Sensitivitatsanalyse

What Is Sensitivitätsanalyse?

Sensitivitätsanalyse, also known as sensitivity analysis or "what-if" analysis, is a financial modeling and Risikomanagement technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions. Within the broader field of quantitative analysis and Finanzmodellierung, it helps to assess the robustness of forecasts and investment decisions by examining how sensitive an output (e.g., net present value, profit) is to changes in inputs (e.g., sales volume, interest rates). The core purpose of Sensitivitätsanalyse is to identify which Eingabeparameter have the most significant influence on a model's Ausgabegröße, thereby providing insights into potential risks and uncertainties.

²⁰, ²¹History and Origin

The conceptual roots of sensitivity analysis can be traced back to the mid-20th century, emerging prominently within the field of Operations Research and management sciences. As quantitative models became more sophisticated and computational power increased, the need arose to understand how uncertainties in input variables propagated through these models to affect their outputs. Early applications were often tied to optimization problems, such as those found in linear programming, where analysts sought to understand how the optimal solution changed if the problem's parameters were altered. Over decades, driven by advances in numerical methods and computing capabilities, sensitivity analysis evolved into a formal discipline, becoming an essential tool across various fields, including economics, engineering, and finance. The ¹⁷, ¹⁸, ¹⁹Institute for Operations Research and the Management Sciences (INFORMS) provides further historical context on the development of this analytical approach.

¹⁶Key Takeaways

• Sensitivitätsanalyse evaluates how an output changes when a single input variable is altered, holding all other variables constant.
• I¹⁵t helps identify the most critical input factors that significantly impact a financial model's outcome.
• This analysis is a crucial component of Risikomanagement, aiding in the understanding and quantification of Wirtschaftliche Unsicherheit.
• It supports informed Anlageentscheidung by highlighting areas of potential Variabilität and risk.
• While powerful, Sensitivitätsanalyse is dependent on the underlying model's assumptions and does not predict the likelihood of parameter changes.

Formula and Calculation

Sensitivitätsanalyse does not rely on a single, universal formula but rather a methodological approach to quantify the relationship between input changes and output results. Conceptually, the sensitivity of an output (Y) to a particular input (X) can be thought of as the partial derivative of (Y) with respect to (X), or for discrete changes, the ratio of the change in output to the change in input.

The general principle involves:

1. Identifying a base case: Establish a set of initial, most likely values for all input parameters.
2. Selecting an input variable: Choose one specific Eingabeparameter to vary.
3. Varying the input: Systematically change the selected input variable by a predetermined percentage (e.g., (\pm 10%), (\pm 20%) or across a defined range.
4. Recalculating the output: Rerun the model with the altered input, keeping all other variables at their base case values.
5. Observing the change: Note the corresponding change in the model's Ausgabegröße.

The "sensitivity coefficient" or percentage change can be expressed as:

Where:

• (% \Delta \text{Ausgabe}) = Percentage change in the model's output.
• (% \Delta \text{Eingabe}) = Percentage change in the specific input variable.

This calculation helps quantify how responsive the output is to shifts in individual inputs. For instance, in a Kapitalbudgetierung model, one might assess how the Netto-Barwert changes with a 5% increase or decrease in sales volume.

Interpreting the Sensitivitätsanalyse

Interpreting the results of a Sensitivitätsanalyse involves understanding the degree to which changes in specific input variables affect the model's output. A higher sensitivity coefficient for a particular input indicates that small changes in that input will lead to proportionally larger changes in the output. This highlights critical variables that warrant closer scrutiny or more robust forecasting. Conversely, inputs with low sensitivity coefficients have less impact on the outcome, meaning less precision is required in their estimation.

The analysis provides context for evaluating financial metrics by revealing their inherent volatility. For example, if a project's Interner Zinsfuß is highly sensitive to the cost of raw materials, management knows that accurately predicting and controlling these costs is paramount to the project's success. It guides decision-makers to focus their efforts and resources on managing the most impactful Eingabeparameter, thereby enhancing the reliability of their Finanzprognose and overall financial planning.

Hypothetical Example

Consider a company, "TechInnovate GmbH," evaluating a new product launch. The core financial model for this project forecasts a Netto-Barwert (NPV) of €5 million based on a set of base case assumptions:

• Initial Investment: €10 million
• Annual Sales Volume: 100,000 units
• Unit Price: €150
• Unit Variable Cost: €70
• Fixed Costs: €2 million per year
• Discount Rate: 10%
• Project Life: 5 years

To perform a Sensitivitätsanalyse, TechInnovate GmbH decides to examine the impact of a (\pm 10%) change in annual sales volume on the NPV, holding all other variables constant.

