Sensitivity Analysis

Every calculation about the future rests on assumptions. Anyone estimating a company’s profit for the next year has to somehow settle on revenue, costs, and interest rates. None of these figures is certain. A sensitivity analysis now answers the question: What happens to the result if one of these assumptions turns out differently? You deliberately change one input variable and observe how strongly the final result reacts to it. The name comes from the English word for sensitivity: you measure how sensitively the result reacts to each individual assumption.

Why a single number as a result is misleading

A model usually delivers a very precise-looking number at the end. This precision is deceptive. It only arises because every uncertainty has previously been boiled down to a fixed value. Sensitivity analysis makes this lost uncertainty visible again.

It also separates what is important from what is not. A typical corporate model contains hundreds of assumptions. Only a handful of them actually move the result. If a one-percentage-point change in growth shifts the company’s value by thirty percent, you know what needs to be discussed. There’s then no need to argue about office costs anymore.

This also guards against a common mistake: trusting results that nobody has questioned. A model whose result flips with small changes is a weak basis for decisions. A model that remains stable across a wide range of assumptions is robust. You can only see this difference by actually moving the assumptions.

From single-variable variation to random simulation

The simplest form changes exactly one variable and holds all others fixed. You run the model through multiple times, say with three, five, and seven percent growth. The results are plotted side by side. This immediately shows how strongly this one variable affects the outcome. Repeating this for every assumption produces a ranking of influencing factors.

Often two variables are changed at the same time. The result is a table with rows and columns, called a data table in spreadsheets. Rows might be growth rates, columns interest rates, and each cell contains the corresponding company value. Such tables can be found in almost every valuation study produced by a bank.

With Monte Carlo simulation, you go one step further. Here, the computer randomly draws all assumptions thousands of times from a plausible range. The result is no longer a single number but a distribution of possible outcomes. You can then say in how many runs a project would have made a loss. It’s important to distinguish this from scenario analysis: there, you build a few internally consistent overall pictures, such as crisis or boom, rather than turning individual figures in isolation.

From stock analysis to model testing in AI

You most often encounter the term in financial reports. Price targets for stocks are almost always published with a range and a sensitivity table. Climate forecasts, election models, and the planning of large construction projects work the same way. When the news says a result is robust, such an analysis is usually behind it.

In AI, the principle also plays a role. There, the question is which inputs most strongly influence a model’s decision. If you change a single word in a query and the answer flips completely, the model is highly sensitive at that point. Such tests are part of explainability, i.e., the effort to make opaque models comprehensible.

One common misconception remains: a sensitivity analysis does not say how likely a scenario is. It only shows what would happen if it occurred. The probabilities still have to be assessed by a human.