# Velocity of Tokens

Oct 31, 2017 · 8 min read

The velocity of tokens is a key aspect that affects future token value; however, it is also one of the least understood. This post attempts to describe velocity, how it impacts any token price over time and analyses the velocity of the Dala token as an example.

## Equation of exchange

The equation of exchange is defined as: MV=PT

Where: M= money supply, V= velocity of money, P= average price level of goods, T= index of expenditures (such as the total number of economic transactions)

In token economies, this has been adopted by two prominent people — Chris Burniske and Vitalik Buterin.

Burniske definition: MV=PQ

Where: M= size of the asset base, V= velocity of the asset (the number of times that an average coin changes hands every day), P= price of the digital resource being provisioned, Q= quantity of the digital resource being provisioned

Using the Burniske definition, valuations typically solve for M by rearranging the equation: M=PQ/V

In order to solve for token price, one must calculate M, by working out the size of the market in dollars (PQ), divide it by the velocity (V) and then divide M by the number of coins in supply.

Buterin definition: MC=TH

Where: M= total money supply (or total number of coins), C= price of the currency (or 1/P, with P being price level), T= transaction volume (the economic value of transactions per time), H= 1/V (the time that a user holds a coin before using it to make a transaction)

Using the Buterin definition, to solve for the token price, one must solve for C:

C=TH/M

In either definition, one can see that the velocity of the coin is inversely proportional to the value of the token i.e the longer people hold the token for, the higher the price of each token. This is intuitive, because if the transactional activity of an economy is \$100 billion (for the year) and coins circulate 10 times each over the course of the year, then the collective value of the coins is \$10 billion. If they circulate 100 times, then the collective coins are worth \$1 billion. Thus, understanding and calculating the velocity in any token economy is extremely important.

# Velocity in a token economy

## Velocity: Too low

From the above equations, it appears that minimising the velocity of the coin will drive the highest valued coin. This is not true because velocity is also correlated to transactional volume (T), thus a certain level of currency movement is needed in a ‘healthy’ economy. An example of this is the M1 money supply in the USA during the last 60 years. There is a direct correlation with recessions (see 2008 for an example) and a decrease in velocity. Since 2008, M1 money supply has fallen from over 10 to 5.535 last quarter. Yannick Roux illustrates in his blog post why a token economy can’t have a velocity of 0, using an example of a ‘funfair’ token to demonstrate a ‘discount to control’ accrued to token economies. Therefore, if you hold all the tokens and nobody trades then the transactional volume collapses and thus so does the price of each coin because there is no demand.

## Velocity: Too high

Many token economies are currently being proposed where the token is purely a medium of exchange token. A hypothetical example would be a decentralised car-hailing economy where all participants require the hypothetical token, TripCoin, to transact in the system. Well, nobody actually wants to hold the coin so the paying passenger would convert from fiat (or BTC) into TripCoin, send it to the driver for the trip, who would convert it straight back into fiat (or BTC). No member of the network wants to hold the coin because all other expenses are in fiat. If the network had to grow to the size of Uber, then the transactional volume would be exceptionally high, but so would the velocity of the system. So overall, the network might have \$20 billion in value, but each individual coin wouldn’t accrue this value.

Vitalik Buterin describes how this system could be easily nudged (manipulated) away from local equilibriums because the system suffers from positive feedback effects. Succinctly, if the price of the token starts to increase, people may store it because it has a perceived higher yield than an alternative token i.e speculation. More speculation drives the price further up, etc. until a new equilibrium is reached. However, the process also works in reverse — as people sell the coin, it becomes more expensive to hold compared to other tokens. The more people sell, the further the decrease in price. Fundamentally, because there is no need to hold the token, the price is only linked to speculation. Furthermore, as decentralised exchanges and other systems are launched, so the velocity should increase further (given even lower barriers to trade the token), which should drive the price even further down.

## Velocity: Goldilocks zone

It is clear that ideally velocity is maintained within a range — too low is as damaging, as is too high. What is less clear is the optimal range for token economies. If the token is to be compared to M1 money, then the velocity of a token should remain in moderate range of between between 4 and 15. However, not all tokens are comparable to M1 money. If the token is seen as a storage of value as Bitcoin is becoming, then the optimal range may be closer to M2 money. Historically, the velocity of M2 money has ranged between 1.4 and 2.2.

