I attended the Risk Management and Climate Change think Tank meeting at the Australian Centre for Financial Studies in Melbourne yesterday. As background I prepared the following notes that are intended to provide a non-technical guide to some technical economics.
Abstract: The real options and insurance literatures alter the way planners think about evaluating infrastructure investments. These literatures target aspects of infrastructure investment decision-making –irreversibility, uncertainty and risk aversion – that are typically very practical considerations. Using such approaches however can involve difficult issues of modeling and computation. These notes draw out the major qualitative insights from these theories and illustrate major ideas using an analysis of an urban water supply investment option to build a desalination plant. The main argument is that while uncertainty and irreversibility coupled with learning provide a case for caution and delay compared to conventional cost benefit analysis that policy-maker risk-aversion can motivate the reverse of these incentives and create a case for decisive early exercise of an investment option.
Suppose government is thinking about undertaking an infrastructure project – for specificity think about a desalination plant. This possible project will have a certain scale and will be constructed either now or at some time in the future or perhaps it will never be constructed. For the moment suppress the scale issue and concentrate on the question of timing. To simplify suppose there are only three mutually exclusive and exhaustive options:
- Build a plant now.
- Build a plant in 20 years time (‘the future’).
- Never build the plant.
The investment is irreversible in the sense that, once the capital investment is undertaken, the capital employed cannot be redirected to an alternative use. This is a plausible assumption. Indeed, few constructed infrastructure projects involve significant reversibility. Roads, highways, bridges, dams, airports, train lines and so on have very limited alternative usage possibilities beyond the purpose for which they were originally designed.
The investment is risky because both costs associated with its construction and operation as well as future benefits from it will be partly unknown at the time of construction. Water demands are uncertain – they have shifted downwards in recent decades – and dam storages will be uncertain because of uncertain rainfall and water demands.
For a desalination plant it is, in principle, straightforward to identify these costs. The plant construction costs will be subject to climatic risks and risks associated with industrial relations and labour costs as they were for the Wonthagii plant in Victoria. Moreover, while desalination technology has become cheaper in the recent past there is some evidence now that increasing raw material prices might reverse this trend. These plants use considerable amounts of energy as a variable input so that secondary energy price risks and the possible impact of carbon pricing will help to drive operational costs. The benefits from the project will depend on the value of the water sold which will depend on the evolution of the demand for water, the availability of water from other sources such as dams and aquifers and the political feasibility of purchasing water from farmers. As mentioned the per capita demand for water itself has fallen markedly in many developed countries, such as Australia and the United States, over recent years although aggregate water demands will also depend on population size and its age structure in the long-term future. As population size largely reflects political decisions concerning the size of the migration intake this too is difficult to forecast so estimates of it are also risky.
For expositional purposes restrict attention to a single source of risk here namely a single water supply risk from a rainfall-fed water supply sector. Precipitation collects into streams and rivers and eventually can be collected in dams where it can be made available for urban use. This precipitation is highly random – indeed, Australia has the most variable rainfall of any continent. Australia has periodically experienced droughts related to El Niño events from the time of white settlement. It might be that such events are becoming increasingly long and severe as a consequence of anthropogenic climate change or this might not be so. This is currently being researched by groups such as the CSIRO.
For illustrative purposes consider only two extreme situations:
- First, that the incidence and intensity of droughts will be almost completely unaffected by climate change for, at least, a significantly lengthy period into the future, say 50 years. In this case rainfall-fed water supplies will not experience an extreme secular decline. Label this state-of-the-world, θ1. Suppose further, that if θ1 is the true state-of-the-world, then short-term water supply needs during a drought are best met by urban water restrictions, drawing on aquifers or buying water from farmers. Desalination technologies are not sensible water supply options because they are too expensive relative to these other options.
- Second and alternatively, suppose that the incidence and intensity of droughts will be strongly driven by climate change over reasonably short-term time horizons. Then rainfall-fed water supplies can be expected to experience an extreme secular decline. Call this θ2. In this state of the world suppose that desalination is a sensible water supply option because droughts are becoming much worse with climate change so that it would be prohibitively expensive to rely on conventional water supply sources.
This extreme characterization of the true state of the world is obviously restrictive and is relaxed below to consider situations where a third intermediate outcome arises – climate has some impact on rainfall-fed water supplies but the impact is not extreme.
The difficulty here is that even with this extreme characterization planners do not know whether the true state-of-the-world is θ1 or θ2. Suppose that planners only have subjective probabilities π and 1-π respectively that these states of the world apply. For example if π = 0.3 installing a desalination plant would be economically unwise because there is a 30 per cent chance that climate change does not significantly worsen drought.