Base Case NPV: €5 million

Scenario 1: Sales Volume increases by 10% (110,000 units)

• New Annual Sales Revenue: (110,000 \times €150 = €16.5) million
• New Annual Variable Costs: (110,000 \times €70 = €7.7) million
• Recalculating the cash flows and NPV with these changes, the new NPV is, for example, €8 million.
• Change in NPV: (€8 \text{ million} - €5 \text{ million} = €3 \text{ million})

Scenario 2: Sales Volume decreases by 10% (90,000 units)

• New Annual Sales Revenue: (90,000 \times €150 = €13.5) million
• New Annual Variable Costs: (90,000 \times €70 = €6.3) million
• Recalculating the cash flows and NPV, the new NPV is, for example, €1.5 million.
• Change in NPV: (€1.5 \text{ million} - €5 \text{ million} = -€3.5 \text{ million})

From this simple Sensitivitätsanalyse, TechInnovate GmbH can see that a 10% change in sales volume leads to a significant percentage change in NPV (a 60% increase for a 10% sales increase, and a 70% decrease for a 10% sales decrease). This indicates that sales volume is a highly sensitive Eingabeparameter for this project's profitability, making it a critical focus for market research and sales strategy.

Practical Applications

Sensitivitätsanalyse is a versatile tool with numerous applications across finance, investment, and business planning. It is widely used in Kapitalbudgetierung to assess the impact of varying project variables (like sales, costs, or discount rates) on key metrics such as Netto-Barwert or Interner Zinsfuß. In Unternehmensbewertung, analysts use it to understand how changes in growth rates, profit margins, or discount rates affect a company's intrinsic value.

Financial institutions, especially banks, employ Sensitivitätsanalyse extensively in Stresstest scenarios. Regulators, such as the Federal Reserve, mandate stress tests for large banks to assess their resilience to various adverse economic conditions, where sensitivity analysis plays a crucial role in understanding how specific macroeconomic variables affect bank capital. The Federal Reserve Bank of San Francisco provides insights int¹², ¹³, ¹⁴o how stress testing helps evaluate financial stability. Furthermore, in project management, it helps identify the proje¹¹ct variables that pose the greatest risk to success, allowing managers to allocate resources more effectively to mitigate those risks.

Limitations and Criticisms

Despite its utility, Sensitivit¹⁰ätsanalyse has several limitations. A primary criticism is that it typically analyzes the impact of changing one input variable at a time, assuming all other variables remain constant. This "one-at-a-time" (OAT) approach may not accurately reflect real-world scenarios where multiple variables often change simultaneously and interact with each other. For example, a decrease in sales volume might also coincide with a decrease in unit price due to market competition, an interaction that a simple OAT sensitivity analysis might overlook.

Another limitation is that Sensitivitätsanalyse identifies crit⁹ical variables but does not quantify the probability of changes occurring or the likelihood of an adverse outcome. It highlights "what could happen" but not "how likely it is to happen." This can lead to a false sense of security or an overemphasis on improbable risks. Furthermore, the quality of the analysis is entirely dependent on the accuracy of the underlying financial model and the initial assumptions. Flawed models or unrealistic base case assumptions will yield misleading sensitivity results. Regulators, like the Office of the Comptroller of the Currency (OCC), emphasize the importance of robust Risikomanagement for models to mitigate potential adverse consequences from incorrect or misused model outputs. The CFA Institute also provides guidance on best practices for ma⁶, ⁷, ⁸naging model risk.

Sensitivitätsanalyse vs. Szenarioanalyse

Sensitivitätsanalys⁵e and Szenarioanalyse are both tools for assessing uncertainty in financial models, but they differ in their approach. The key distinction lies in the number of variables changed and the nature of the assumptions.

While Sensitivitätsanalyse isolates the effect of individual changes, Szenarioanalyse creates comprehensive, internally consistent views of the future, such as an optimistic scenario (e.g., high sales, low costs) or a pessimistic scenario (e.g., low sales, high costs, economic recession). They are complementary techniques; sensitivity analysis can identify ⁴which variables to include in scenarios, while scenario analysis provides a more holistic view of combined impacts.

FAQs

What is the primary goal of Sensitivitätsanalyse?

The primary goal of Sensitivitätsanalyse is to understand how the output of a model changes when individual input variables are altered. It aims to identify the most critical or impactful Eingabeparameter that significantly influence the final outcome, thus highlighting areas of greater risk or opportunity.

How does Sensitivitätsanalyse help in decision-making?

Sensitivitä², ³tsanalyse helps in decision-making by revealing which variables have the greatest impact on a project's viability or a company's financial performance. This knowledge allows decision-makers to focus their efforts on obtaining more precise forecasts for highly sensitive variables or developing contingency plans to mitigate associated risks, thereby making more informed Anlageentscheidung.

Is Sensitivitätsanalyse sufficient for comprehensive risk assessment¹?

No, Sensitivitätsanalyse is a valuable but not sufficient tool for comprehensive Risikomanagement. It typically analyzes one variable at a time, which may not capture the complex interplay of multiple changing factors in the real world. For a more holistic view, it should be complemented by other techniques like Szenarioanalyse or Monte Carlo simulations, which consider simultaneous variations and probabilities.

Can Sensitivitätsanalyse predict future outcomes?

Sensitivitätsanalyse does not predict future outcomes. Instead, it quantifies the impact of hypothetical changes to input variables on an output, given the existing model structure and assumptions. It provides insights into the "what-if" aspects of a situation rather than offering a probabilistic forecast of what will happen.