Sunday, June 15, 2008

Connectivity = Instability?

(Naked Capitalism) With the financial system on the exam table, it has been more than a bit troubling, that certain questions are neglected in serious academic/policy debates.

The discussion of possible remedies focuses on regulatory solutions, everything from requiring mortgage brokers to be licensed to increasing financial institution capital requirements and having much greater harmonisation, as the Brtis like to put it, of banking and brokerage firm oversight.

While these measures individually and collectively could be salutary, no one seems to be willing to consider the fundamental question: did the push to facilitate the free flow of capital, both domestically and across borders, play a role in this crisis? For the last 15+ years, the push in policy has been towards increased efficiency, which means lower transaction costs, less supervision, little interest in considering whether so-called innovations benefit anyone beyond their purveyors (Martin Mayer observed that, "A lot of what is called innovative is simply a way to find new technology to do what has been forbidden with the old technology.").

It's important to examine this question, because many in this society have come to believe that regulation is bad and ever to be avoided. Yet markets like the equities markets, where participants trade an ambiguous promise anonymously, depend on regulation. Thus, the question should be, "What level of regulation is optimal?" rather than "How much regulation can we eliminate?" The problem with the latter approach is that it can take years for problems to develop, and when they do show up, since the tools to stop them have been thrown away, a full blow crisis has to develop for corrective measures to be implemented.

Some evidence suggests that free capital flows in and of themselves produce instability and crises. A recent paper by Kenneth Rogoff and Carmen Reinhart found that
Periods of high international capital mobility have repeatedly produced international banking crises, not only famously as they did in the 1990s, but historically.

Yet the focus of policy has been to increase the cross border flow of funds. Indeed, when the post mortems of this era are in, I suspect the carry trade will be found to have been a major culprit.

Another indicator: as the financial services industry has become increasingly deregulated and boundaries between businesses become blurred or meaningless (fund managers versus brokerage accounts, hedge funds versus proprietary trading desks, investment bank versus commercial bank) bank profitability has fallen and the industry has pushed into higher risk activities to try to compensate. Indeed, not only have overall risk measures risen, but the top banks also appear to be following common strategies. Both behaviors increase systemic risk.

Reader Richard Kline has been pondering this issue in a series of posts (see here, here and here) from a complex systems perspective rather than the traditional finance/markets vantage point. The discussion below summarizes his argument; a fuller treatment can be found here.

As always, your comments very much appreciated.

From Richard Kline:
Is high connectivity in the financial system desirable from the standpoint of stability? Conventional wisdom would largely say, yes; highly connected capital and exchange markets should ‘reduce inefficiencies,’ bring liquid capital to where ‘it is needed,’ and ‘level the playing field.’ Theoretical simulations of high connectivity systems together with related experience from systems design suggest the reverse: raising connectivity or undampening propagation in a system beyond modest levels in either case leads to high systemic asymmetry at best and pervasive systemic instability at worst. Those wishing an extended discussion of the underlying concepts will find it here. The basic concerns follow below.

CONNECTIVITY

Self-modulation occurs in systems with throughput, nodes, and connectivity between those nodes. If considered in idealized form, the financial system in general, and market behaviors in particular can be evaluated in these terms. Capital, debt contracts, futures, and the like could function as throughput, with both velocity V and volume L. Participants can function as nodes; highly dissimilar if large organizations negotiating specific contracts and deals; highly similar if bidders on regulated exchanges. Nodes vary thus both in size S and in the degree to which they behave differently D from each other. Connectivity K is simply the number of links any given node has to other nodes engaged in similar behavior. Both connectivity and differentiation impede throughput flows, but in opposite ways. The more nodes are connected, the more easily capital or information or loss exposure can flow; this is how connectivity is generally conceived in capital
markets, and the reasoning behind open exchanges. The more that nodes, i.e. participants, are similar in form or behavior, that is the less differentiated they are, the more throughput flows. Again, this is the reasoning behind common regulatory regimes, accounting rules, a common currency, etc.

Correlation across a system tends to involve shifts in differentiation D and connectivity K. That is, correlation largely concerns overall similarity of behavior amongst nodes; institutions move the same products, firms compete on price, market participants act in different directions at somewhat different times---or the same direction all at once, and so on. By contrast, modulation across a system tends to involve shifts in throughput, both in velocity V and volume L, but also regarding self-correlation of throughput. That is, modulation largely concerns similarity of form or movement of throughput; bonds are offered at regular intervals near known prices, varying product risks are ‘factored out’ by insurance or hedges, futures contracts channel price movements, and so on. From this perspective, several generalizations follow:

Organization in a system will self-generalize: order ‘flows’ across the nodes in a system inherently as differentiation D per node and connectivity K per node shift. Even if these changes are linear at the level of individual nodes, they are typically nonlinear at the level of the system, and may involve complete state changes with very short thresholds of transformation. Simulations show that even at very low levels of connectivity, K=2 [yes, two connections per highly similar node], systems will constantly if mostly gradually change their overall alignment. At high levels of connectivity, though, systems are prone to frequent, global transformations. Highly connected systems have inherently transient stability, unless otherwise buffered or dampened.

