Analysis of Risk: Qualitative and Quantitative Techniques and Forecasting
From description to numbers
Qualitative analysis - risk matrices, heat maps, Delphi panels, scenario workshops - prioritizes exposures when data are thin. Quantitative analysis estimates frequency and severity and combines them. The core identity is expected annual loss = expected frequency x expected severity.
Choose distributions deliberately: frequency is often Poisson or binomial; severity is often normal, lognormal, or Pareto (heavy-tailed). Mean and standard deviation describe a distribution, and the coefficient of variation (sigma/mu) compares relative variability across exposures of different size. A lower CoV means more predictable losses and more credible support for a retention decision.
Traps
Expected loss is not the worst case - it is the long-run average. Do not compare standard deviations across exposures of different size; use the CoV. The law of large numbers improves prediction with more similar units, and the central limit theorem makes sums and averages approach normality only as sample size grows - small samples stay skewed. Correlation destroys diversification benefits. Maximum possible loss (worst case) and maximum probable loss (realistic worst) are different figures. Trend historical losses for inflation and exposure growth before use, and state assumptions and confidence ranges rather than a single number.
Rule of thumb: quantify, then sensitivity-test - if a 20% error in severity flips the decision, the model is not robust.
Worked example: Warehouse A has mean loss $40,000 and standard deviation $20,000 (CoV 0.50). Warehouse B has mean $80,000 and standard deviation $24,000 (CoV 0.30). B has the larger expected loss but the more predictable losses, so a funded retention may be easier to defend for B despite the bigger number.