What Is Sensitivity Analysis?
Sensitivity analysis is an analysis technique that works on the basis of what-if analysis like how independent factors can affect the dependent factor and is used to predict the outcome when analysis is performed under certain conditions.
It is commonly used by investors who take into consideration the conditions that affect their potential investment to test, predict and evaluate results. There are different methods that help conduct this analysis to provide conclusions as accurate and reliable as possible.
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Sensitivity Analysis Explained
Sensitivity analysis, as the name suggests, observes how sensitive a dependent variable is to the changes in the value of the independent variables being used in the process. Conducting this analysis helps users determine how the uncertainty of an independent variable makes a financial model subject to a certain level of uncertainty.
It is similar to the what-if approach where analysts learn about what would happen to a model or assumption if the scenario changes. This technique is widely used by analysts in the financial industry as they get to determine or assess how the financial models would perform when the independent variables are sensitive to fluctuations and likely to cause the dependent variable to change with respect to the same.
Sensitivity analysis can be of two forms – local and global sensitivity analyses.
#1 – Local Sensitivity Analysis
The local method, as the name suggests, includes obtaining data from one single point. It is based on derivatives, which can either be numerical or analytical. takes into consideration one parameter at a time to study its effect on the entire process. In the process, the rest of the parameters or variables are kept constant.
This method is suitable when the analysis is conducted to serve simple purposes, like cost functions, etc. However, it is not recommended for complex models as the derivatives are local and may not represent an ideal dataset.
#2 – Global Sensitivity Analysis
Global analysis, on the other hand, is the method that considers a wide array of datasets from different points to analyze the data on q wider space. It uses Monte Carlo techniques, along with other methods as well that have been listed as follows:
- Differential sensitivity analysis: It is a direct method where the independent variable’s coefficient is calculated from the dependent variable’s partial derivative. The calculation is done with respect to the independent variables. Though this method is good to go, solving complex equations becomes difficult.
- Factorial analysis: This method involves selecting samples based on specific parameters and then figuring out combinations. The resultant is used for further parameter analysis.
The formula for sensitivity analysis is basically a financial model in excel where the analyst is required to identify the key variables for the output formula and then assess the output based on different combinations of the independent variables.
Mathematically, the dependent output formula is represented as,
How To Do?
There is a series of sensitivity analysis methods that one must be aware of before conducting it. Knowing this helps users deploy the required measures wisely to obtain more reliable results. Let us have a look at the step-by-step process:
- Firstly, the analyst is required to design the basic formula, which will act as the output formula. For instance, say NPV formula can be taken as the output formula.
- Next, the analyst needs to identify which are the variables that are required to be sensitized as they are key to the output formula. In the NPV formula in excel, the cost of capital and the initial investment can be the independent variables.
- Next, determine the probable range of the independent variables.
- Next, open an excel sheet and then put the range of one of the independent variable along the rows and the other set along with the columns.
- Range of 1st independent variable
- Range of 2nd independent variable
Let us consider the following examples to check how to do sensitivity analysis in Excel on the data provided:
Let us take the example of a simple output formula, which is stated as the summation of the square of two independent variables X and Y.
In this case, let us assume the range of X as 2, 4, 6, 8, and 10, while that of Y as 1, 3, 5, 7, 9, 11, and 13. Based on the above-mentioned technique, all the combinations of the two independent variables will be calculated to assess the sensitivity of the output.
For instance, if X = 3 (Cell B2) and Y = 7 (Cell B3), then Z = 32 + 72 = 58 (Cell B4)
Z = 58
For the calculation of Sensitivity Analysis, go to the Data tab in excel and then select What if analysis option. For the further procedure of sensitivity analysis calculation, refer to the given article here – Two-Variable Data Table in ExcelTwo-Variable Data Table In ExcelA two-variable data table helps analyze how two different variables impact the overall data table. In simple terms, it helps determine what effect does changing the two variables have on the result.