Irreversibility and risk have been discussed but a third crucial component of the real options approach is that, as time proceeds, a learning process proceeds so that planners learn more accurately about the true state of the world. Thus if an investment is deferred until the future, planners are in a better position to judge the true state of the world.
In the specific example analyzed this learning would take the form of knowing more definitely whether or not worsening droughts will be associated with anthropogenic climate change. More generally in an urban water planning context if you wait to invest there will be better knowledge of such things as demographic changes, the success of water conservation efforts and hence of aggregate water demands.
To make sharp the role of modeling in the specific example discussed suppose:
- In 20 years time – in the “future”, planners will know precisely which of the two states-of-the-world θ1, θ2 are correct.
This learning must occur for it to be sensible to delay a final decision on the plant. If a planner will be confronted with exactly the same risk-assessment in the future as is available today then there is no need to defer the investment decision. It can be taken immediately on the basis of expected returns and, either way, will continue to be the sensible decision into the future.
In the specific example discussed it is not obvious that uncertainty about the impact of climate change on drought will be resolved in 20 years. Australian rainfall trends are so highly random that isolating the effect of gradual climate change might be statistically difficult. If planners expect to face the same uncertainty in 20 years that they do now it is pointless to avoid taking decisions now in order to acquire future information.
The structure of the task can now be summarized generally. An infrastructure investment decision is being envisaged where: (i) The investment is irreversible; (ii) returns to the investment are risky but (iii) knowledge of the returns to the investment improve over time through a learning process.
In this setting the simplest real option objective is to adopt a development decision which maximizes the planner’s expected return – to maximize expected present value. Note here that this objective is both simple and conventional. Importantly, there is assumed to be no aversion to risk so the economic objective is linear in expected profit. Subsequently account for risk-aversion will be accounted for.
A specific model
To summarize in state θ1 the desalination project is not a sensible option and will impose a net cost relative to other water supply options. In state θ2 the project will yield significant benefit. The key issue is whether the project should be initiated now or its consideration should be deferred to the future.
For this question to make sense it must be the case that the initial expected benefits of the project must exceed the expected costs. If this were not the case it would always make sense to defer. Thus the development decision being investigated is whether, despite the fact that expected net benefits are positive, it might still make sense to defer. Should construction not begin immediately?
The key insight of real options approach is that there can be a case for deferring a project even if the expected benefits from the project, calculated now, are positive.
The intuitive reason for this is that embarking on the investment is irreversible so that, if state θ1 arises, one is unavoidably stuck with ongoing costs. However not embarking on the project now is a decision that can be reversed. If state θ2 is observed to occur in the future – here in 20 years time – then the initial decision to not build the plant can be reversed and construction can proceed in the future. Thus there can arise – but there need not arise – some extra value in waiting to invest since then extra potentially valuable information can arise. If expected benefits now from proceeding are significantly greater than expected costs then waiting to access this valuable new information may be worth less than proceeding now.
The standard rule of cost-benefit analysis of projects is that a project should proceed when the expected, discounted benefits from a project (EB) exceed the expected costs (EC). This is the rule that one gets when random variables in a cost-benefit comparison are replaced by their expected values.
Real options theory shows that application of such rules can lead to less expected net present value when investments are irreversible and risky and when a planner’s knowledge of the risks improves, through learning, with time. The correct rule for not delaying investment in the two period model outlined is:
EB > EC + QOV
where QOV is what is referred to as a quasi-option value a positive number reflecting the expected value of the extra information obtained from waiting to invest. Since QOV is positive, this is a stricter rule than that using the standard approach of replacing random variables with their expected values. Thus implementing standard cost-benefit approaches will lead when implemented across a range of projects to overinvestment – in the sense of an excessive initial infrastructure investment effort – and investments that occur too soon.
An extension: Insurance
The specific model by assuming risk-neutrality discussed does not allow for risk-aversion. With respect to commodities such as water (or electricity) it could be that planners seek to avoid risks of extreme shortages. There are perceived to be political risks that might limit reelection prospects based on water shortages and power blackouts.
Risk-averse planners might seek to insure against such risks.
The idea of risk aversion is easy to explain. A householder might be willing to pay $1000 annually to insure the possessions in their home against theft even if the cost of the policy exceeds the expected value of the possible theft. For example in a low crime neighborhood with only a 1% chance of a theft of $80,000 worth of belongings, the householder might still pay $1000 to ensure against the risk because sustaining a large loss of $80,000 would be an extremely adverse event for them. The difference between the cost of the policy and the expected claim is $200 which measures the insurance premium.
