The "Inverse Sympathetic Principle" in financial markets

A case study with applications

Thanks cobben for the idea!

---

The principle of sympathetic magic, as catalogued by Frazer in The Golden Bough (1890), holds that objects which resemble each other are linked across the substance of the world. The voodoo doll and the targeted individual. The waxen image and the king it portrays. The footprint and the foot which made it. Like acts upon like. The principle has been studied for over a century in anthropological, ritual, and theological contexts.

Its inverse has not.

Until now.

The Inverse Sympathetic Principle, which the present author proposes to formalise here, addresses a category Frazer did not begin to consider: objects which are similar in form but demonstrably non-identical in substance. Classical sympathetic magic requires resemblance to function. The Inverse Sympathetic Principle requires resemblance and non-identity, and produces a different effect entirely: mutual annihilation within the system that contains both.

The principle has remained outside the anthropological canon because the systems in which it operates are not religious or ritual systems. They are financial systems. This current paper offers three empirical case studies in which the Inverse Sympathetic Principle can be observed, measured, and in two cases confirmed by the issuing parties themselves.

The first specimen concerns the relationship between SLV, the iShares Silver Trust exchange-traded fund, and physical silver bullion. Both are denominated in troy ounces. Both purport to track the same underlying metal. The resemblance is, by design, near-total. Yet one is paper, a security held in custody by a trustee, and the other is matter. Similar. Non-identical.

Under the Inverse Sympathetic Principle, we predict mutual annihilation: the paper claim and the physical metal cannot coexist in the same accounting system without one cancelling the other.

The empirical test is straightforward. We consult the SLV prospectus. There, in language drafted by counsel and approved by regulators, we find that shareholders have no right to demand physical delivery of silver from the trust, that the trust may settle redemptions in cash rather than metal, that the trustee may suspend creation and redemption activity at its sole discretion, and that the silver held by the trust may be subject to claims that reduce the per-share entitlement.

The issuing party has stated, in advance and in writing, that the paper claim does not constitute ownership of the metal it appears to represent.

The Inverse Sympathetic Principle is therefore not merely confirmed by observation. It is confirmed by stipulation.

The second specimen concerns bitcoin and gold. Both are described by their respective adherents as stores of value. Both are claimed to function as protection against monetary debasement. The resemblance is functional rather than physical, but resemblance under the principle does not require shared substance, only shared claim. One is information, a ledger entry secured by cryptographic consensus. The other is matter. Similar in stated function. Non-identical in everything else.

Under the Inverse Sympathetic Principle, the prediction is mutual annihilation.

Empirical confirmation in this case is more elegant than in the SLV specimen, because the parties to the cancellation perform the verification themselves. Bitcoin proponents assert that gold is obsolete, demonetised, a relic of a pre-digital monetary order. Gold proponents assert that bitcoin is a confidence trick, a digital tulip, an instrument that will eventually print itself to zero through proliferation of competing chains. Each side claims the other is worthless.

The principle predicts both claims are simultaneously correct. The observation is consistent with the prediction.

It should be noted that under classical sympathetic magic, we would expect the two assets to move together, since they purport to perform the same monetary function. They do not. They move in opposition more often than not. This anomaly has been a recurring puzzle for the modern financial press, which has variously attributed it to risk-on/risk-off rotation, generational preference, or liquidity flows between the two communities. The Inverse Sympathetic Principle offers a more parsimonious explanation: similar function, non-identical substance, mutual cancellation.

The third specimen concerns the United States Dollar Index, commonly abbreviated DXY, and the currency it purports to measure.

The DXY is constructed as a weighted geometric mean of the dollar’s exchange rate against six other currencies. The weights, fixed since 1973 with one minor adjustment to accommodate the introduction of the euro, are: the euro at 57.6%, the Japanese yen at 13.6%, the British pound at 11.9%, the Canadian dollar at 9.1%, the Swedish krona at 4.2%, and the Swiss franc at 3.6%. The basket, in aggregate, is overwhelmingly dominated by the euro and yen.

We must now ask in what sense these currencies are non-identical to the dollar.

They are not identical in their issuing authority. The euro is administered by the European Central Bank, the yen by the Bank of Japan, the dollar by the Federal Reserve. They are not identical in their underlying economies, their political constituencies, or their reserve status. These are real differences, and they are precisely the differences the index purports to measure.

Yet under any meaningful structural classification, the euro, yen, pound, Canadian dollar, krona, and franc share with the dollar the following properties: each is a fiat currency, issued without commodity backing; each is administered by a central bank operating under a broadly similar mandate; each constitutes a liability of the issuing institution; each expands and contracts in supply through the same operational mechanisms; each is subject to the same broad macroeconomic forces and frequently to the same coordinated policy responses. They are similar. They are non-identical. The conditions of the Inverse Sympathetic Principle are satisfied.

The prediction follows. When the dollar is measured against currencies that are similar to it in structure but non-identical in administration, the two cancel. The DXY, therefore, does not measure the dollar against anything external to itself. It measures the dollar against a permutation of itself.

This conclusion is unfamiliar but not novel. During periods of synchronised global monetary debasement, that is, periods in which the dollar, euro, yen, and pound are all expanding their respective monetary bases at comparable rates, the DXY can remain stable, or even rise, while the purchasing power of every currency in the basket simultaneously declines. Orthodox monetary theory treats this as an anomaly requiring further explanation. The Inverse Sympathetic Principle treats it as the expected outcome. A scale which weighs an object against permutations of itself will report stability regardless of changes in the underlying mass.

The same may be said of the Bank for International Settlements’ broad effective exchange rate measures, of trade-weighted indices generally, and of any benchmark in which the measured object and the measuring instrument share substantive properties. The principle, once recognised, accounts for the persistence of these measures in policy discourse despite their evident analytical limitations.

It is a tautology. It has always been a tautology.

The Inverse Sympathetic Principle does not introduce the tautology. It merely names it.

Three case studies, three confirmations. The principle, having predicted observed behaviour in markets for precious metal certificates, digital scarcity instruments, and reserve currency benchmarks, may have broader application. Preliminary observation suggests it operates also in the relationship between exchange-traded fund net asset values and the underlying securities they reference, between accounting identities and the economies they purport to describe, between derivatives notional and the assets they nominally hedge, and between sovereign debt instruments denominated in the issuer’s own currency and the currency itself. Each pairing exhibits the diagnostic features: surface resemblance, substantive non-identity, observable mutual cancellation within the containing system.

Further research is warranted. The present author concedes that controlled experimental verification remains methodologically difficult, given the impossibility of isolating financial systems from observer effects, regulatory intervention, and what Mauss in a related context termed total social facts. The principle resists falsification not because it is unfalsifiable, but because the systems in which it operates routinely respond to attempts at measurement by reorganising themselves to preserve the cancellation.

This last property suggests the principle may belong to a class of phenomena that includes quantum measurement, ritual efficacy, and political polling.

Its full classification awaits further work.

— The Mathematical Anthropologist