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Sensitivity Analysis: What It Is For and Example

 The sensitivity analysis is a technique that determines how different values of an independent variable impact a dependent variable on a set of assumptions. Study how the uncertainty in the result of a mathematical model or system can be assigned to different sources in its input variables.


This technique is used within specific limits that depend on one or more input variables, such as the effect that changes in interest rates (independent variable) have on bond prices (dependent variable).


Sensitivity analysis, given a certain range of variables, is a way of predicting the outcome of a decision. It is also known as simulation analysis or "what if". By creating a given set of variables, an analyst can determine how changes in a variable affect the result.


A related practice is uncertainty analysis, which focuses more on the quantification and propagation of uncertainty. Ideally, the uncertainty and sensitivity analysis should be run together.


What is it for?

One of the key applications of sensitivity analysis is in the use of models by managers and decision makers. All the content necessary for the decision model can be used through repeated application of sensitivity analysis.


It helps decision analysts understand uncertainties, pros and cons, with the limitations and scope of a decision model.


Most decisions are made under uncertainty. One technique for reaching a conclusion is to replace all uncertain parameters with the expected values; then sensitivity analysis is carried out.


Assessment of confidence in the model

It would be a respite for a decision maker to have some indication of how sensitive the choices will be when changing one or more input variables. Good modeling practice requires the modeler to perform a confidence assessment in the model.


First, this requires quantifying the uncertainty in the results of any model (uncertainty analysis); and second, assess how much each entry contributes to the uncertainty of the result.


Sensitivity analysis addresses the second of these points (although uncertainty analysis is a necessary precursor), playing the role of ranking the strength and relevance of the input variables to determine the variation in the result.


In models that involve many input variables, sensitivity analysis is an essential ingredient for model construction and for quality assurance.


Applications

- The key application of sensitivity analysis is to indicate the sensitivity of a simulation to uncertainties in the input values ​​of the model.


- It is a method of predicting the outcome of a decision if a situation turns out to be different when compared to key predictions.


- Helps to evaluate the risk of a strategy.


- It serves to identify how dependent the result is with respect to a particular input variable. Analyze whether the dependency helps to assess the associated risk.


- Helps to make informed and appropriate decisions.


- It is used to search for errors in the model, by finding unexpected relationships between the inputs and the results.


How to do it?

A sensitivity analysis, also known as a "what-if" analysis, is most often used by financial analysts to predict the outcome of a specific action when performed under certain conditions.


The sensitivity analysis is performed within defined limits, determined by the set of independent input variables.


For example, sensitivity analysis can be used to study the effect of a change in interest rates on bond prices if interest rates increase by 1%.


The question "What if ...?" It would be: What happens to the price of a bond if interest rates go up 1%? This question is answered with sensitivity analysis.


The analysis can be performed in a Microsoft Excel sheet, in the "Data" section of the options menu, using the "Hypothesis analysis" button, which contains "Seek objective" and "Data table".


There are different methods to carry out the sensitivity analysis:


- Modeling and simulation techniques.


- Scenario management tools through Microsoft Excel.


Techniques

There are mainly two techniques to analyze sensitivity:


Local sensitivity analysis

It is based on derivatives (numerical or analytical). The local term indicates that the derivatives are taken at a single point. This method is suitable for simple cost functions.


However, it is not feasible for complex models, such as models with discontinuities, since they do not always have derivatives.


Mathematically, the sensitivity of the cost function with respect to certain parameters is equal to the partial derivative of the cost function with respect to those parameters.


Local sensitivity analysis is a "one at a time" technique. Analyze the impact of a single parameter at a time on the cost function, keeping the other parameters fixed.


Global sensitivity analysis

Global sensitivity analysis is the second approach to sensitivity analysis, which is often implemented using Monte Carlo techniques. This approach uses a global set of swatches to explore the design space.


Example

John is in charge of sales for Holiday CA, which sells Christmas decorations at a mall. John knows that the holiday season is approaching and that the mall will be crowded.


You want to know whether an increase in customer traffic at the mall will increase the store's total sales revenue, and if so, by what amount.


The average price of a package of Christmas decorations is $ 20. During the holiday season last year, Holiday CA sold 500 packages of Christmas decorations. This resulted in a total sales of $ 10,000.


After conducting a sensitivity analysis, it is determined that a 10% increase in customer traffic at the mall results in a 7% increase in total sales.


Using this information, John can predict how much money the store will make if customer traffic increases by 20%, 40%, or 100%.


Based on the sensitivity analysis shown, it can be seen that there will be an increase in total sales of 14%, 28% and 70%, respectively.


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