The decision to insure depends, in general, on the insurance premium charged relative to the risk, the costs consequent to the risk and the householder’s degree of risk aversion. Mathematically risk-aversion is related to the curvature of the householder’s utility of wealth function. In simple terms this reflects how the marginal utility of wealth increases as wealth decreases. If a householder attaches much larger disutility to reductions in wealth when their wealth is low rather than large the householder is risk-averse.
The same idea applies to the analysis of infrastructure projects. The extent of risk aversion here reflects the amount planners would be willing to pay to avoid critically low levels of supply of an output like water or electricity.
One can adapt real option techniques to assess such issues by attaching a high value to scarce water. This might reflect the judgment of planners or might be inferred by planners from the behavior of consumers who might be induced to pay extra to avoid low water supplies.
This leads to another way of thinking about the cost of a technology such as desalination. It might be the case that water supplied by a desalination plant is more expensive to deliver than water supplied by rainfall-fed dams. But it could also be the case that rainfall-dependent water supplies are subject to a drought risk whereas desalination water is not. Thus using a desalination technology can be understood as taking out insurance against the prospect of drought that threatens to leave a community severely short of water.
The key question then is whether the insurance premium paid for desalination is excessively expensive or not.
This is difficult to judge without knowing either the risk attitudes of planners or of the community that they serve and whose risk-attitudes it might be hoped they respect. Naturally taking out an insurance policy against the risk of inadequate rainfall does not address risk-aversion towards the possibly other substantial risks such as energy price risks which might bear substantially on a technology such as desalination.
Indirect evidence on this issue can be obtained by examining the extra cost that desalination options imposed on state economies over cheaper rainfall-dependent options. The Productivity Commission (2011, p. xxv) estimate that the extra cost Melbourne and Perth paid for desalination was $2.2b over 10 years (this figure is the average of their low and upper-bound estimates of this cost, $1-8 and $2-4b). Averaged over current population sizes in these cities and over a 10 year period this turns out to be $38 per citizen or $152 for a household of 4. The question of whether this additional cost is excessive can therefore be restated in terms of whether households would be prepared to pay $152 to have insurance against severe water shortages in the future as a consequence of climate change. The Productivity Commission thought this extra cost was excessive but it seems to be an issue of judgment.
As a general issue the willingness-to-pay for security of service supply can be determined using ‘stated preference ‘ – ‘contingent valuation’ or ‘experimental economics’ – techniques from environmental economics: See e.g. Kolstad, 2011.
Policy implications and a check list
What are the general implications that can be deduced from the example discussed above?
Value of Waiting. The major insight from real options approaches with risk neutrality is that the analysis of risky investments changes when a planner can learn about the likely payoffs from a project by waiting-to-invest. This does not necessarily mean that it is always desirable to wait to improve information but it does mean that irreversible investment commitments, which inevitably forgo this possible additional source of value, must clear more stringent net benefit hurdles than those which arise without any benefits from waiting.
Learning. The value of learning here is enhanced the better the learning. A research effort that seeks to improve knowledge of an uncertain world will increase the payoff to waiting at a cost. The most convenient assumption to make here is that research efforts are separate from investments themselves so that strategies for optimizing investments can be carried out independently of research strategies. However this might not be so in all real option applications. It is possible in some situations that investments themselves – perhaps carried out on a small scale – might improve knowledge of, for example, technologies, in which case as Miller and Lad (1984) have pointed out quasi-option values could then be negative because of favorable learning-by-doing.
This last possibility is however unlikely with respect to rainfall and temperature forecasts where the learning processes are almost certainly independent of adaptive measures designed to deal with them. Furthermore it is not clear when comparing forecasts of these climate variables from the Third and Four Assessment Reports of the IPCC that, if learning has occurred, that it has resulted in a reduction in the range of likely future climate trends.
Auxiliary policies. The economics of waiting can also be improved by having auxiliary policies in place which reduce the costs of waiting. For example, in an urban water supply setting, pricing water higher when water storages are low (“scarcity pricing’) will reduce the quantity of water demanded thereby stretching out the availability of the scarce resource. This means that rules to initiate investments in desalination that are based on extant water supply levels can be tightened and the investments postponed until lower critical storage levels are breached.
