What Is Risk?
In quantitative risk analysis, risk is defined as the expected loss from an uncertain event: the size of the loss if it happens, multiplied by the probability that it happens. This gives a single number in monetary (or other impact) units that can be compared across different risks.
Expected loss is a planning tool, not a prediction that the loss will occur in any single instance. Over many repetitions, however, the average loss tends toward this expected value, which makes it useful for budgeting, insurance, and prioritizing which risks to mitigate first.
Formula
Risk (expected loss) = P(loss) × Impact
where:
P(loss) = probability that the loss event occurs
Impact = the loss amount if the event happens
Applications
- Prioritizing risks in a project risk register
- Setting insurance premiums or contingency reserves
- Deciding whether a security investment is worth its expected savings
- Ranking operational risks by their expected financial impact
Sources
- Hubbard, D. W. (2020). The Failure of Risk Management: Why It Is Broken and How to Fix It (2nd ed.). Wiley.
- Montgomery, D. C., & Runger, G. C. (2018). Applied Statistics and Probability for Engineers (7th ed.). Wiley.