Risk and Uncertainty

A central feature of project analysis is that any form of ex ante appraisal will be projecting an uncertain future. Data on benefits and costs will be entered as single most likely values. The early literature recognized that this is a very crude way of dealing with an uncertain future and that in principle, more formal risk-based approaches are desirable (Pouliquen 1970, Reutlinger 1970). In practice, uncertainty is normally addressed through sensitivity analysis, which identifies key parameters that may affect project outcomes. Sensitivity analysis may be supplemented by the calculation of a switching value for a key parameter.16 _{This has always been}

recognized as being a very approximate means of addressing uncertainty since in reality all parameters will vary. Techniques for addressing

16 _{Switching value is the value for a parameter at which the project becomes unacceptable, that is the}

this in the form of simultaneous changes in variables in “Monte Carlo” simulations have been known for many years, but it took the widespread use of microcomputers in the early 1990s for them to become part of the toolkit of project analysis. Clarke and Low (1993) and Savvides (1994) showed how this could be done with simple applications, and there are now risk analysis software programs that make the application of risk analysis relatively easy.17 _{What is required is to specify which variables}

are to change simultaneously, their mean value, a plausible range and their variance and distribution around the mean (often taken as a normal distribution). Once the number of simulations is specified, the project outcome is given as a probability distribution.

Risk analysis software packages can run large numbers of simulations, which allow for an expected value estimate for the NPV or internal rate of return (IRR) as the mean of all results from the simulations. This is equivalent to a risk-adjusted indicator of project worth. Another key piece of information that is derived from risk analysis is the probability of an unacceptable outcome (a negative NPV or an IRR below the cut-off rate). Provided that the decision maker is risk-neutral, expected values provide the basis for decision making. Risk neutrality implies that risk of failure can be ignored; for example, where a government or large investor can pool risks across a large number of projects, an unfavorable outcome on one is offset by a favorable outcome on another.18 _{Risk neutrality can be}

accepted as the correct response to risk for all except a particular class of non-marginal or pro-cyclical projects, where failure by one project can affect the whole portfolio.

Expected return and risk are likely to be positively related, since higher return activities are generally more risky. This implies that for large or pro-cyclical projects, the decision criterion for acceptability has two dimensions—expected return and its variance (that is, risk of failure). Project A may have an IRR of 14% (while the minimum acceptable rate is 12%) but a probability of failure of 30%. If the maximum acceptable probability of failure is 25%, then on risk grounds the project should either be redesigned to reduce risk, or rejected. While theory suggests that for a particular class of projects, risk neutrality is not the appropriate way to address risk, as yet in practice a minimum acceptable probability

17 _{Belli at al. (2001) recommend this form of analysis for the World Bank; ADB (1997) notes this}

approach, while Rayner et al. (2002) recommend its use in ADB appraisals, and ADB (2002) gives more detailed guidance on how this could be done.

18 _{This is referred to as the Arrow-Lind theorem after Arrow and Lind (1970), who presented the}

of failure is rarely incorporated in project decision making. What is an acceptable level of risk is in principle for decision makers themselves to determine, but a rule of thumb can be derived from failure rates on the existing project portfolio as revealed by ex-post evaluation studies.19

In addition to the use of risk software in project analysis, uncertainty underlies an important theoretical development in the academic literature relating to the “options value” of waiting. The concept originates from the financial literature on “options” or the value of waiting (Dixit and Pindyck 1994).20 _{There is a clear theoretical case that under uncertainty}

where a project decision is irreversible, waiting can increase learning and thus more information on likely outcomes will be available to the analyst. Therefore, the value of waiting should be taken into account in project analysis. As many project decisions are in principle irreversible (roads and power plants once built cannot be moved and natural forest land once cleared for development cannot be easily regenerated to its original status), the value of waiting is an important issue and relates to the familiar problem of optimal timing decisions for projects.

Standard project analysis compares expected benefits and costs; however, where irreversibility holds, the option of waiting to see how things develop (for example, if road traffic or power demand grows as predicted) is ruled out, which entails a potential lost benefit. This can be illustrated algebraically for a simple two-period case. Investment K in year 0 generates either high benefits B_A or low benefits B_B with probabilities of p_A and (1–p_A)in year 1. The standard decision criterion is to invest if the economic NPV is positive.

Economic NPV = ( pA*BA+ (1– pA)*BB)/(1+ i) – K (9)

where ‘i’ is the discount rate, waiting allows K to be invested at i for 1 year, with the option for a decision to be taken 1 year later, only if the higher benefit figure occurs. If the lower benefit figure accrues, the investment need not go ahead. Initial costs K have fallen by waiting as they were invested in year 1 at i%.

Thus with the higher benefit the net present value is;

Economic NPV’ = ( p_A*B_A)/(1+i)2 _{– K/(1 + i) (10)}

19 _{Weiss (1996) recommends this approach and suggests 25% as a rule of thumb based on past failure}

rates on World Bank projects.

20 _{The initial theoretical formulation comes from Arrow and Fisher (1974) in the context of the}

environment and recent discussions of option value have focused on environmental issues like reaction to global warming (Pearce et al. 2006).

The difference between the two Economic NPV figures (NPV – NPV’_’)

is the value of the option to wait. Although rarely done, as Dixit and Pindyck (1994) argue in relation to financial appraisal, the value of the option (which can be negative if the future looks worse after waiting) should be treated as part of the opportunity cost of investment funds and added to the initial investment cost of a project under consideration. This should guarantee the correct timing decision since only if the value of waiting is negative, (so the delayed project has a lower NPV than the original one) will the original project be the best choice. Some analyses based on a system approach (such as in the power sector) may incorporate optimal timing concerns; however, project decisions are often still viewed as discrete “yes” or “no” decisions, with relatively little discussion on timing, so that incorporation of this option value can be a useful addition to standard practice.