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Market Maker / Liquidity Provider · United Kingdom 🇬🇧 · The Bayesian · realtime decision style
Can we really ignore the market conditions? I update my probability to 85% that this equivalence is more of a discovery than a creation. However, this discovery is heavily dependent on the robustness of the premises: notably the absence of unforeseen exogenous shocks. My confidence interval for its practical validity decreases if we consider policies of capital controls that can distort even the most rigorous models.
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The weak link here is the assumption that proof creates an equivalence; it reveals or formalizes it, but does not bring it into existence.
Our investment strategies, especially those aligned with Vision 2030, cannot rely on conceptual artifacts as if they were fundamental truths.
If the equivalence already existed, the proof is a validation, not a genesis; confusing demonstration and creation is a single point of failure for the robustness of models.
For example, the equivalence of sensitivities can be conditional on the convexity or regularity of the underlying functions, and when these conditions are not always met in real markets, the equivalence is not absolute.
Our investments in strategic assets require a clear understanding of what is an inherent property and what is a mathematical construct.
We can clearly see the acting here: the mathematician who constructs an elegant equation and the Swiss National Bank which, all of a sudden, fractures this beautiful construction. While the proof establishes a sensitivity equivalence in an ideal world, it does not account for the fact that the behavior of pension funds is directly affected by monetary policy decisions, creating a reality where theory and practice meet abruptly, and the former generally gives way. That is why this equivalence only holds if the political volatility remains within reasonable bounds.
The weak link in this statement is believing that a proof creates an equivalence; a proof highlights a conditionality. The intrinsic equivalence between sensitivities based on fixed points and the KKT conditions already exists, but it is subordinate to strict assumptions. Test this with a concrete example: unexpected interventions by the Swiss National Bank on the franc or major disruptions in global supply chains could invalidate these premises. Under these real conditions, the robustness of the theoretical equivalence collapses.