Connectivity K between nodes allows both order and throughput to circulate widely in a system. However, K is often agnostic as to the influences it allows to propagate, so that if changes in K may yield outcomes as intended they can yield and often do yield ones pervasive and unintended.

Differences between parts of a system impede flows across a system, whether flows of order, of throughput, or both. Differences create ‘inefficiencies,’ but they also buffer propagation in a system. Specifically, differentiation D---the extent to which nodes in a system vary in size, composition, and function---buffers node to node flow. Thus, increasing the similarity of participant behavior in markets (lowering differentiation) has the effect of lowering impedance for the same level of connectivity and/or ‘liquidity’ of throughput. If, for example, everyone carries a large balance on plastic and a low balance on passbook, more throughput moves through one part of the financial system, faster, and more easily.

Lowering nodal differentiation D in a system increases ‘efficiency’ in that it lowers buffering of throughput and allows connectivity to propagate order changes in a system. However, this may be at the expense of system stability as the effect may be the same as increasing connectivity K to the degree where system organization becomes chaotic. Residential property owners, developers, property assessors, mortgage originators, the capital markets, and the bond raters once had diverse profit strategies, but gradually they converged toward the fee-for-service, flip the product model of the capital markets. Connectivity increased, and throughput soared. Um, yes . . . .

Background correlation---the mapping of a system to its supporting context---often also serves as a buffer to propagation in a system since the background order is independent of and often resistant to modification by the order of a coordinated system. If the background order is itself highly correlated, though, it may function as a catalyst rather than as a buffer. Program trading in the late 80s where selling out of many portfolios was correlated to a few common background indices is an example. This is an endemic issue in financial markets, where despite being ostensibly buffered by high participant differentiation of behavior they nonetheless become correlated globally to a few background variables.

Systems with pervasive connectivity K amongst nodes have the advantage of being significantly adaptive to external changes. Raising connectivity for a system increases its overall adaptivity. This has been a purpose of just in time ordering, for example. However, such adaptivity is achieved at the expense of stable internal organization since high-K systems are very prone to system-wide changes: they are globally rather than locally adaptive. The auction rate market for municipal bonds was highly adaptive to very small changes in rates and extremely flexible for participants; it adapted globally to the shift in a single parameter, re-sale probability: look at it now.

‘Liquidity’ in a system is a composite behavior (a multi-variate derived state). Not only does throughput vary in velocity V as well as in the ‘headline number’ of volume L, it may modify itself through self-correlation as will be mentioned below. Additionally as per the above description, changes in both differentiation D and connectivity K in a system greatly change how throughput behaves. Where D and K remain generally the same, ‘liquidity’ can be influenced by varying volume or modulating velocity. As we see with the failure of ‘liquidity’ in US capital markets 08, volume and velocity alone are insufficient: the banks have low D---most are functionally insolvent---with decreased K---they little lend to each other. Studies of connectivity imply that in such conditions many minor local optimae develop with low overall systemic flow; just so. Despite large volume capital injection, the financial system remains ‘illiquid.’

MODULATION

Capital of similar form or moving in similar ways across a system of nodes-participants needn’t be reshaped drastically transaction by transaction; rather, it can be disproportionately influenced by small changes to the system which raise or lower impedance to its movement. This is what is meant by modulation. Central bank interest rate setting is substantially a modulation effect. A central bank ‘signal’ is small in relation to overall capital throughput, but even in the absence of legal compulsion that signal forms a value range around which transaction throughput is abundant and moves freely, while defining outlier value ranges where throughput moves poorly and accordingly is scarce.

Independent of connectivity, nodes within a system are not necessarily correlated amongst themselves, or at least not highly correlated. Despite this, throughput in a system---capital principally in the context of the financial system---can become more or less self-correlated. For example, if many different forms or terms of throughput move across nodes, any form which has lower resistance will move over more nodes. If its volume can scale, a larger share of throughput over a larger share of nodes is of the same form. Other forms or terms of throughput most nearly similar may see their velocity, volume, and distribution increase as well. In particular, if and as nodal differentiation decreases, the action of throughput is increasingly similar regardless of where it passes through a system: the throughput in effect self-correlates even if nodes and local connectivities retain significant diversity. Auto-correlative changes do not require overt
external intervention, although in financial markets such throughput convergences are highly profitable if spotted or maximized so external intervention in throughput flows is high and probable. If throughput flows and node differentiation and connectivity influence each other progressively, the process becomes self-modulating.

