March 29, 2018
The technique used to determine how independent variable values will impact a particular dependent variable under a given set of assumptions is defined as sensitive 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.
It helps in analyzing how sensitive the output is, by the changes in one input while keeping the other inputs constant.
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
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 till 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.
There are different methods to carry out the sensitivity analysis:
There are mainly two approaches to analyzing sensitivity:
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:
Through the sensitivity index one can calculate the output % difference when one input parameter varies from minimum to maximum value.
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.
Sensitivity analysis is one of the tools that help decision makers with more than a solution to a problem. It provides an appropriate insight into the problems associated with the model under reference. Finally the decision maker gets a decent idea about how sensitive is the optimum solution chosen by him to any changes in the input values of one or more parameters.