The simplest form of quantification of risk is by applying optimism bias contingencies to costs or timeframes to reflect the systematic tendency for project teams to be over-optimistic about key parameters. The adjustments can be based on past empirical experience of similar projects and should be reduced at different stages of the business case development as progressively better estimates are made. While simple, the disadvantages are that it reflects downside risks only and is unlikely to effectively manage or mitigate risks.
Single-point probability analysis
An expected value can be calculated for each significant risk by multiplying the likelihood of the risk occurring (probability) by the size of the consequence. This risk premium is expressed in monetary terms and provides an estimate of the cost of accepting all the risk.
It is best used when both the likelihood and consequence of the risk event can be estimated reasonably well. The disadvantage is that it provides no information about the underlying variability in outcomes or consequences, particularly at the extremes when decision-makers may prefer not to accept the risk of the event occurring.
Quantitative risk analysis (QRA)
Quantitative risk analysis (QRA) is a modelling technique that makes risks, and the financial impact of those risks, more explicit to decision-makers when considering the business case. This recognises that using single point estimates for comparing options can provide relatively limited information about the underlying trade-offs.
QRA of costs is mandatory as part of the development of a Detailed Business Case (DBC) for significant projects or programmes monitored by the Treasury. The Ministry of Business Innovation and Employments consultancy panel maintains a list of accredited quantitative risk analysis experts for use by Government agencies.
Quantitative risk analysis can provide a better understanding of the sources of risk to project outcomes and more accurate estimates of the likely costs or benefits. Generally a quantitative risk analysis approach is considered to be superior to an approach that solely relies on optimism bias or contingencies. Quantitative risk analysis should be used as the first-best basis and is required for high risk, large scale investment proposals.
Quantitative risk analysis conducts detailed sensitivity analysis and analysis of the likely effect of these scenarios on project outcomes. This involves assessing each probability and consequence and modelling project outcomes based on simulations of each risk. The final probability distribution describes the range of outcomes and their relative likelihood.
Monte Carlo analysis
Monte Carlo analysis is a specific risk modelling technique that uses statistical sampling and probability distributions to simulate the effects of uncertain variables on model outcomes. The approach provides a systematic assessment of the combined effects of multiple sources of risk in key variables and can also allow for known correlations between these variables. Using Monte Carlo can require expert advice to develop the model and interpret the results.
The Monte Carlo approach is more suited to proposals where there are several key variables with significant and/or correlated uncertainties, and when simpler sensitivity analysis approaches are unable to adequately describe the resulting variation in net benefits between competing options.
-  Refer to the HM Treasury Green Book supplementary guide at https://www.gov.uk/government/publications/the-green-book-appraisal-and-evaluation-in-central-governent