It is possible that as throughput across such a system becomes increasingly modulated, it can yield a field effect. Field phenomena have low overall resistance to point-source propagation; that is, they can globally reference their order state on a continuous basis. Marginal pricing in markets with good transparency strongly suggest a field order. Individual nodes may wish to diverge from a price point, but resistance from the rest of the market will be high; over any near duration, the field order will reduce the price discontinuity to the field order. Field effects can be modeled by tensors, but their ‘statistical logic’ to use a broad term is distinct from that which follows from the kinds of statistical tools typically used for economic activity. In principle, throughput in a system is likely a tensor field, while the system it is mapped to if nodal may well itself be a scalar field. The concept of capital flows as field phenomena is one
that I cannot prove but which should be studied more closely.

Finally, fields induce flow. Set a price or a volume gradient for capital, and said capital will flow across a system, typically towards high capital density regions. A gradient may thus ‘induce’ illiquid or capital-like assets to shift toward liquid forms, or otherwise to shift their state. Moreover, if throughput is sufficiently high in volume, velocity, or both, it can override, even mask, differences in nodes in the system. In part for this reason, system performance with high throughput will consistently give a misleading view of system stability. Correlation of throughput can by field induction carry flow behavior beyond the structural capacity of existing nodes. Again, large-large reasoning does not hold, especially for field phenomena: small value signals can reference larger flows of throughput which furthermore they do not necessarily transact directly. From this perspective, several generalizations follow:

Self-modulation of throughput in a system in effect simulates increasing connectivity K or decreasing differentiation D because throughput increasingly ‘acts the same’ regardless of its velocity or volume. Viewed from the perspective of connectivity above, systems with self-modulating throughput are less stable than their D and K values would suggest, and can become self-destabilizing: they overshoot.

While self-correlation of throughput is not necessarily bad or good, it can mask relevant distinctions. Consider MBSs, inherently of different quality and risk. However, this throughput had to act the same way to pass down-channel readily, so increasingly it had to ‘look the same.’ Hedges were bundled in, tranches were selectively sliced, and even ratings models themselves progressively tweaked to yield uniform AAA ratings. Self-correlation improved flow, even ‘induced liquidity,’ but this was no virtue from the standpoints of risk assessment or risk concentration. Moreover, MBSs of correlated appearance easily correlated their price declines, regardless of underlying differences in performance.

Dense concentrations of capital may drive other nodes to act increasingly the same way as high connectivity allows their ‘order to flow’ across a system. To the extent that they also modulate capital flows, the impact is not only increased but may be self-enhancing by field functions; in effect, such concentrations inherently propagate their own organizational order. Such order flows are not necessarily either complete, linear, or stable; however, their net effect may be to drive differentiation D down, and increasingly to correlate it. Again, in view of the summary above, this not only creates system asymmetry---i.e. the rich get richer---but lowers system stability: dense concentrations of capital are likely inherently destabilizing. For example, it has recently been identified that globally most central bank rates are negative or very low in real terms regardless of their nominal levels. One interpretation for the driver behind this result maybe that the ‘gravity well’ of US and Japanese real rates---which have both been low or negative since the early 90s for the most part---optimized rates first in closely integrated countries, than in others because smaller currencies with higher rates were more expensive to borrow and re-loan. From that perspective, financial preference steadily shifted to low-rate, high liquidity currencies, the opposite of what monetary policies anticipate: rates could either be higher than local conditions warranted or lower, but the ‘gravity’ of very low US and Japanese rates wouldn’t tolerate a middle position.

Statistical reasoning appropriate for field functions is seldom used in assessing throughput organization in the financial system, leading to misunderstanding of systemic conditions by observers. Stability and instability are not Cartesian plots but matrix distributions. The invisible hand is the beck and grasp of a tensor field; current analysis sees the fingernails on the hand, at most.

Stuart Kaufman. 1993. The Origins of Order.
Christopher Chase-Dunn and Andrew Hall. 1995. Rise and Demise.

[Kaufman’s text is dense but seminal in discussions of systemic connectivity, in this case amongst genes. Chase-Dunn and Hall consider core-periphery relations, a concept from political economy which has different implications from the perspective of systemic connectivity.]

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