In summary, to maintain a healthy token economy (and sustainably ensure token value), the token economy design should optimise the ratio T/V where T and V are related. For token economies, the optimal ratio is still uncertain and most likely is different for each individual economy. I hope more rigorous research is performed on the velocity of token economies in the future.

# Velocity altering levers

There are multiple levers which token economics can use to adjust velocity. These all involve incentivising token users to hold their tokens for an extended time. Implicitly, there is a cost to token holders who hold for an extended period. This cost is the loss of yield if their wealth was held in another token. This cost must be factored in when deciding on which levers a system wants to implement. If the utility benefit of the system doesn’t exceed the holding cost then the system will struggle to achieve adoption. The possible velocity altering levers include:

A profit share mechanism: A profit sharing mechanism is when token holders are paid for performing work for the network. However, the worker must own the token for their right to work for the profit share. This incentivises users to acquire and hold more tokens, which reduces the velocity. The reduction happens because, as the market price of the token decreases, its yield, from profit share, increases. If the yield becomes too high, then market participants seeking yield will buy and hold the token, increasing the price and reducing velocity.

Staking functions into the protocol: Staking functions reduce the velocity of the token because they lock-up tokens for a period of time. Extended staking periods can reduce velocity significantly as the assets are illiquid while staked. Most staking mechanisms require the user to stake their reputation against the stake and if they fail to perform a function (or perform it inadequately), they lose their stake.

The “network utility expansion” mechanism: This is harder to justify, but succinctly, if there are a set number of tokens, then these tokens access a defined percentage of the network. If the absolute capacity of the network grows, then the amount of absolute utility each token can acquire grows. E.g. in a computer storage sharing economy, each token is worth a fixed percentage of the network and as it grows in size, so each token can purchase more megabytes. Thus, the anticipation of greater future utility will cause token holders to hold their stake which will reduce the velocity.

Importantly, if users are anticipating growth in the network then they will hold onto their tokens as their tokens value should grow over time. However, as the network reaches a steady-state or begins to decrease in size, then users may start trading their token as they may worry that tokens start falling in value, therefore increasing velocity. Thus, Network protocols that offer a reasonable expectation of absolute utility through their design are those that should endure.

Becoming a cryptocurrency: This is non-trivial. It requires people to implicitly trust the stability of the token compared to their other alternative. It occurs when people start holding a currency so they can purchase goods and services through the token at a later time. This reduces velocity as holding periods are introduced. In a File Storage example economy, if the users of the network are also providers to said network they are not likely to trade out their token. If a user has a spare hard drive at home which earns StorageToken, but spends those same tokens to access cloud storage on their laptop where they need extra storage space, then they are unlikely to sell the token in the meantime. As StorageToken is held within the File Storage network economy to: a) be used at a later date given that holders are both providers and users of the network and b) be held given a reasonable expectation of being able to purchase more storage capacity as the network utility expansion effect takes hold, we have positive reinforcement from (a) and (b) that has the effect of reducing StorageToken’s velocity to a healthy combination of transactional, and holding, activity.

These levers were first published in draft form by Kyle Samani and have been republished here with his consent. As this is a developing space, they are expected to be adjusted and improved over time. If you have any ideas on potential levers, let me know!

# Conclusion

The velocity of any token is a very complex topic, with little data available to draw analogies from. However, for any token investment, understanding the long-term velocity implications is critical. There appears to be a goldilocks zone which should maximise the overall token economy and the token’s ability to capture this value.

Any token which is solely a medium-of-exchange token has a high likelihood of suffering from price manipulation because it is easy to ‘nudge’ the price to new equilibriums. There are a number of levers which can prevent token velocity from falling below or rising above this Goldilocks zone.

The best analogy to the initial velocity of Dala is mobile money, demonstrated as having a velocity of between 2 and 5. However, it is posited that Dala’s initial velocity might be close to double that range (between 4 and 10). This is closer to the velocity of M1 money supply, and is well within the Goldilocks zone. As Dala is adopted, the three different velocity levers (staking, network utility expansion and becoming a cryptocurrency) should keep Dala’s velocity within the Goldilocks zone. Ensuring that the velocity is maintained within this zone is important for the initial and long-term price of Dala, as it is indicative of a healthy Dala economy. A strong economy should, in turn, sustainably increase Dala’s price.

Let me know your thoughts or ideas on any other velocity adjusting levers in the comments below or on twitter.

Thanks to Llew Claasen, Inge Lok and Justin Swart for reviewing this post.

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