## What is Sensitivity Analysis?

The technique used to determine how independent variable values will impact a particular dependent variable under a given set of assumptions is defined as sensitivity analysis. It’s usage will depend on one or more input variables within the specific boundaries, such as the effect that changes in interest rates will have on a bond’s price.

It is also known as the what – if analysis. Sensitivity analysis can be used for any activity or system. All from planning a family vacation with the variables in mind to the decisions at corporate levels can be done through sensitivity analysis.

Sensitivity analysis works on the simple principle: Change the model and observe the behavior.

The parameters that one needs to note while doing the above are:

*A) Experimental design:* It includes combination of parameters that are to be varied. This includes a check on which and how many parameters need to vary at a given point in time, assigning values (maximum and minimum levels) before the experiment, study the correlations: positive or negative and accordingly assign values for the combination.

*B) What tfo vary:*The different parameters that can be chosen to vary in the model could be:

a) the number of activities

b) the objective in relation to the risk assumed and the profits expected

c) technical parameters

d) number of constraints and its limits

*C) What to observe:*

a) the value of the objective as per the strategy

b) value of the decision variables

c) value of the objective function between two strategies adopted

## Measurement of sensitivity analysis

Below are mentioned the steps used to conduct sensitivity analysis:

- Firstly the base case output is defined; say the NPV at a particular base case input value (V1) for which the sensitivity is to be measured. All the other inputs of the model are kept constant.
- Then the value of the output at a new value of the input (V2) while keeping other inputs constant is calculated.
- Find the percentage change in the output and the percentage change in the input.
- The sensitivity is calculated by dividing the percentage change in output by the percentage change in input.

This process of testing sensitivity for another input (say cash flows growth rate) while keeping the rest of inputs constant is repeated until the sensitivity figure for each of the inputs is obtained. The conclusion would be that the higher the sensitivity figure, the more sensitive the output is to any change in that input and vice versa.

## Methods of Sensitivity Analysis

There are different methods to carry out the sensitivity analysis:

- Modeling and simulation techniques
- Scenario management tools through Microsoft excel

There are mainly two approaches to analyzing sensitivity:

- Local Sensitivity Analysis
- Global Sensitivity Analysis

Local sensitivity analysis is derivative based (numerical or analytical). The term local indicates that the derivatives are taken at a single point. This method is apt for simple cost functions, but not feasible for complex models, like models with discontinuities 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* (OAT) technique that analyzes the impact of one parameter on the cost function at a time, keeping the other parameters fixed.

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

The various techniques widely applied include:

*Differential sensitivity analysis:*It is also referred to the direct method. It involves solving simple partial derivatives to temporal sensitivity analysis. Although this method is computationally efficient, solving equations is intensive task to handle.*One at a time sensitivity measures:*It is the most fundamental method with partial differentiation, in which varying parameters values are taken one at a time. It is also called as local analysis as it is an indicator only for the addressed point estimates and not the entire distribution.*Factorial Analysis:*It involves the selection of given number of samples for a specific parameter and then running the model for the combinations. The outcome is then used to carry out parameter sensitivity.

Through the sensitivity index one can calculate the output % difference when one input parameter varies from minimum to maximum value.

*Correlation analysis*helps in defining the relation between independent and dependent variables.*Regression analysis*is a comprehensive method used to get responses for complex models.*Subjective sensitivity analysis:*In this method the individual parameters are analyzed. This is a subjective method, simple, qualitative and an easy method to rule out input parameters.

## Using Sensitivity Analysis for decision making

One of the key applications of Sensitivity analysis is in the utilization of models by managers and decision-makers. All the content needed for the decision model can be fully utilized only through the repeated application of sensitivity analysis. It helps decision analysts to understand the uncertainties, pros and cons with the limitations and scope of a decision model.

Most if not all decisions are made under uncertainty. It is the optimal solution in decision making for various parameters that are approximations. One approach to come to conclusion is by replacing all the uncertain parameters with expected values and then carry out sensitivity analysis. It would be a breather for a decision maker if he/she has some indication as to how sensitive will the choices be with changes in one or more inputs.

## Uses of Sensitivity Analysis

- The key application of sensitivity analysis is to indicate the sensitivity of simulation to uncertainties in the input values of the model.
- They help in decision making
- Sensitivity analysis is a method for predicting the outcome of a decision if a situation turns out to be different compared to the key predictions.
- It helps in assessing the riskiness of a strategy.
- Helps in identifying how dependent the output is on a particular input value. Analyses if the dependency in turn helps in assessing the risk associated.
- Helps in taking informed and appropriate decisions
- Aids searching for errors in the model