33 In estimating the future costs and benefits associated with particular proposals, there will inevitably be variation between these estimates and the actual costs and benefits realised. This will be over and above the impact of optimism bias, and will be as a result of random factors unforeseen at the time of appraisal.
34 For the public sector as a whole, such random factors will tend to cancel out, taking all proposals together. But in some cases, this would not be expected to happen. Some projects - for example transport use - will tend to have appraisal risks that are systematically related to the overall performance of the economy. Because the majority or all of such projects will be affected by this same factor, appraisal errors will not cancel out between projects.
35 A decision-maker who is risk averse cares about this potential variability in outcomes, and is willing to pay a sum in exchange for certainty (or willing to put up with variability on receipt of compensation).This compensation is the cost of variability, and should be included in appraisal when it is considered appropriate.
36 Generally, a variability adjustment may be required when:
❑ Risks are large relative to the income of the section of the population that must bear them (including very large risks borne by the whole population); or
❑ When risk is correlated systematically with income or GDP, and so cannot be diluted by spreading across the economy.
37 The fraction of income worth paying for certainty (C) is approximated by the expression:
C= - var(y) / 2y*
where y is the net additional income resulting from the proposal, and y* is the total expected income or benefits (including the project income) of those impacted by the proposal.
38 Given the size of national income relative to the scale of most individual projects, the cost of variability for projects that benefit the community as a whole is usually negligible.