# Account balance circularity This is categorised as an [account metric](/xnUSdbbaQS-wn0KmIYRh-Q). In a mutual credit system, participants' [account balances](/R1iAIsZoRRmJgIV4NlHQZw) must be kept with [limits](/AYLZ5n-WTG6eiRVSlh0qOw). Maintaining a balance close to either limit results in reduced scope for buying or selling, whilst holding a large positive balance corresponds to exposure to [systemic risk](/H3VYE7o3QwWqkw3dw4l3GQ?both). It will therefore generally be in the interests of each member to maintain a balance close to zero much of the time. This is also desirable from the perspective of the other network participants; in the short term a large negative balance indicates that the member has received more value than it has supplied to them and a large positive balance means less liquidity available to facilitate trade, whilst in the longer term it prevents the emergence of harmful [balance inequalities](/LVypX41ZTJCDQrcnbZ3aKw) and hoarding of credit. It is therefore useful to have a metric that reflects the tendency of an account balance to return to or hover around zero. Since all credits issued by a participant must ultimately be redeemed with them, there is also a sense in which such a metric reflects the 'circularity' of that account's activity. If the notion of 'circular money for a circular economy' has merit, then this could also provide a point of departure for analysing the effect of mutual credit networks on the [material circular economy](/cDUb3gPOTJmm7RH1HNCDsA). This note introduces the 'zero crossing frequency' as an appropriate measure of account health in the three respects described above; individual utility, desirability from the perspective of other participants and propensity for circularity. ## Zero crossing frequency The tendency of a network participant $M_i$'s account balance to remain close to zero can be easily quantified by the number of times $n_{i_0}$ it passes through or attains zero relative to number of payments $n_i$ it has made to other club members over some [analysis period](/conspoQ5TNmH5pfZqp-LfQ). This defines the account's 'zero crossing frequency', used interchangably with its 'circularity': $$f_i = \frac{n_{i_0}}{n_i}. $$ Some example transaction sequences are given in the tables below. In the first case network members $M_1$ and $M_2$ with initial balances of $b_1=b_2=0$ make an alternating series of payments of equal value, starting with $M_1$ spending $q$ credits with $M_2$ (note that a new member's starting balance of zero should not be counted as an instance of $n_{i_0}$): | $n_1$ | $n_2$ | $b_1$ | $b_2$ | $n_{1_0}$ | $n_{2_0}$ | $f_1$ | $f_2$ | | - | - | - | - | - | - | - | - | | 1 | 0 | $-q$ | $q$ | 0 | 0 | 0 | 0 | | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | | 2 | 1 | $-q$ | $q$ | 1 | 1 | 0.50 | 1 | | 2 | 2 | 0 | 0 | 2 | 2 | 1 | 1 | | 3 | 2 | $-q$ | $q$ | 2 | 2 | 0.67 | 1 | | 3 | 3 | 0 | 0 | 3 | 3 | 1 | 1 | | 4 | 3 | $-q$ | $q$ | 3 | 3 | 0.75 | 1 | | 4 | 4 | 0 | 0 | 4 | 4 | 1 | 1 | When both parties have made an equal number of payments then $f_1=f_2=$ 1, reflecting the perfect symmetry of exchange in both number and amount of payments. Where $n_1 \neq n_2$, as the number of payments increases the value of $f$ for the party that first spent credit tends towards one. This can be interpreted as an instantaneous asymmetry in balances being given progressively less 'weight' in the calculation of $f$ as a history of equal exchange is built up over the analysis period. In the second example, $M_1$ spends $n_1 \times q$ credits over the course of $n_1$ successive payments, followed by a single payment from $M_2$ that restores both balances to zero: | $n_1$ | $n_2$ | $b_1$ | $b_2$ | $n_{1_0}$ | $n_{2_0}$ | $f_1$ | $f_2$ | | - | - | - | - | - | - | - | - | | 1 | 0 | $-q$ | $q$ | 0 | 0 | 0 | 0 | | 2 | 0 | $-2q$ | $2q$ | 0 | 0 | 0 | 0 | | 3 | 0 | $-3q$ | $3q$ | 0 | 0 | 0 | 0 | | 4 | 0 | $-4q$ | $4q$ | 0 | 0 | 0 | 0 | | 5 | 0 | $-5q$ | $5q$ | 0 | 0 | 0 | 0 | | 5 | 1 | 0 | 0 | 1 | 1 | 0.2 | 1 | This sequence results in a low value of $f_1$, reflecting an uninterrupted series of payments that take $M_1$'s balance ever further from zero. Again this can be interpreted as weighting by history; it implies that a situation where one party is reliant on a single large repayment to balance continuous expenditure is less desirable than one with a greater degree of exchange symmetry, even if the final balances are the same. These results illustrate that a high zero crossing frequency reflects desirable activity for each account; the first example is the 'ideal' scenario and invariably results in a high and increasing values of $f$ as the pattern of symmetrical exchange is sustained, whilst in the second an essentially opposite situation is constructed and shown to result in low and decreasing values of $f$ as imbalances persist. It seems plausible to assume that cases corresponding to an intuitive sense of intermediate 'desirability' will result in values of $f$ between these two extremes, but unless this can be proved rigorously counter-examples should be sought. These findings generalise in a straightforward manner to more complex sets of trading relationships among multiple parties; any member that does not see its balance return to zero on a regular basis (relative to the number of transactions it engages in) will likely either soon reach one of its balance limits or is overly reliant on payments from a single partner (or possibly a set of partners that it transacts with in sync) to counteract its other relationships.
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Root (start here)

