# What is Sensitivity Analysis?

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Definition:

A sensitivity analysis is a financial modeling tool that explores how the outcome of a decision shifts based on changes in variables that affect it.

## 🤔 Understanding sensitivity analyses

Investing and most financial decisions are based on many assumptions, but nothing is certain. Sensitivity analysis is one way to explore how changes in conditions might affect your results. Sensitivity analysis is a financial modeling tool that helps you analyze how different values of a given variable (a factor that can vary) affect the outcome, assuming other conditions stay the same. This tool is often known as a “what-if” analysis or a simulation analysis because it helps you predict how an outcome might change “if” a variable in that situation changes. For example, it can help you estimate how changes in inflation might affect interest rates or how variations in material costs will affect profit.

Example

Let’s say you run a coffee shop in a mall, and you know it is busiest in December. If you’d like to know how the increased foot traffic might impact your revenue, you can conduct a sensitivity analysis.

You could start by taking your average coffee price of \$3 and multiplying it by the average number of cups sold for each of the last five Decembers. Let’s say you sold 10,000 cups of coffee to make \$30,000 worth of income. You might then look at how a drop or increase in foot traffic might affect your sales.

For example, if the mall’s footfall drops by 10% this December, you might be looking at a \$3,000 drop in sales. On the flip side, a 25% increase in shoppers might boost your sales by \$7,500. As a result of your sensitivity analysis, you now have a rough idea of how the mall’s foot traffic will impact your sales.

## Takeaway

A sensitivity analysis is like a 10-day weather forecast…

A 10-day forecast gives you a rough idea of whether it’s going to rain next Saturday. The prediction is based on the typical weather this time of year and conditions at this precise moment. But the weather can change fast. By the time Saturday rolls around, the forecast might turn out to be wrong. A sensitivity analysis works the same way: It can use historical data to predict what might happen in a given situation, but that prediction isn’t necessarily going to be right.

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## What is a sensitivity analysis?

A sensitivity analysis is a financial modeling tool companies use to determine how changes to a given variable might affect an outcome, assuming other conditions stay the same. It’s also called a “what-if” analysis or a simulation analysis.

To conduct a sensitivity analysis, you need to consider two types of variables: input variables and target variables.

An input variable, also known as an independent variable, is a condition you can change in an experiment or simulation. It isn’t affected by any other variables involved.

A target variable (or dependent variable) is the condition you typically measure in an experiment. Companies conduct a sensitivity analysis by looking at how changes to an input variable might affect a target variable.

You can use a sensitivity analysis to test a wide range of variables. For example, if you run a small bakery, you might do one to work out how an increase in the price of cocoa could impact your annual profit. By looking at changes in the price of cocoa price (your input variable), you’d be able to assess how your profit (your target variable) goes up or down.

Analysts also often use what-if simulations to predict how the stock prices of public companies may change by looking at variables like quarterly earnings and financial ratios.

Although it may sound a bit complicated to run mathematical models like a sensitivity analysis, it can often be a relatively simple process. Tools like Microsoft Excel come with pre-installed features that can run a sensitivity analysis based on what you enter into a spreadsheet.

## What is the purpose of sensitivity analysis?

The purpose of a sensitivity analysis is to help companies and investors make more informed decisions. By conducting a sensitivity analysis, they can get a better idea of how different variables affect outcomes by simulating changes.

For example, you might want to look at how a decrease in shareholder dividends may affect the price of shares in a publicly traded company. Those simulations could inform your decision making process about whether to invest in that company’s stock.

Sensitivity analyses also enable companies to explore which elements of their business operations are more sensitive to change than others. If a particular variable experiences big fluctuations when one or more factors change in a simulation, that could mean a company needs to think about how to make that business element more resilient. That’s why companies often carry out sensitivity analyses as part of their risk analysis strategies.

## How does sensitivity analysis work?

A sensitivity analysis works by exploring how a change in one variable can affect an outcome, if other variables stay the same.

Again, a sensitivity analysis uses two types of variables: input variables and target variables. Input variables are the fields in which you’d like to make changes to see how they affect a given target variable. Target variables are the fields in which you’d like to measure the effects of changes.

By making changes to one input variable at a time, a “what if” analysis can demonstrate what impact (if any) those changes may have on your target variable.

When performing a sensitivity analysis, only change one input variable at a time. If you change too many fields simultaneously, you won’t know which variables did or didn’t affect an outcome. You can try changing other input variables later — Just make sure you only alter one at a time.

## What are the methods of measurement for sensitivity analysis?

A sensitivity analysis measures the sensitivity of a target variable when input variables change. In other words, it measures how the value of one thing changes when the value of something else goes up or down.

The most common type of measurement technique is the “one-at-a-time” (OAT) method. The OAT method measures how an outcome shifts when the value of one input variable changes. You measure how something responds to a single change and then repeat the simulation by changing another input variable.

A different method to measure sensitivity is the Monte Carlo technique. This one is slightly more complicated and uses probability distribution and big sample sizes to run lots of simulations at the same time.

