averagerisk

Averagerisk is a statistical measure used in risk management to summarize the overall risk exposure of a system by averaging potential losses weighted by their probabilities. It expresses the expected loss or average severity of outcomes across a defined set of scenarios or states of the world, providing a single scalar value that can be used for comparison and prioritization.

Calculation of averagerisk can be straightforward in discrete settings. If there are n scenarios with probabilities p1, p2, ..., pn and corresponding losses L1, L2, ..., Ln, the averagerisk is the sum of the probability-weighted losses: sum over i of p_i times L_i. In a continuous framework, where the loss variable X has probability density f(x), averagerisk is the expected value E[X], represented by the integral of x f(x) dx over the relevant range. In insurance and finance, this is often referred to as the actuarial expected loss or the mean loss, and it is sometimes called the average annual loss (AAL) in periodic contexts.

Averagerisk is commonly used as a baseline or initial risk metric in risk assessments, budgeting, and portfolio construction. It complements tail-focused measures such as Value at Risk (VaR) and Expected Shortfall (ES) by emphasizing the mean level of exposure rather than extreme outcomes. Its simplicity is advantageous for quick comparisons but also a limitation, as it can mask tail risk, be sensitive to unit scales, and overlook the distribution shape or dependencies among risks.

Related concepts include expected value, VaR, ES, and risk concentration analysis.