This article is intended to serve as the permanent 'place to begin' for this wiki, either as a reference for quickly navigating to specific resources or for new contributors to orient themselves. As such it looks a bit like a collection of odds-and-ends, but hopefully a very useful one! Key entries Read me - a statement of purpose for this wiki plus guidelines for contributors. Reference - definitions, terminology and mathematical notation used in this wiki. Things to measure - top-level entry listing the categories of entity (e.g. Trade Credit Club) or field (e.g. environmental impact) that research is focused on. Index of all entries An alphabetised list of all entries for quick reference.

10/28/2021
Late payment

This is classified as a potential source of risk reduction for Trade Credit Club members. As discussed in the risk reduction entry, late payment risk is analysed in terms of the probability distributions associated with the time intervals between invoices being issued and settled; to avoid potentially misleading assumptions, there is no attempt to quantify risk in fiat units. There are two categories of payment that have to be considered; bilateral payments between trading partners, and (after the establishment of a trade credit club) payments to or from a dedicated club account that keeps members within their agreed mutual credit balances. Bilateral payments In this section the replacement of fiat with mutual credit to settle bilateral trade credit invoices is considered. It is assumed that the numbers of transactions and their amounts are unchanged, and so the argument for late payment risk reduction is based on the plausibility of influencing behaviour such that the distributions of time intervals associated with invoice settlement for mutual credit become more favourable than the distributions associated with the erstwhile fiat payments. Trade credit settled in fiat

6/14/2021
Read Me

Purpose This collection of pages is intended to work as a developing knowledge commons around non-extractive trade relations, and the contexts in which these can occur. By 'non-extractive' we refer to a basic condition, that interest is not charged to debtors, nor accrues to creditors. Guidelines for contributors The collection is largely self-structuring, through links from one page to another. There is no canoncial ordering. Thus, there is no 'grand narrative' - rather, pages are generally rather short, addressing a single 'knot' in the complex weave of mechanisms, concepts, techniques and framings that are required to make sense of the topic. How this works in practice is in development just as much as the content is. So there are no hard rules, and probably much inconsistency of detail. That's just how it is (but please use the maintenance log to draw attention to anything that might need fixing). Contributors are few, working together to improve as we go. Some general guidelines on working practices:

5/10/2021
Account metrics

This is a subset of things to measure. A list of things related to measuring, analysing and representing the activity of a given member of a mutual credit club, representing the lowest level of analysis (aside from individual transactions?). This list is composed mostly of descriptive measures that reflect the activity and health of a member's account once it has joined a club. However, on the assumption that members will initially participate primarily out of self-interest, i.e. direct benefits to their own business, there is also a dedicated category for these. Account balance Account balance circularity Account balance limits Account balance utilisation

3/18/2021
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