Assessing Project Contingency Reserves with the Expected Cost Overrun Risk Measure

This paper proposes a coherent risk measure to assess project cost overrun contingency reserves: the project expected cost overrun ($ECO$). It is shown that the traditional project cost-percentile metric does not qualify as a coherent risk measure and, therefore, that the $ECO$ metric should be adopted. Obtained from the tail expectation of the project cost probability distribution, it measures the average value of project costs exceeding, at any significance level, the project cost baseline. A positive, unique, and exact closed-form solution to the $ECO$ risk measure is devised under, among others, the normal probability distribution. The resulting project cost overrun contingency reserve may be interpreted as an insurance contract covering contingent risk factors and claimable by project managers from their project director once preidentified and agreed-upon contingent high-risk cost impacts are taken into account. The project $ECO$ risk measure is extended to assess the project expected time overrun ($ETO$) and the project expected time overrun penalty ($ETOP$) risk measures, quantities that will prove indispensable for successfully tendering under any contractual form the minimum value of project time and project cost bids. They will be covering, at the very least, all relevant potential low-probability high-risk contingent risk factor impacts.