Similarly having access to water from alternative sources such as aquifers or from recycling technologies facilitates waiting by delaying the costs of doing so. So too does having access to demand management policies such as water use restriction policies on outdoor water use. There are costs of employing all these policies – for example there are consumer surplus losses from using water restriction policies that have been estimated to be $275m in 2010 dollars for cities such as Sydney. It is important, however, to see the benefits that stem from allowing increased delay of irreversible investment projects such as the Kurnell desalination plant which, in comparable dollars, cost $1.8b. This is a general point. These auxiliary policies need to be assessed in terms of their costs net of benefits derived including the benefit of increased investment flexibility.
Preplanning. A further auxiliary policy that deserves explicit attention is that of preplanning possible irreversible investment projects whenever such preplanning is low cost but time intensive. Planning decisions over large scale investment projects can, to some extent, be taken well in advance, environmental approvals sought, potential contractors identified and perhaps even activities such as site clearing and preparation can be undertaken at a cost which is low relative to the overall cost of a project. For example, the decision to proceed with the Wonthagii desalination plant was initiated by the Victorian Government in June 2007. Two years later the successful tenderer was announced for the project and construction began on October 6, 2009. The intention was for output to be delivered in late 2011 about two years later although the potential starting date has been extended to December 2012. Thus the intended construction time was only slightly greater than the time taken from deciding to proceed with the project to the appointment of the successful tenderer. Simple pre-planning would seem to potentially improve flexibility in making such decisions.
Practical constraints on political decision-making and the character of our democracy could potentially limit such gains. Most large investment projects encounter environmental and other objections that a government might seek to avoid if a project was merely a hypothetical possibility.
Modular design. Instead of all-or-nothing construction or deferral decisions modular design issues involving choice of scale can arise in many large-scale investment projects. A smaller pilot project can be initiated which embodies the option to be scaled-up in the future should the need to do so arise. There are benefits and costs of doing this.
There are several sources of benefit from building on a small scale initially that can be clarified by considering the desalination example. Firstly by supplying an additional, perhaps limited, source of rainfall-independent water it increases the community’s ability to wait before investing on a larger scale. Conversely the losses associated with such a project are less if it turns out that the technology was a poor choice. It can also provide pilot study information on costs via learning-by-doing although this would be more important if similar facilities had not yet been constructed in Australia.
The costs are the lost scale economies in not carrying out construction on a larger scale immediately. There are economies of scale in constructing desalination plants so the choice here involves assessing the tradeoff between such lost scale economies and the increased option value benefits obtained from constructing on a smaller scale.
Risk aversion. Introducing risk-aversion into real options modeling changes the analysis markedly. If the failure to deliver can infrastructure project can result in very severe social losses in certain states of the world or, more cynically, politicians were judged to be highly risk averse because of failed reelection prospects in certain states of the world – then it might make sense to pay an insurance cost premium to advance a project early.
The difficulty here is that by supposing enough risk-aversion any project can be justified even if expected costs greatly exceed expected benefits. One way around this is to determine whether the implied insurance premium is consistent with the community’s willingness-to-pay for security of service. In principle this can be determined using contingent valuation or experimental economics procedures.
Pure uncertainty and ignorance. It is worth remarking that while real option approaches offer an advance over traditional cost benefit analysis that replaces random variables by their expected values that both new and traditional approaches have, at their core, the notion that probabilities can be attached to different possible states of the world. Procedures then emerge for decision-making based on this quantitative way of describing decision-maker ignorance.
In some cases it may be possible to determine or delimit probabilities using evidence. Historical records on rainfall and stream-flow data can help, for example, to characterize the future water supply situation. Even here however the future water market is difficult to pin down when climate change bears on it and when the demand for water is driven by as yet unspecified population policies. Urban water markets are characterized by uncertainties that are difficult to pin down using probabilities. For example CSIRO (2008) estimates of climate change impacts on rainfall in the Murray-Darling Basin do not unambiguously identify the sign of climate change effects – climate change is forecast to either increase precipitation by 70 per cent or to decrease it by the same amount.
Given that option pricing approaches are data- and technique- intensive are there less demanding analytical frameworks that can help decision-makers think through infrastructure investment planning in such settings?
For situations of uncertainty where planners know the possible states of the world that can emerge but do not have subjective probability information about the likelihood of these states there are heuristics based on classical decision rules that are worth considering. One is the minimax criterion which seeks to undertake an investment if that cost-effectively avoids the worst possible state of the world imaginable. This is not a particularly useful rule in the current setting although it might reflect the thinking of politicians. It is important to understand that this rule involves infinite risk aversion towards adverse states of the world no matter how remote or implausible they might be. The rule moreover dictates policy inaction if in one state of the world considered policy action would be ineffective. Policy in this situation would never be implemented because the worst outcome is that the adverse state of the world occurs along with a failed costly policy. Thinking sensibly about the minimax rule should involve trying to persuade politicians (and others) from not acting on it.
