The Decay Function of Marketability: Toward a Computable Menger-Fekete Framework

In 1892, Carl Menger asserted that money is merely the most saleable commodity, and that saleability is a spectrum along which every good can be ranked. He identified the characteristics that determine a good's saleability — divisibility, durability, transportability, widespread demand, freedom from weaponization — but he offered no mathematical machinery for placing an arbitrary instrument on the spectrum. The concept was qualitative.

Sixty years later, Fekete sharpened one specific end of the spectrum into a measurable diagnostic: the gold basis, defined as the spread between the gold futures price and the spot price, adjusted for carry. When the basis compressed toward zero or inverted into backwardation, Fekete treated this as empirical evidence that the paper claim on gold was losing its saleability relative to the metal itself. The basis was Menger's abstract spectrum, made concrete for a single good.

No one, to my knowledge, has extended Fekete's analytical machinery to cover the full Mengerian spectrum — to propose a framework in which the saleability of any financial instrument, not merely gold, could be directly measured from observable market data. This essay proposes that framework. I will call it the decay function of marketability.

The claim is that every layer of derivation from a physical, directly-held asset imposes a measurable haircut on saleability, that these haircuts are invisible in normal market conditions but become observable as spreads under stress, and that the rate at which those spreads compress or widen across a crisis cycle carries predictive information about where the next liquidation-only event will originate.

Why "liquidity" is the wrong variable

Modern finance has a well-developed vocabulary around liquidity: bid-ask spreads, depth of book, turnover ratios, amortized cost of execution. None of this captures what Menger and Fekete meant by saleability.

Liquidity, in its standard contemporary usage, is a measure of transaction cost under normal market conditions. It answers the question: "how much do I give up to trade out of this position right now?" Marketability, in Menger's sense, is a measure of the conditions under which exchange remains possible at all. It answers a different question: "in a crisis, will my counterparty still accept this instrument on the terms implied by its nominal price?"

These are not the same property, and they diverge sharply in stress. A AAA mortgage tranche in 2006 had excellent liquidity and essentially no marketability. A one-ounce gold coin in a private safe has poor liquidity and essentially perfect marketability. Most of the financial system's sophisticated risk models collapse every stress scenario onto a liquidity axis, and therefore systematically under-price the difference.

Fekete's gold basis captured the correct variable for one asset. The decay function generalizes it.

The proposal, stated

For any financial instrument $X$, define $M(X)$ as its marketability — a scalar between 0 (completely unsaleable under any conditions) and 1 (unconditionally saleable at nominal value).

For an asset held directly, in physical form, under the holder's unmediated control, $M$ is at its maximum for that asset class. Each subsequent transformation — custody, rehypothecation, securitization, derivatization, tranching, synthetic replication — imposes a marketability haircut. The cumulative haircut across $n$ transformations is the decay function.

The functional form I propose, as a working hypothesis, is exponential:

$M(X_n) = M(X_0) \cdot e^{-\lambda n \sigma(t)}$

where $n$ is the number of derivative hops between the directly-held asset and the instrument in question, $\lambda$ is an asset-class-specific decay constant, and $\sigma(t)$ is the current market stress level (observable through any standard stress indicator — the VIX, credit spreads, repo haircut movement).

The key properties of this framework:

1. In normal conditions ($\sigma(t) \to 0$), $M(X_n) \to M(X_0)$ for all $n$. Every derivative layer appears fully saleable. This is why, in tranquil periods, the decay function is invisible. It is also why modern risk models routinely treat a mortgage-backed security as functionally equivalent in marketability to the underlying property. That equivalence is a regime-specific illusion.

2. As $\sigma(t)$ rises, $M(X_n)$ decays exponentially with $n$. Instruments further from the physical asset lose marketability faster. A fourth-order derivative under stress is saleable at a fraction of its nominal value; the directly held asset is saleable at close to nominal.

3. The decay constant $\lambda$ is itself a property of the instrument, not a free parameter. It can be estimated empirically from the historical behavior of the asset class across prior crisis episodes. A physical commodity has one $\lambda$; a Treasury bill has another; a triple-A-rated structured product has a third, higher, $\lambda$.

The proposal is not that this specific functional form is correct. The proposal is that some such function exists, that its parameters are estimable from data, and that its predictions are testable.

Observable proxies

The decay function cannot be observed directly. But its signature — the widening of spreads between instruments at different points on the marketability hierarchy under stress — is directly observable in market data. Here are five readily computable proxies that together provide a Mengerian dashboard.

1. The paper-physical premium in precious metals. The spread between the spot price of gold or silver and the delivered price of physical coins or bars at major retail and institutional dealers. Widens in stress; compresses in calm. This is the modern successor to Fekete's original basis concept, and the most immediately readable.

2. On-the-run versus off-the-run Treasury spread. The yield difference between the most recently issued Treasury of a given maturity and older issues of near-identical characteristics. In principle these should trade nearly identically. In practice the on-the-run issue carries a premium that reflects its superior marketability in stress. The magnitude of that premium, tracked over time, is a marketability indicator for the Treasury complex itself.

