# moving at the speed of money

*“Man cannot change a single law of nature, but can put himself into such relations to natural laws that he can profit by them.”* – Edwin G. Conklin

Natural sciences have fundamental laws, those rules upon which hypotheses are built to form a framework of how nature fits together. Every so often new findings requiring new frameworks come along which allow us to see the world more clearly for what it is. These frameworks come and go over time but their underlying laws tend to remain constant.

While the payments industry has plenty of generally accepted frameworks and knowledge, the only laws cited – as far as I can tell please enlighten if you know of any – are ones lifted from economics. That’s not to say supply and demand curves aren’t relevant, but payments as its own field glaringly lacks any theorems of its own. This immediately raises several questions:

- Are there any fundamental laws of payments?
- If so, what are they?
- What can these laws tell us about how payments are evolving?

### seeking truth

Payments receives little attention from academia though it is clearly deserving of much more. Payments have existed since the birth of civilization and are a startling constant of human society and behavior. They are the tangible exchange of intangibility – emotion, worth, trust, and time are bundled together in a single interaction between individuals, groups, and societies.

Their enduring structure suggests an underlying and consistent logic. From ancient bartering systems to modern trade finance, payments throughout history and across cultures have shared the same characteristics – originators, recipients, amounts, trust, etc. Advances in technology and society have done little to eliminate these components. With this factually based understanding, it is safe to declare there are underlying laws to payments, and it is worthwhile to attempt to solve for them.

### a stab in the dark

We begin our derivation with defining the phenomena described. This appears simple for payments as there are so few obvious components:

*Velocity*: The length of time between payment initiation and receipt*Value*: The amount transferred*Risk*: The uncertainty between the originator and recipient

With the pieces laid out, assembly is straightforward. To start, the velocity of a transaction corresponds directly with its value – the higher the speed, the lower the payment:

Velocity = 1 / Value

Why? High values drive slower transactions due to their increased risk. A formula emerges, and we are left with a formula revealing the speed of a transaction within a given channel of exchange:

Velocity = Risk / Value

The higher the risk or value, the longer the payment duration. This leads to the permutations:

Risk = Value * Velocity

Value = Risk / Velocity

These conceptually check out. Risk is influenced by value and speed – higher speeds and higher values translate into higher risk. For its part, higher value correlates with higher risk and slower velocity.

Notwithstanding a deeper peer review, we have our first step towards establishing the laws of payments.

### digging deeper

To further understand this proposed law it is worth dissecting its most nebulous variable – Risk. Risk represents a measurement of uncertainty – what is the likelihood something will go wrong with the payment, causing it to be misdirected, appropriated, or halted? Simply put:

Risk = 1 - Certainty

Wherein a sure thing (a Certainty of 1) would result in no Risk. Although by definition wholly unknowable and unverifiable, some major components of Risk are apparent:

*Jurisdictions*: The number of regulatory jurisdictions crossed*Parties*: The number of parties involved in a payment (e.g. intermediaries)*Timing*: The time between the payment and the transfer of the good / service (positive for pre, negative for post)*Vulnerability*: The inherent vulnerability of a payment’s medium to be compromised*Relationship*: The unfamiliarity between the originator and the recipient*Frequency*: How often, if at all, payments have occurred between the parties

Setting them equal to Risk and playing with the relationships reveals a potential formula. We start with Jurisdictions. The more regulatory jurisdictions, the higher the risk. (Note: I’m pretty distant from my math lessons at this point, so forgive my sloppy notation here)

Risk = Jurisdictions

Now we add parties. While conceptually payments are made between an originator and recipient, in practice modern payments are facilitated by a number of brokers and intermediaries. For instance, a typical credit card payment has at least five involved participants, if not more. The higher the number of parties involved, the higher the risk of something going wrong. We spread this risk over the payment by adding it as a multiplier to the right-hand side:

Risk = Jurisdictions * Parties

Next is Timing. The greater the time difference of when a payment is made before a service or receipt of a good increases risk, while the longer afterwards decreases it. To capture this timing impact in both directions we add timing to the right-hand side rather than insert it as a multiple (i.e. as a multiple, a negative value would result in negative risk every time).

Risk = Parties * Jurisdictions + Timing

Now the payment channel itself comes into play, represented by the variable Vulnerability. Vulnerability’s influence over risk varies on the channel’s type, input mode, current state and other characteristics. For instance, an in-person payment over a card network may have greater risk than a bank-enabled wire. In aggregate these features total to a constant risk modifier spread across the entire payment, and as such, we add Vulnerability as a multiplier to the entire right-hand side.

