Model assumptions

What Are Model Assumptions?

Model assumptions are the foundational inputs and estimates that underpin any financial model, serving as the starting points or beliefs about future conditions that drive the model's outputs. These assumptions are crucial in financial modeling, a branch of quantitative finance, used to project a company's financial performance, assess investment opportunities, and make strategic decisions. Without clear and defensible model assumptions, a financial model's ability to provide reliable forecasts and support robust valuation efforts would be significantly diminished. They dictate the behavior and results of the model, influencing everything from projected revenues and expenses to cash flow figures and overall risk management strategies.³⁰, ³¹

History and Origin

The concept of using assumptions in financial calculations is as old as finance itself. However, the formalization and scrutiny of model assumptions gained significant prominence with the increasing complexity and widespread use of quantitative models in financial markets, particularly from the late 20th century onward. The 2008 global financial crisis served as a critical turning point, exposing severe vulnerabilities stemming from flawed or inadequately understood model assumptions. Many models, especially those used for valuing complex instruments like credit default swaps and mortgage-backed securities, made independence assumptions that proved to be unrealistic when market conditions deteriorated.²⁸, ²⁹

In response to these failures, regulatory bodies intensified their focus on model risk management. A notable development was the issuance of Supervisory Letter SR 11-7 by the United States Federal Reserve Board and the Office of the Comptroller of the Currency (OCC) in April 2011. This guidance provided a comprehensive framework for banks on managing risks associated with financial models. SR 11-7 explicitly defined a model as "a quantitative method, system, or approach that applies statistical, economic, financial, or mathematical theories, techniques, and assumptions to process input data into quantitative estimates," thereby highlighting the central role of assumptions within a model's structure.²⁶, ²⁷

Key Takeaways

• Foundational Element: Model assumptions are the bedrock of any financial model, directly influencing its outputs and conclusions.
• Driver of Forecasts: They dictate future projections for key financial statements like the income statement, balance sheet, and cash flow statement.
• Source of Model Risk: Inaccurate or poorly understood model assumptions are a primary cause of model risk, potentially leading to significant financial losses or poor decision-making.
• Dynamic Nature: Effective model assumptions are not static; they require continuous review and adjustment based on new information, changing market conditions, and evolving business strategies.
• Transparency and Documentation: Thorough documentation of all model assumptions is essential for transparency, auditability, and effective communication among stakeholders.

Interpreting Model Assumptions

Interpreting model assumptions involves understanding their basis, their impact on the model's outputs, and the degree of confidence one can place in them. Since assumptions reflect beliefs about an uncertain future, they are inherently subjective and require careful evaluation. Analysts often employ techniques such as sensitivity analysis and scenario analysis to test the robustness of their models against varying assumptions.²⁴, ²⁵

• Sensitivity Analysis: This involves changing one input variable (an assumption) at a time to observe its isolated impact on the model's outcome. It helps identify which assumptions are most critical to the final results.
• Scenario Analysis: This method involves simultaneously altering multiple assumptions to reflect different plausible future states (e.g., best-case, worst-case, base-case scenarios). This provides a more holistic view of potential outcomes under different economic or business environments.

By rigorously testing model assumptions, users can gain a clearer understanding of the model's limitations and the range of possible financial outcomes, enabling more informed decision-making.

Hypothetical Example

Consider an analyst building a financial model to forecast the future revenue of a software-as-a-service (SaaS) company. A key model assumption for revenue might be the average monthly churn rate, which is the percentage of customers who cancel their subscriptions each month.

Scenario:

• Current Subscribers: 10,000
• Average Revenue Per User (ARPU): $50
• Historical Churn Rate: 2% per month
• New Customer Growth Assumption: 100 new customers per month

Calculation for next month's subscribers based on initial assumption:

Current subscribers: 10,000
Lost subscribers (churn): (10,000 \times 0.02 = 200)
New subscribers: 100
Next month's subscribers: (10,000 - 200 + 100 = 9,900)

Next month's projected revenue: (9,900 \times 50 = $495,000)

Now, if the analyst were to perform a sensitivity analysis and change the churn rate assumption to 3% (a slightly worse, but still plausible, scenario):

Lost subscribers (churn): (10,000 \times 0.03 = 300)
Next month's subscribers: (10,000 - 300 + 100 = 9,800)

Next month's projected revenue: (9,800 \times 50 = $490,000)

This simple example illustrates how a minor adjustment to a single model assumption—the churn rate—can lead to a significant difference in the forecasted revenue. This impact would compound over longer forecasting periods, underscoring the importance of careful consideration when setting these inputs for financial statements.

