Sensitivity analysis

Sensitivity analysis examines how a model’s output changes when selected inputs change. It shows which assumptions matter most, which decisions are robust and where better evidence could improve the choice.

When to use it

• Understand the range of outcomes around a plan or valuation.

• Identify assumptions capable of reversing a recommendation.

• Detect model errors, discontinuities and hidden dependencies.

• Prioritise research on the inputs with the greatest decision value.

• Distinguish one-at-a-time sensitivity from scenarios and probabilistic uncertainty analysis.

Origins

Sensitivity reasoning predates computers and appears in mathematics, engineering, economics and operations research. Digital calculation made it accessible at scale. VisiCalc, launched in 1979, helped popularise spreadsheet modelling; Lotus 1-2-3 and later Microsoft Excel made rapid “what-if” analysis routine. Monte Carlo methods provide a different but complementary approach by propagating probability assumptions through a model.

What it is

Local sensitivity changes one input near a baseline and observes the result. One-way analysis varies inputs individually; multi-way analysis varies several together; threshold analysis finds the value at which the decision changes. Global sensitivity examines variation across a wider input space and can attribute output uncertainty to individual variables and interactions.

Sensitivity is not the same as uncertainty. A highly sensitive output may still be well known if the input is certain; an uncertain input may matter little if the output barely responds. Combine the model’s responsiveness with a defensible range or distribution.

For example, an insurer pricing term life coverage for smokers aged 60 or above might vary mortality, lapse, expense, interest and selection assumptions. A Monte Carlo model can produce an outcome distribution, but random sampling does not repair biased life tables, omitted dependence or an unsuitable pricing objective.

How to use it

Use a disciplined process:

1. Define the decision, model and outputs. State the baseline, time horizon, constraints and the outcome that changes the decision.

1. Select inputs and defensible ranges. Use evidence, expert elicitation and scenarios. A stated 80 per cent interval needs a method and should not be confused with the full plausible range.

1. Run one-way analysis. Vary each input while holding others at the baseline. Identify thresholds, non-linearity and inputs with little influence.

1. Examine interactions and dependence. Use multi-way scenarios, correlated sampling or global methods. Do not remove a variable merely because its one-way effect is small if it interacts with another.

1. Summarise for the decision. Use tornado charts, response surfaces, distributions or tables. Report assumptions, ranges, sources and the combinations that reverse the conclusion.

Sensitivity analysis may identify a robust “best bet,” but it does not choose strategy automatically. Include risk appetite, optionality, implementation and non-modelled consequences.

Top practical tip

Pair every sensitivity range with evidence and every chart with a decision threshold. Then ask which uncertain input is both influential and learnable; that is where additional research has the greatest value.

Top pitfall

Do not vary correlated inputs independently or infer joint downside from isolated cases. The 2008 financial crisis illustrates how common exposures can create simultaneous failure; model dependence, feedback and structural breaks explicitly.

Further reading

• Saltelli, A., Ratto, M., Andres, T. et al. (two thousand and eight). Global Sensitivity Analysis. Wiley.
• Eschenbach, T.G. (nineteen ninety-two). “Spiderplots versus Tornado Diagrams for Sensitivity Analysis.” Interfaces.