Circular Dependencies in Finance and Financial Models

Iterative calculations setting in a spreadsheet

Nvidia, OpenAI, Microsoft, and other major AI companies have large, interweaving investments that have stirred headlines about a possible bubble. Capital markets generally frown on circular contracts because they obscure sustainable demand. In computer engineering and in Excel modeling, circular dependencies cause similar problems. They confound resolution, and best practice says to avoid them.

Acyclic dependencies are much nicer to work with, in capital markets and in software alike. But the world is messy, and sometimes circularity is the best option.

When circularity arises in financial modeling

Even though circular references are strongly discouraged in financial models, there are situations where they are the most practical path. Two common examples:

  • Determining revolver draws and repayments when interest expense depends on the average revolver balance over the period

  • Sizing debt proceeds defined on a loan-to-cost basis where cost includes interest expense, as in commercial real estate development loans

Sometimes there are clean paths to avoid circularity algebraically, but often formulas are disjointed, deeply indirect, or span multiple periods. In those cases, circular dependencies are the only practical option.

How spreadsheets resolve circularity

Solving circularity in Excel is straightforward. You enable iterative calculations in the settings and set maximum thresholds for number of iterations and change in value. Annoyingly, Excel is not good at recovering from accidentally divergent formulas. Best practice uses a "circuit breaker" to reset calculations by toggling the calculation flow to an acyclic path.

Under the hood, the iterative solution process in a spreadsheet is less efficient than acyclic resolution but conceptually simple. There are clear, directed edges between a known set of nodes. Solving requires setting an initial value for each node and then iteratively recalculating values by following the dependency chain. Every node and edge is known beforehand, which makes the graph easy to construct and walk.

How Orcaset resolves circularity

Orcaset follows the same general process, known as fixed-point iteration:

  • Construct a directed graph of nodes and edges

  • Break the circularity by initializing back edges with some starting value

  • Iteratively walk through the dependency tree and update values

  • Stop when changes for all node values fall below a convergence threshold, or when a maximum number of iterations is reached

The challenge is that Orcaset is not a spreadsheet. Values can depend on partial periods which are automatically interpolated between date boundaries. Additionally, line items don't require an end date assumption, so the set of nodes could, in principle, be unbounded. This means the nodes in the dependency graph can't be fully enumerated ahead of time. They must be built on demand in response to a query.

Once the graph is constructed, Orcaset applies the same optimizations you would expect for efficient resolution: identifying strongly connected components, resolving acyclic branches in a single pass without entering the iterative route, and converging efficiently on the cyclic portions.

Knowing when to break the rules

None of this means you should reach for circular calculations casually. They are less efficient and harder to audit than acyclic formulas.

A financial modeling tool is only as useful as its ability to express users' intent. Orcaset includes traceable resolution for both acyclic and cyclic formulas, over any past, present, or future value reference, so that the tool never becomes the bottleneck.