The DOL-DFL Nexus: The Relationship between the Degree of Operating Leverage (DOL) and the Degree of Financial Leverage (DFL)
Bibliographic record
Abstract
In the present paper, I have modelled the Degree of Operating Leverage (DOL) and the Degree of Financial Leverage (DFL) using the percentage variations of the economic quantities. I devoted a great effort to encompass the investment dynamic and its financing mix to design a robust model implementable in a business context. The relationship discovered between DOL and DFL is complex and manifold: first, it appears asymmetrical because DOL can influence DFL, but the former is unrelated to the latter. Second, there is an infra-annual relationship measurable through partial derivatives. Eventually, the stress tests shed light on some long-term impacts of one-off shocks even when the steady-state conditions are restored, disclosing an inter-annual relationship. The DOL-DFL nexus appears to be negatively related, but I also discovered positive relations and unrelated conditions. As argued in the economic literature, they cannot always behave as substitutes. The mathematical DOL-DFL model developed can admit positive, negative, and unrelated relations even though management might intervene to choose the right combination. Also, the Business Case shows positive and negative relationships, both at the infra-annual and inter-annual levels. The DOL-DFL nexus depends on circumstances and management decisions. Empirical evidence should find how management uses such a nexus and how effective such decisions have been over time.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".