiane, ‘Using an Event Study Methodology to Compute Damages in International Arbitration Cases’ (2011) 28 Journal of International Arbitration, Issue 4, pp. 327–342.
 Although there are very few precedents on the use of the market capitalisation approach based on trends of benchmark companies in investment arbitration, the technique has been widely applied in securities litigation. Cornell and Morgan (1990), for example, analyse the application, similarities and differences of the two techniques under the market capitalisation approach, as applied to securities litigation: the market trends of benchmark companies (referred to as the ‘comparable index approach’) and the event study. See Cornell, Bradford and Morgan, R. Gregory. 1990. ‘Using Finance Theory to Measure Damages in Fraud on the Market Cases’, UCLA Law Review 37, No. 5: 883-924. In investment arbitration, the market capitalisation technique has been used in a few instances in both mining and crude oil cases. In the Quasar matter, the claimant successfully argued that its shareholding in Yukos had been adversely affected by the actions of the state, as evidenced by the significant decline in the stock price of Yukos, which commenced in April 2004 just before the state’s first expropriation actions. Damages were derived by constructing a but-for scenario based on an index of four Russian Yukos competitors whose stock was traded, and whose past evolution was comparable to that of the actual stock price of Yukos prior to the measures. See Renta 4 S.V.S.A, Ahorro Corporación Emergentes F.I., Ahorro Corporación Eurofondo F.I., Rovime Inversiones SICAV S.A., Quasar de Valors SICAV S.A., Orgor de Valores SICAV S.A., GBI 9000 SICAV S.A. v. The Russian Federation, SCC No. 24/2007, available at: www.italaw.com/cases/915#sthash.VkFo5hKM.6KIxzC8y.dpuf. In the mining sector, the tribunal on the Crystallex v. Venezuela matter likewise accepted the use of a market capitalisation approach to valuation, noting that it accurately reflected the market’s actual assessment of the present value of Crystallex’s future profits and was suitable given that Crystallex was effectively a one-asset company holding the target asset of Las Cristinas’ gold mine in Venezuela. See Crystallex International Corporation v. Bolivarian Republic of Venezuela, ICSID Case No. ARB(AF)/11/2, available at: www.italaw.com/cases/1530#sthash.iACLVKfv.dpuf.
 The roots of event studies can be traced to the 1969 seminal work of Fama, Fisher, Jensen and Roll. See Fama, Eugene, Fisher, Lawrence, Jensen, Michael C., and Roll, Richard. 1969. ‘The Adjustment of Stock Prices to New Information’, International Economic Review 10: 1–21. See also MacKinlay, Craig. 1997. ‘Event Studies in Economics and Finance’, Journal of Economic Literature 35: 13-30, and Binder, John J. 1998. ‘The Event Study Methodology Since 1969’, Review of Quantitative Finance and Accounting 11: 111-137.
 See Patell, James M. and Wolfson, Mark A. 1984. ‘The Intraday Speed of Adjustment of Stock Prices to Earnings and Dividend Announcements’, Journal of Financial Economics 13: 223–52.
 In cases other than full expropriation, the affected asset might still be traded after the wrongful conduct of the state. In such cases, distinguishing the relevant time period of the wrongful actions and the movements in stock price related to firm-specific information directly attributable to the state’s conduct makes the exercise more complex, possibly requiring the use of the event study technique. In addition, other adjustments might be needed, such as accounting for differences between a marketable minority stake (as reflected by traded stock prices) and the asset under analysis, and taking into account lost dividends during the relevant period under analysis, among others.