Risk = Vulnerability * (Parties * Jurisdictions + Timing)

Now comes the Relationship between the originator and recipient. This is measured in the unfamiliarity between the parties - a strong familiarity encourages good behavior and promises a known avenue for resolving any issues, while low familiarity suggests the opposite. Essentially a stand-in for the trust between the recipients, we add this variable as an exponent to the Parties variable. Small changes in trust has a large influence on the overall risk (with lower familiarity resulting in higher Relationship values):

Risk = Vulnerability * ((Parties ^ Relationship) * Jurisdictions + Timing)

Finally comes Frequency, representing the history of payments between the originating and receiving parties. The greater the history of payments between parties, the less risk in something going wrong with a subsequent payment. We add Frequency as a divisor to the Relationship variable, because relationships are made closer by interaction. With this, we have a full (for the time being) equation for Risk:

Risk = Vulnerability * ((Parties ^ Relationship / Frequency) * Jurisdictions + Timing)

Substituting the right-hand side into the original equation allows us to solve for each variable in turn:

Velocity = Vulnerability * ((Parties ^ Relationship / Frequency) * Jurisdictions + Timing) / Value

Value = Vulnerability * ((Parties ^ Relationship / Frequency) * Jurisdictions + Timing) / Velocity

Jurisdictions = ((Velocity * Value / Vulnerability) – Timing) / (Parties ^ Relationship / Frequency)

Parties = Relationship * Log ((Velocity * Value / Vulnerability) – Timing) / Jurisdictions * Frequency

Timing = (Velocity * Value / Vulnerability) - (Parties ^ Relationship / Frequency) * Jurisdictions

Frequency = Relationship / Parties * Log ((Velocity * Value / Vulnerability) – Timing / Jurisdictions)

Relationship = Parties * Frequency * Log ((Velocity * Value / Vulnerability) – Timing / Jurisdictions)

Vulnerability = (Velocity * Value) / ((Parties ^ Relationship / Frequency) * Jurisdictions + Timing)

For the most part, these proposed formulas are irrelevant – nobody will ever need to solve for these variables. Yet their fundamental relationships with one another are guiding: the more parties to a transaction suggest less history, a pre-service transaction is more likely when the value is lower, etc. Their worth is in that they tell us yes – there is a logical framework which underpins the structure of a payment, and this framework requires balance in order to function.

### breaking the model

The trouble with proofs outside of mathematics is none of them can ever be proved factually correct. Mathematic laws only require logical consistency, whereas natural science laws must instead be constantly tested against observations to prove their continued relevance. Proving, refining, and likely rewriting the above formulas must involve applying ongoing observations against them and seeing what happens.

An admitted lack of time necessitates postponing an in-depth check for this essay. Instead, let us quickly gut-check the logic: the more parties and jurisdictions involved, the more risk. Advance payments increase risk, while post-payments reduce it. The relationship has profound influence – unfamiliarity between the originator and recipient can exponentially increase risk. Conversely, the relationship’s uncertainty is mitigated by repeated payments between the parties.

Generally, the logic makes sense at this time and we look forward to revisiting and revising this in the future.

### holding steady

It is easy to assume this equilibrium will soon receive a rebalance. A globalized, digital economy demands payments at their extremes: transactions that can be made near instantaneously, involve dozens of parties, and cross multiple jurisdictions. New enabling technologies and payment models continue to emerge at a rapid clip, powered by the likes of blockchain, novel messaging standards (e.g. ISO20022) and cloud computing. Could these fundamental relationships break when pushed to such limits?

A look back at the proposed laws in light of these and other modern changes makes it clear the logical underpinnings of payments will not be upset anytime soon. Velocity has increased, as has risk; value has diminished while velocity has increased; vulnerability spikes for new channels and is mitigated over time with refinements, and so on. Much like how the laws of motion apply the same to a sparrow as a fighter-jet, the inherent relationships between payment characteristics appear constant.

### a payment in motion…

The constancy of the framework provides a powerful insight – payments will continue to evolve in pushing these variables to their extremes, and mitigations will emerge in retaining the overall balance of their relationships. A strange, fabulous future begins to emerge through these proposed laws:

*Liquid Money*: As the velocity of transactions continues to approach real-time, values will continue to decrease. Smaller and smaller payments will eventually force a ‘phase change’ from discreet, individual transactions to a continuous flow. Like the transition of ice to water, payments will grow more ‘fluid-like’ in order to mitigate the growing risk driven by the sophistication of the digital realm.*Low Value Crime*: Instant, irrevocable payments will be highly vulnerable to malevolent actors. This will be mitigated by low values complexity paired with higher frequency. It is easy to imagine larger payments being preceded by a series of low value, authentication transactions.*Point to Point*: Interconnectedness will enable direct payments in different jurisdictions, eliminating the need for go-betweens and reducing the number of involved parties.*Just in Time Payments*: Risk will decrease as advances shrink the absolute time between provision of a service or good and the payment itself. It is possible to imagine “per use” or “per service” payments instead of the more encompassing payments we are familiar with today.

Science is so fascinating not because of the natural laws themselves, but in how the universe wraps itself around them. Understanding the nature of payments by codifying their fundamental rules allows us to contextualize their characteristics and better derive innovations in the field. What new laws are yet to be discovered in the land of payments? ￼

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