What is Sensitivity Analysis?

Sensitivity analysis, also referred to as simulation analysis, is a technique employed in financial modeling to determine how different values of a set of independent variables can influence a particular dependent variable under certain specific conditions and assumptions. It is used to ascertain how the overall uncertainty in the output of a mathematical model is affected by the various sources of uncertainty in its inputs. The application of sensitivity analysis spans a wide range of fields such as engineering, biology, environmental studies, social sciences, chemistry and economics. It is most often used in mathematical models where the output is an opaque function (i.e. one that cannot be subjected to an analysis) of several inputs.

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How is a Sensitivity Analysis Used?

Sensitivity analysis is popularly known as what-if analysis since the technique is used to measure varying outcomes using alternative assumptions and conditions across a range of independent variables. At the risk of oversimplification, sensitivity analysis can be said to observe changes in behavior for every change brought to the model. Sensitivity analysis can either be local or global. There are certain parameters that analysts need to be mindful of when undertaking such an activity. For starters, it is essential to determine the input variables for which the values will be altered during the analysis. Secondly, it is also necessary to ascertain how many variables will be affected at any given point in time. Thirdly, maximum and minimum values need to be assigned to all pertinent variables before the analysis commences. Lastly, analysts must scrutinize correlations between input and output and assign values to the combination accordingly. The values that can be altered include technical parameters, the number of activities and constraints, and the overall objective with respect to both the assumed risk as well as expected profits. Stipulated observations include the value of the objective with respect to the strategy, the values of the various decision variables, and the value of the objective function between two adopted strategies.

Steps in Sensitivity Analysis

Once the values of the input variables have been determined, sensitivity analysis can be performed in the following steps:

1. Defining the base case output: The first step is to define the corresponding base case output for the base case input value for which the sensitivity is to be measured.
2. Determining the new output value: During this step, we determine the value of the output for a new value of the input, given that the values of all other inputs are constant.
3. Calculating the change: We then compute the percentage changes in the output as well as the input.
4. Calculating sensitivity: This final step calculates sensitivity by dividing the percentage change in output by the percentage change in input.

Variations in Assumptions

Applications of Sensitivity Analysis

Sensitivity analysis has a wide variety of applications from something as trivial as planning a road trip to developing business models. Below are some of its most common applications.

• Sensitivity analysis is used in the study of Black Box Processes, which are processes that can be analyzed on the basis of their inputs and outputs, without having to determine the complexities of their inner workings.
• It is employed in Robust decision-making (RDM) frameworks in order to assess the robustness of the results of a model under epistemic situations that involve uncertainty.
• It is used in the development of evolved models by identifying and analyzing correlations between observations, inputs and forecasts.
• It is utilized in reducing uncertainty in models by identifying and omitting inputs that bring about significant uncertainty in the output.
• Sensitivity analysis is also commonly used as a tool for model simplification by identifying and omitting inputs that are redundant or do not have any significant effect on the output.
• It is used to generate sustainable, coherent as well as compelling recommendations that aim to enhance communication between modelers and decision makers.

Sensitivity analysis has become an integral part of Policy Impact Assessments (IAs) conducted by both national as well as international agencies.

Illustration of Sensitivity Analysis

Let us assume that a company C1 is involved in the manufacture and sale of snow plows. Joe, a sales analyst at the company is trying to understand the impact of an early advent of winter on total sales of snow plows. Company analysts have already determined that sales volume typically peaks during the last quarter of the year, i.e. during the months October through December. This increase in sales is driven by the anticipation of snowfall during late December, January and early February. However, Joe has determined from historical sales figures that during forecasts of early winter, snow plow sales have also peaked accordingly. For calendar years that have had snowfall 15 days earlier than usual, there has been a five percent rise in total sales volume. Based on this simple equation, Joe is able to construct a financial model as well as perform sensitivity analysis utilizing various what-if scenarios. According to Joes sensitivity analysis, whenever snowfall precedes the norm by 21, 15 and nine days, the total snow plow sales of C1 can also be expected to increase by seven, five and three percent respectively.