3. Repo haircut dispersion. The distribution of haircuts (the percentage reduction from market value that a lender requires against collateral) across asset classes in tri-party repo markets. In calm conditions, haircuts on similar-quality collateral are tightly clustered. Under stress, the distribution widens dramatically: dealers demand larger haircuts on instruments they consider less saleable in the event they need to liquidate the collateral. The dispersion metric, rather than any individual haircut, is the marketability signal.

4. FX basis deviations from covered interest parity. Under frictionless conditions, the forward exchange rate, the spot rate, and the interest rate differential between two currencies are tied by arbitrage. Deviations from this equality — the so-called "cross-currency basis" — represent the premium that parties on one side of the trade are willing to pay for immediate dollar liquidity relative to synthetic dollar liquidity assembled through derivatives. A widening basis indicates saleability stress in the dollar's payment infrastructure itself.

5. ETF premium/discount to NAV in crisis windows. Under normal conditions, ETFs trade at or very near their net asset value because of the creation/redemption arbitrage mechanism. In stress, ETFs can trade meaningfully below NAV when the underlying market becomes difficult to trade (as happened dramatically to fixed-income ETFs in March 2020). The depth and duration of these discounts are a direct measurement of how the ETF wrapper's marketability has decayed relative to the marketability of its constituents.

Each of these is a partial, asset-class-specific window into the decay function. Together they constitute a composite indicator of where in the financial system marketability is eroding first.

Marketability half-life

A second quantitative construct follows naturally. Borrowing from nuclear physics: define the marketability half-life of an instrument as the time required for a stress-induced spread to compress back to half its peak deviation from the pre-stress baseline. An instrument with a short half-life is one whose marketability recovers quickly after a shock — its apparent saleability impairment was transient. An instrument with a long half-life is one whose saleability impairment was structural; the market is repricing the instrument's long-term marketability rather than reacting to a short-term funding event.

The half-life metric disambiguates two different classes of market stress that superficially look alike. A liquidity event in an otherwise sound instrument has a short marketability half-life. A solvency event in an instrument whose apparent saleability was itself an illusion has a long half-life and, in the limit, an infinite one — the spread never recovers because the market has revised its estimate of the instrument's saleability permanently.

In 2008, the paper-physical spread in gold exhibited a long half-life for the first time in the modern era. The spread opened and, critically, did not fully close. This was Fekete's signal that the 2008 event was not a liquidity event but a structural event. The metric has continued to oscillate around an elevated baseline ever since, which Fekete interpreted — correctly, in retrospect — as evidence that the entire post-2008 monetary regime is operating at a permanently impaired marketability level.

What this framework predicts

Three predictions follow from the decay function framework that are non-trivial relative to standard finance models.

First: as a crisis unfolds, marketability will decay from the most derivative end of the spectrum inward, not uniformly across the market. The first instruments to lose saleability in any stress episode will be those most distant from their underlying physical claims. This is empirically validated by essentially every modern crisis: the first instruments to break in 2008 were the synthetic CDOs, not the underlying mortgages; the first instruments to break in 2020 were high-yield ETFs, not the underlying bonds. The framework predicts this pattern will continue to hold.

Second: the order in which instruments lose saleability in a future crisis can be partially pre-computed from their current $n$ and estimated $\lambda$. Instruments with high $n$ and high $\lambda$ are the canaries; they will show marketability decay first. A composite Mengerian stress indicator built from the five proxies above, weighted by estimated $\lambda$, would have led most modern crises by several weeks.

Third: central bank interventions that inject liquidity without addressing the underlying marketability impairment will produce a characteristic signature in the data: the liquidity-sensitive spreads will compress while the marketability-sensitive spreads remain elevated. This is the signature of what Fekete called a "false resolution." It is precisely what has occurred repeatedly since 2008. Each QE cycle compresses liquidity spreads to zero while leaving the Fekete-style marketability spreads — the paper-physical premium in gold, the FX basis, the off-the-run Treasury spread — quietly elevated. The Federal Reserve can manufacture liquidity. It cannot manufacture marketability.

Why this matters now

The utility of this framework is not academic. In an environment where petrodollar saleability is gradually eroding, where central banks are being forced to monetize gold reserves into a weakening bid, where algorithmic trading concentrates liquidity provision into six firms, and where the cryptographic substrate under every digital claim is approaching an existential technology threat — the question of which instruments retain marketability under stress is a first-order question for every allocator of capital on earth.

The decay function framework does not answer that question. It reformulates it in a computable form. The next step — which I will begin in a forthcoming essay focused on the cryptographic dimension of marketability — is to assemble the actual dashboard and begin tracking the signals in real time.

Menger gave us the insight that money is the most saleable good. Fekete gave us the first tool for measuring saleability in a single market. The work of building the general measurement apparatus is what remains. It is the central open problem of the New Austrian Economics, and it is overdue.

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Next in this series: how open market operations — introduced illegally into the Federal Reserve's toolkit in 1922 and now automated through algorithmic trading — convert the decay function into a closed-loop mechanism for systemic capital destruction.