## What are the types of sensitivity analysis?

There are two main types of sensitivity analysis: local sensitivity analysis and global sensitivity analysis.

### Local sensitivity analysis

A local sensitivity analysis takes a one-at-a-time approach, changing one variable at a time and keeping others fixed in order to see the effect on the outcome. The method can be used for simple “what if” questions, but doesn’t work for more complex models.

### Global sensitivity analysis

A global sensitivity analysis uses values brought in from a representative set of samples to conduct simulations. This is often done as part of a Monte Carlo simulation — a type of global sensitivity analysis that looks at how the probability of an outcome can change by systematically substituting the numbers in the input field.

## How is sensitivity analysis used?

A sensitivity analysis is used to figure out how changes in a given variable affects the outcome of a decision.

Companies can use it to simulate how changes in one business area might impact another. For example, a business could test how lowering the price of a product would affect sales numbers. Knowing this outcome would help managers decide whether changing the price is a good idea.

Sensitivity analysis can also examine how external changes could impact a company — for example, how a drop in footfall at a mall affects sales of a particular item.

Sensitivity simulations are also often used by analysts to work out whether the share price of a company’s stock might be overvalued or undervalued, and if buying or selling those shares is a smart move.

On the whole, sensitivity analysis can help you understand risk by estimating what happens if any of your initial assumptions are incorrect.

## What is the difference between sensitivity and scenario analysis?

A sensitivity analysis and a scenario analysis are both models used to simulate future risks, but they aren’t the same.

Although a sensitivity analysis may look at a wide range of variables to predict an outcome, a simulation must isolate each variable and change them one at a time. This helps you understand how a change in one variable affects your results.

A scenario analysis works differently. It involves considering what outcomes are possible under a variety of possible future scenarios. Often, it looks at the best-case scenario (all inputs assume the best projections), worst-case scenario (all inputs are the worst possible), and base case (average) scenario (all inputs are set to average). Knowing these potential outcomes can help investors and leaders make better decisions.

For example, a scenario analysis might look at all the elements of your business in the event of a financial crash and run the three different scenarios. You can estimate what happens to your profits if all inputs are as rosy as can be under the circumstances, if they get as bad as possible, or if they remain average for historical crashes.

## What are the benefits and limitations of sensitivity analysis?

Sensitivity analyses can help decision-makers come up with better-informed choices to steer their businesses. But like any financial modeling tool, they come with advantages and disadvantages.

One of the benefits of conducting a sensitivity analysis is that it enables companies to carry out in-depth studies on each variable in a given scenario. What-if simulations can explore how both direct and indirect changes to a variable affects the business.

A direct change is when you use specific data to make changes to a variable field, and an indirect change is when you change a variable by a certain percentage. For example, say you want to test how your sales change every time footfall increases in your store by 5%. You’d be making an indirect change to your input variable. By contrast, you could test how sales change when footfall reaches specific points (50, 100, and 125 customers). Because the changes don’t match an incremental percentage increase, that would be a direct change to your input variable.

The resulting play-by-play analysis helps companies and investors understand future risks and make more reliable predictions to drive business decisions. A sensitivity analysis can also show companies areas that need improvement. For example, if one element of your supply chain is negatively affected by changes in base interest rates, a sensitivity analysis can help you predict when to act in order to lessen or avoid those impacts.

But there is also a major limitation to sensitivity analyses: the results are not always robust. Although simulations can help you look at the potential impact of changes, your analysis only offers predictions based on historical data. That’s why it can be worth taking the results of a sensitivity analysis with a grain of salt.

## How do you perform a sensitivity analysis?

To do a sensitivity analysis, start by considering which variables you’d like to explore as part of the simulation. Choose the target variable you’ll be measuring for sensitivity and the independent variable you’d like to change. All other inputs should be kept the same.

Next, change the value of the independent variable. Depending on the type of sensitivity analysis you’ve chosen, this could be a percentage increase to a value you’ve chosen, or it could be a specific value.

When you change the input of one independent variable, keep all other variables constant — Otherwise, it’ll be difficult to figure out how changes to one field affect the others.

You should then be able to assess how changing the value of that single variable affects your target variable or outcome. You can then continue testing other independent variables. Again, be sure you’re only changing one variable at a time.

Depending on the data you’re working with, you may be able to perform a local sensitivity analysis on your own relatively easily. But if you’re working with more complicated figures, or if you’d like to conduct a global sensitivity analysis, you may need to use software to complete the simulation.

## How do you calculate a sensitivity analysis?

If you’re working with Microsoft Excel or a similar application, calculating a sensitivity analysis can be a relatively easy process.

First, create a standard format table in Excel with all the variables you’d like to include. Add an extra column at the end and label it as the independent variable you’d like to experiment with. Finally, highlight the table, navigate to the “data” dropdown, and click on “what-if analysis.”

Then just tell Excel which column you’d like to change and enter the change you’d like to make.

Let’s say you want to see how a 10% increase in prices might affect your sales revenue. That should automatically change the values in your input variable column, and you’ll be able to see how rising prices affect how much money you bring in.

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