Dynamic financial modeling versus traditional and statistical models

Financial modeling is the foundation for forecasting and valuation. It ultimately determines the relative values of a company’s securities which investors use to make trading decisions. I will review the currently prevailing modeling approaches and their limitations, and introduce the new dynamic modeling approach.

1.       Traditional 3-statement modeling

Traditional financial models forecast a company’s entire financial statement. It starts by assuming the future values of revenue, cost, working capital (such as receivables and payables), then reversely deduces the cash flow and balance sheet values based on financial accounting rules. As a forecasting tool, the limitations of these models are:

(i)                   Putting results ahead of causes.

Flows (cash, inventory, receivable etc.) are the causes that generate the financial results. By assuming the financial results first, then reversely solving the flows, traditional models put the effects ahead of the causes, leading to less predictive power of the forecast. For example, realized revenue is predicated on many internal conditions of a company. Does the company have enough inventory to sell? How long does it take to manufacture from raw materials? How much cash is available to purchase inventory? What is actually the most optimal sales target? By simply picking a value of next year’s revenue, the forecast leaves out the key elements that a predictive model is supposed to evaluate.

(ii)                 Impossible to make scenario and uncertainty analysis.

Traditional financial models can only manually assuming different possible outcomes on the financial results – base, best and worst, because the financial results are assumed other than derived. It is highly cumbersome for the financial results to be generated from the different scenarios of the underlying operation and financing actions.

(iii)               Forecast does not lead to valuation.

Because valuation is the expected value of the distribution of possible financial outcomes, the lack of the ability to derive different scenarios makes the traditional models unable to use their forecast to value a company’s debt.

2.       Statistical models (including ML and AI models)

Statistical models do not forecast a company’s entire financial statement, but focus on a few chosen predictive variables, for example, a company’s default probability and recovery rate. The models start by observing the long-term historical average values of the predictive variables over large sample of companies. They aim to discover statistical patterns between the predictive variables and other observed variables, which may be a large set of financial, operational, macro, or even alternative data variables. The limitations of these models are:

(i)                   Backward-looking

Because the statistical data are observed over long-range historical period, the statistical relationship observed is backward-looking.

(ii)                 Linear complexity

As a practical matter, the statistical models have to treat each observed variable linearly, because the number of possible combinations of the observed variables are exponentially higher than the number of observed variables, rendering the method ineffective given the amount data points available. The more observed variables are included, such as in ML and AI models, the more interactions among the variables are ignored, thus the more likely for the method to miss the key derivers of the predictive outcome.

(iii)               Path independent

In order to maximize usable observed data sample, statistical models typically treat data points from different time intervals as independent samples, unable to predict effectively the highly path dependent nature of corporate finance.

3.       Advanced models

3.1.  Structural models

Structural models, based mainly on Merton’s model, model default as the result of a company’s total asset market value falling below a fixed debt barrier. This is actually a primitive form of dynamic model as it generates the process that leads a company into default. The limitations are:

(i)                   Simplistic definition of default

The model assumption of default does not correspond to how default occurs in reality. Company defaults because they run out of cash, not because they have negative equity.  The total asset market value is not even an observable quantity. A company’s debt is not fixed. Because of these limitations, the structural models are implemented in practice as statistical models, using the model default probability as an additional statistical input (renamed as distance to default).

(ii)                 Cannot predict recovery rate.

In structural models, default occurs when total asset market value touches the fixed debt barrier, but the model cannot predict the debt recovery rate. Without recovery rate, the model alone cannot value a company’s debt.

3.2.  Reduced form models

Reduced form models specify the general mathematical form of default probability with free parameters to be fitted from historical data. The limitations are (i) backward-looking; (ii) non-company-specific; (iii) does not integrate recovery rate with default.

Dynamic modeling of corporate finance

Dynamic financial modeling is a new approach I developed over the past five years. It combines my experiences from structured credit modeling and fundamental corporate financial analysis. The approach is based on the modeling principles of physical science and implemented numerical with large computational program. The key foundations of the approach are:

1.       Modeling the laws of change other than the results.

In quantitative physical science, models are expressed as partial differential equations which specify how a system change incrementally. The system’s future state is predicted by applying these laws to the system’s initial condition and boundary condition. The predictive power of physical models rests exactly in the fact that the outcomes are derived other than specified. Can the laws of incremental change be specified for corporate finance? Yes, they have all been specified in the financial accounting rules.

2.       Modeling a corporate as a whole

In tradtional and statistical forecasts, focuses are often given to isolated variables or metrics (cash level, debt level, EBITDA level). In reality, a company's financial balance sheet must change as a whole and the variables must change inter-connectedly. When modeling a physical system, the powerful law to be specified even before the actual equations are specified are symmetry or conservation laws. These laws establish the principle that lay powerful restrictions on how different variables must change inter-connectedly. Corporate finance also has one such overreaching symmetry law – the balance of the balance sheet. The law is instilled in every corporate finance accounting rules.

3.       Modeling a corporate’s adaptivity

Unlike a physical system, a corporate is a living entity that makes adaptive decisions in order to survive and thrive. A realistically predictive model of a corporate must model how corporates make these decisions. These state-of-the-mind actions may seem impossible to model, but they can be. All corporates have common goals. First, survival, that is avoiding default and bankruptcy. Second, growth, that is increase spending and sales. When deciding actions such as capital expenditure or debt borrowing, a corporate evaluates these goals based on realized data to each the most optimal action. A complete dynamic model of corporate finance must incorporate these feedback loops in the model.

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The ultimate outcome of a dynamic financial model is the incremental changes of a company’s entire financial statement deterministically generated from initial and boundary conditions. It separates the source of uncertainties from the deterministic dynamics, and thus is able to generate the entire time-dependent distribution function of a company’s future financial statement. This leads to a forward-looking and company-specific valuation of a company’s capital stack in all seniorities, including both debt and equity.