A more interesting though again imperfect heuristic is minimax regret. This suggests taking action when action can avoid catastrophic consequences at relatively low cost. This is the rule that justifies the IPCC case for global action to address climate change itself. Action should be taken because there are potentially catastrophic consequences of climate change (with trillions of dollars of consequent costs) and these can be averted at low cost (e.g. a small percentage loss of GDP). This has an appeal to it – avoid very costly possible situations if you can do so at low cost – although there is an implicit assumption that the probabilities of the catastrophic event are not negligible and this opens up the door to arbitrariness. No government would invest half of its national GDP eliminating a 10-23 risk that an asteroid might crash into the planet even if the investment cost here is low relative to the damage cost.
The minimax regret criterion has the attractive feature of focusing on extreme risks – for example the (non-negligible) possibility that a city may have no water supply – and then seeks inexpensive ways to avoid this.
The most realistic situation to consider – if the most intractable – is the decision-problem where neither subjective probabilities nor an exhaustive catalogue of possible states of the world can be articulated. This is described as gross ignorance. In practice about all that can be said about this realistic though intractable situation is to anticipate the unexpected, to avoid initial tunnel vision theorizing in making investment decisions and to be prepared to be adaptive in making development plans by being prepared to reconsider plans that show evidence of being unsuccessful. This is difficult with respect to large, discrete public investment projects.
With respect to climate change it is wise to consider scenarios where climate change was, in turn, much more severe and much less severe than anticipated.
Learning with time or through experience is fundamental to the assessment of risky, irreversible investment projects. Quasi-option values measure the extent to which conservatism should prevail in the assessment of such prospects when decision-makers are only concerned about expected returns. With risk-neutrality there is a case for making more cautious judgments than would be suggested using standard cost-benefit analysis. If decision makers are risk averse then measures of their risk-aversion provide the basis for quantitatively determining the extent to which they will pay to avoid such risks and there could be a shift towards lower degrees of caution in undertaking investments.
Fostering learning, using auxiliary policies, preplanning and the use of modular design in the implementation of projects are the primary ways that infrastructure project planners can improve outcomes in settings with risk and irreversibility.
With respect to urban water the view has been advanced (Productivity Commission, 2011) that the round of desalination investments made over the past decade in Australia in response to the Millenium Drought was an excessively expensive way of securing Australia’s urban water future. The record high rainfall received around Australia provides some ex post wisdom that the unwise see as supporting this argument. But there now seems to be enough water supply capacity to service Australia’s cities for at least the next decade or so.
Thus for urban water supply provision there is some temporal space to rethink urban water planning. A key general issue is that because desalination technologies are now in place in all capital cities that the value of future desalination plants is reduced in the sense that a hedge against unfavorable drought events has now been achieved. Sensible planning in the future will seek water sources that offer cost effective supply that is uncorrelated with existing supplies. Dams and other options become attractive given that desalination technology is now in place. Future key uncertainties that might need to receive more emphasis are energy price uncertainty that might reduce the future attractiveness of energy-intensive options such as desalination.
Thus history matters when it comes to expanding infrastructure options. Once one source of uncertainty is addressed others will become relatively more prominent.
H. Clarke, “Planning Urban Water Investments with an Uncertain Climate”, Economic Papers: A Journal of Applied Economics and Policy, submitted, 2012.
CSIRO, Water Availability in the Murray-Darling Basin: A Report to the Australian Government from the CSIRO Murray-Darling Basin Sustainable Yields Project, Commonwealth Scientific and Industrial Organisation, Australia, 2008.
A. Dixit & R. Pindyck, Investment Under Uncertainty, Princeton University Press, Princeton, 1994.
McDonald & Siegel, “The Value of Waiting to Invest”, Quarterly Journal of Economics, 101, 4, 1986, 707-727.
C. Kolstad, Environmental Economics, Oxford University Press, Oxford, 2011.
J. Miller & F. Lad, “Flexibility, Learning And Irreversibility in environmental Decisions: A Bayseian Approach, Journal of environmental Economics and management, 11, 2, 1984, 161-172.
Productivity Commission, Australia’s Urban Water Sector, Final Inquiry Report, Canberra, August 2011.