Let us take another example of bond pricing where the analyst has identified the coupon rate and the yield to maturity as the independent variables, and the dependent output formula is the bond price. The coupon is paid half-yearly with a par value of $1,000, and the bond is expected to mature in five years. Determine the sensitivity of the bond price for different values of coupon rate and yield to maturityYield To MaturityThe yield to maturity refers to the expected returns an investor anticipates after keeping the bond intact till the maturity date. In other words, a bond's returns are scheduled after making all the payments on time throughout the life of a bond. Unlike current yield, which measures the present value of the bond, the yield to maturity measures the value of the bond at the end of the term of a bond..
In this case, the analyst has taken the range of coupon rate as 5.00%, 5.50%, 6.00%, 6.50%, and 7.00%, while that of coupon rate as 5%, 6%, 7%, 8%, and 9%. Based on the above-mentioned technique, all the combinations of yield to maturity and coupon rateCoupon RateThe coupon rate is the ROI (rate of interest) paid on the bond's face value by the bond's issuers. It determines the repayment amount made by GIS (guaranteed income security). Coupon Rate = Annualized Interest Payment / Par Value of Bond * 100% are taken to calculate the sensitivity of the bond priceBond PriceThe bond pricing formula calculates the present value of the probable future cash flows, which include coupon payments and the par value, which is the redemption amount at maturity. The yield to maturity (YTM) refers to the rate of interest used to discount future cash flows..
Therefore, the calculation of Bond Price is as follows.
Bond Price =$102,160
For the calculation of Sensitivity Analysis, go to the Data tab in excel and then select What if analysis option.
Advantages & Disadvantages
It is vital to learn about the pros and cons of the process to understand the sensitivity analysis meaning better. For investors and financial analysts, it is significant to explore the positives and negatives of this analysis so that they can decide on its use further:
|It is an in-depth analysis where users get a chance to analyse each and every variable individually.
|It is an assumption-based analysis.
|When the study is deep, the users learn about the weak points and therefore, they prepare themselves even for the worst situations.
|It considers each variable individually for outcomes. But in reality, the variables are inter-related and cannot stand alone.
|Investment decisions are wisely made after a thorough analysis.
|Allocation of resources is done better when the strengths and weaknesses are identified.
A sensitivity analysis is a technique which uses data tableUses Data TableA data table in excel is a type of what-if analysis tool that allows you to compare variables and see how they impact the result and overall data. It can be found under the data tab in the what-if analysis section. and is one of the powerful excel tools which lets a financial user understand the result of the financial model under various conditions. It can also be seen as the perfect complement to another excel tool, which is known as the scenario managerScenario ManagerScenario Manager is a what-if analysis tool that works with many scenarios that are supplied to it. It uses a set of ranges that have an effect on a certain output and can be used to generate different scenarios such as bad and medium depending on the values., and as such, it adds more flexibility to the valuation model during the process of analysis and, finally, in case of the presentation.
As such, it is very important for an analyst to appreciate the method of creation of a data table and then interpret its results to ensure that the analysis is heading in the desired direction. Further, a data table can be an effective and efficient way for presentation to the boss or client when it comes to expected financial performance under different circumstances.
This has been a guide to what is Sensitivity Analysis. We explain it with examples, formula, how to do it, types, advantages, disadvantages & importance. You can learn more about financial modeling from the following articles –
- Top Advantages and Disadvantages of NPV
- Marginal Cost of CapitalMarginal Cost Of CapitalMarginal Cost of Capital is the total combined cost of debt, equity, and preference taking into account their respective weights in the total capital of the company. It denotes the cost of raising any additional capital and decision making options.
- One Variable Data Table in ExcelOne Variable Data Table In ExcelOne variable data table in excel means changing one variable with multiple options and getting the results for multiple scenarios. The data inputs in one variable data table are either in a single column or across a row.
- Regression Excel Analysis