# Sensitivity Analysis Definition

Sensitivity analysis consists of studying the effects of changes in variables on the outcomes of a mathematical model. Furthermore, a model may consist of numerous input variables and one or more output variables. By changing an input variable, and measuring how the outcomes are affected by that change, the analyst can gauge how sensitive the model is to the individual input variable.

## Sensitivity Analysis in Business Decision-Making

Use sensitivity analysis in business decision-making. It is a way of measuring and quantifying uncertainty. The analyst can create a model based on the relationships between inputs and outputs. Once the model is set up, the analyst can tweak the inputs to see how the outputs are affected. The analyst can also alter the model to create hypothetical scenarios such as a best case scenario, a worst case scenario, and a most likely scenario.

For example, an analyst might use sensitivity analysis to measure a project’s net present value (NPV) for various expectations of costs, revenues, capital investment, macroeconomic factors, and other relevant variables.

## Problems with Sensitivity Analysis

First, the accuracy of the sensitivity analysis depends on the quality of the assumptions built into the model. If the model contains erroneous assumptions, then the output of the sensitivity analysis will be inaccurate. Second, sensitivity analysis may not account for interdependencies among input variables. Finally, the assumptions built into the model may be based on historical data. Therefore, it cannot necessarily be relied upon to predict future results. Also, subjectivity may taint the analysis.

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# Arbitrage Pricing Theory Definition

The arbitrage pricing theory (APT) is a multifactor mathematical model used to describe the relation between the risk and expected return of securities in financial markets. It computes the expected return on a security based on the security’s sensitivity to movements in macroeconomic factors. Then use the resultant expected return to price the security.

The arbitrage pricing theory is based on three assumptions. First, that a factor model can be used to describe the relation between the risk and return of a security. Then, idiosyncratic risk can be diversified away. Finally, efficient financial markets do not allow for persisting arbitrage opportunities.

In addition, the arbitrage pricing theory calculates the expected return for a security based on the security’s sensitivity to movements in multiple macroeconomic factors. Whereas the standard capital asset pricing model (CAPM) is a single factor model, incorporating the systematic and firm specific risk related to the overall market return, the arbitrage pricing theory is a multifactor model.

Then, set up the arbitrage pricing theory to consider several risk factors, such as the business cycle, interest rates, inflation rates, and energy prices. The model distinguishes between both systematic risk and firm-specific risk. It also incorporates both types of risk into the model for each given factor.

## Arbitrage Pricing Theory Formula

The formula includes a variable for each factor, and then a factor beta for each factor, representing the security’s sensitivity to movements in that factor. Because it includes more factors, consider the arbitrage pricing theory more nuanced – if not more accurate, than the capital asset pricing model.

A two-factor version of the arbitrage pricing theory formula is as follows:

r = E(r) + B1F1 + B2F2 + e

r = return on the security
E(r) = expected return on the security
F1 = the first factor
B1 = the security’s sensitivity to movements in the first factor
F2 = the second factor
B2 = the security’s sensitivity to movements in the second factor
e = the idiosyncratic component of the security’s return Strategic CFO Lab Member Extra

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