Practical Applications

Model assumptions are pervasive across various financial disciplines and industries, forming the backbone of quantitative models used for critical functions:

• Investment Banking and Corporate Finance: In investment banking, analysts use model assumptions extensively in valuation models for mergers and acquisitions, initial public offerings (IPOs), and capital raising. For instance, assumptions about future growth rates, profit margins, and capital expenditures directly impact the projected financial performance of a target company.
• ²², ²³ Risk Management: Financial institutions rely heavily on model assumptions for assessing and managing various types of risk, including credit risk, market risk, and operational risk. Stress testing, a key risk management tool, involves imposing extreme hypothetical scenarios by adjusting underlying assumptions (e.g., sudden interest rate hikes or severe economic recession) to gauge a firm's resilience.
• ²⁰, ²¹ Regulatory Compliance: Regulators, such as the Federal Reserve, mandate robust model risk management frameworks for supervised banking organizations. Supervisory Guidance SR 11-7 outlines expectations for how model assumptions should be developed, documented, and validated to ensure compliance and mitigate systemic risk.
• ¹⁹ Portfolio Management: Portfolio managers use assumptions about asset class returns, volatilities, and correlations to construct diversified portfolios and optimize asset allocation strategies. These quantitative models guide decisions on where to invest capital to meet specific return objectives while adhering to risk tolerances.
• Actuarial Science and Insurance: Actuaries build complex models using demographic and economic assumptions to price insurance products, calculate reserves, and manage long-term liabilities. Assumptions about mortality rates, policyholder behavior, and investment returns are paramount.

Limitations and Criticisms

Despite their indispensable role, model assumptions come with inherent limitations and are subject to significant criticism. A central challenge is that models are simplified representations of complex real-world phenomena. Therefore, the assumptions made to simplify reality may not fully capture all nuances, leading to potential inaccuracies.

On¹⁸e major criticism, highlighted during the 2008 financial crisis, is the danger of "model on, brain off" — an over-reliance on model outputs without critical thought about the underlying assumptions. For instance, models used to price mortgage-backed securities often assumed low correlations between individual mortgage defaults, which proved catastrophically wrong during the widespread housing market collapse.

Eman¹⁶, ¹⁷uel Derman, a prominent quantitative analyst, argues that "finance isn't science" in the same way physics is; financial models are attempts to "capture human emotions and instinctual feelings" rather than absolute physical laws. He emphasizes that models tell us "what something is like" rather than "what something is," implying that their predictive power is limited by the subjective and ever-changing nature of human behavior in markets. Econo¹⁵mic models, in particular, have often failed to predict significant downturns, partly due to their simplifying assumptions about how economic agents interact or their dismissal of "outliers" that don't fit statistical theories.

Furt¹⁴hermore, the process of setting model assumptions can be prone to human biases, such as confirmation bias, where analysts might consciously or unconsciously select assumptions that lead to a desired outcome. The complexity of some models can also make it difficult to fully comprehend all underlying assumptions, particularly when models are developed by different individuals or teams and lack comprehensive documentation.

Char¹³les W. Calomiris's work on model risk and the Great Financial Crisis also points to the failure of "economic capital models" used by large banks prior to 2008, noting that overly optimistic assumptions about market liquidity and correlations led to an underestimation of required capital.

M¹²odel Assumptions vs. Model Validation

Model assumptions and model validation are inextricably linked but represent distinct concepts within the broader field of financial modeling.

Model Assumptions refer to the specific inputs, parameters, and beliefs about future conditions that are explicitly or implicitly built into a financial model. These are the "givens" or estimates upon which the model's logic and calculations are based. For example, in a discounted cash flow (DCF) model, assumptions include revenue growth rates, expense ratios, discount rates, and terminal growth rates. They are the initial premises of the model.

Model Validation, on the other hand, is the process of independently verifying that a model is performing as intended, its methodology is sound, and its outputs are accurate and reliable. A critical component of model validation is the rigorous assessment of the underlying model assumptions. This involves:

• Challenging Assumptions: Reviewing whether the assumptions are reasonable, well-supported by data and expert judgment, and appropriate for the model's intended use.
• Testing Sensitivity: Analyzing how changes in assumptions affect the model's output to understand its robustness.
• Data Quality: Ensuring that the data used to derive or support assumptions is accurate, relevant, and complete.

While model assumptions are the building blocks of a financial model, model validation is the quality assurance process that scrutinizes those blocks and the overall structure to ensure the model's integrity and fitness for purpose. Effective model validation provides assurance that the model, including its embedded model assumptions, can be relied upon for decision-making.

F⁹, ¹⁰, ¹¹AQs

Why are model assumptions important?

Model assumptions are critical because they are the foundation upon which all financial forecasts and analyses are built. They directly influence the outputs of a financial model, determining its accuracy and reliability for making investment decisions, managing risk, and planning business strategies.

⁷, ⁸How do you identify good model assumptions?

Identifying sound model assumptions involves a combination of historical data analysis, industry benchmarking, market trend assessment, and expert judgment. Good assumptions are reasonable, well-documented, and based on defensible logic, reflecting realistic future conditions rather than overly optimistic or pessimistic views.

⁵, ⁶Can model assumptions change?

Yes, model assumptions should be dynamic and subject to change. As new information becomes available, market conditions evolve, or business strategies shift, the underlying assumptions of a financial model must be reviewed and updated to maintain the model's relevance and accuracy.

⁴What happens if model assumptions are wrong?

If model assumptions are incorrect or flawed, the model's outputs will be inaccurate, leading to potentially poor financial decisions, misjudged risks, and erroneous valuations. This can result in significant financial losses, reputational damage, or a misallocation of resources for a company or investor.¹, ², ³