# Sensitivity: Overview, Benefits, Examples

## What Is Sensitivity?

In finance, sensitivity is the magnitude of a market instrument's reaction to changes in underlying factors, most often in terms of its price response to other factors. Financial instruments, such as stocks and bonds, are constantly influenced directly and indirectly by a myriad of factors. Sensitivity accounts for these factors that impact a given instrument in either a negative or positive way.

The objective of sensitivity analysis is to learn how much a certain factor impacts the value of a particular instrument.

### Key Takeaways

• Sensitivity refers to the impact on a security given a change in some relevant factor.
• A bond, for instance is measured by its price sensitivity to interest rate changes (its duration), as well as the duration's sensitivity itself to changes in rates (its convexity).
• Sensitivity analysis determines how different values of an independent variable affect a particular dependent variable under a given set of assumptions.

## Understanding Sensitivity

Sensitivity determines how an investment changes with fluctuations in outside factors. Stocks and bonds are especially sensitive to interest rate changes. The discount rate is an important factor in deriving the theoretical value of stocks. Also on a macro level, changes in economic growth and inflation rates are influential on the value of stocks and bonds. Sensitivity analysis is also conducted on a micro level. A company may want to know the sensitivity of its revenues to a product price change, for example.

## Example: Bond Sensitivity

Fixed-income investments are very sensitive to interest rate changes. A bond's duration reflects changes in the bond's price for each 1% fluctuation of the interest rate. For example, a bond with a duration of four means the bond price decreases/increases 4% for every 1% increase/decrease in interest rate. A bond with a long maturity and low coupon has a longer duration and therefore is more sensitive to rate fluctuations.

Meanwhile, a bond's convexity is a measure of the curvature, or the degree of the curve, in the relationship between bond prices and bond yields. Convexity demonstrates the sensitivity of the duration of a bond changes as the interest rate changes. Portfolio managers will use convexity as a risk-management tool, to measure and manage the portfolio's exposure to interest rate risk.

Buying a bond at a low-interest rate means the bond will be less valuable when rates rise and other bond yields are higher. This is simply because fixed-income investors will buy the higher-yielding bond, all else equal. Assets that are considered fixed income-like such as utility stocks and preferred stocks are two examples of rate-sensitive assets.

## Benefits of Sensitivity Analysis

Sensitivity analysis helps determine how stock and bond valuations move with changes in key variables. An investor needs to determine how certain changes in variables will affect potential returns. Criteria for success, a set of input values, a range over which the values can move, and minimum and maximum values for variables must be preset to determine whether the desired outcome has been reached. After determining profitability forecasts, an investor can make better-educated decisions regarding where to place assets while reducing risks and potential error. Sensitivity analysis is at the heart of risk models.

A wide array of modelers in the banking and insurance sectors rely on running multiple changes of variables in their models to see results of what-if scenarios. Across all other corporate industries, treasury and finance departments are increasingly being required to disclose sensitivity analysis or other risk measurements in financial statements.

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