Definition
Sensitivity analysis is an analytical technique that measures how much a model's output changes when a single input is varied while the other inputs are held constant.
Why it matters
Every model result depends on the assumptions that produce it, and the practical question about any result is which assumptions the result actually turns on. Sensitivity analysis answers that question by isolating one input at a time and tracing its effect on the output. A result that is highly sensitive to a specific assumption is a finding about that assumption more than about the underlying structure; a result that is stable across reasonable variation in a specific assumption is a more durable finding. Retirement analysis often surfaces surprising sensitivities that reshape what the individual should focus on.
How it works
A sensitivity analysis holds all inputs to a model at their central values, varies one input across a specified range, and records how the output changes. The output can be plotted against the varied input to produce a sensitivity curve, or reported as a partial derivative if the model is smooth enough. Consider a cost-of-income calculation for the focal individual configuration (67F, $500,000, plan to 90) at a 3 percent real discount rate: varying the discount rate from 1 percent to 6 percent while holding all other inputs constant produces a specific cost-of-income figure at each rate, and the shape of the resulting curve reveals whether the finding is stable across the plausible rate range. In the Longevity Standard corpus, the pooling multiplier rises from approximately 1.23 at 6 percent real to approximately 1.33 at 1 percent real for the focal individual, which is the finding that pooling becomes relatively more valuable as rates fall. The finding is a sensitivity result: the underlying model is deterministic, and varying the rate one input at a time is what surfaces the relationship. Sensitivity analysis of correlated inputs one at a time can be misleading when the inputs are not actually independent in the real world, which is one motivation for using scenario analysis to vary related inputs jointly.
In practice
An individual receiving a retirement projection should ask which inputs the projection is most sensitive to, and what the result looks like at plausible variations from the central values. A projection that is highly sensitive to the assumed return rate is telling the individual that the projection is mostly a bet on the return assumption; a projection that is stable across reasonable return variation but highly sensitive to the assumed inflation rate is a different bet. Sensitivity analysis is what turns a single-number projection into a legible structural finding, and the individual should expect the professional producing the projection to disclose the key sensitivities.
Related terms
- Scenario analysis
- Stress testing
- Deterministic modeling
- Discount rate
- Real versus nominal discount rate
- Duration
- Convexity
- Pooling multiplier