The “Holistic” Theorem

Applying it to explain why financial institutions should welcome mandatory centralized clearing of derivatives trades



The Holistic theorem is the idea that “The more people participate in a system, the more it makes sense for a central authority to mediate their relationships/communication; No matter what the cost for setting up this central authority, as the number of participants increase, this cost is dwarfed by the benefits of centralized mediation on a linear vs. quadratic basis.”

The “Holistic Theorem” compares to other statistic models of social organization such as Zipf Law.

This idea helps explain why financial institutions should welcome mandatory centralized clearing of derivatives trades and provides insights into other economic and current affairs’ issues

<para><b> <br></b> </para> <sec><heading>Centralized Clearing of Derivatives Benefits All</heading><para> <b> <a href=”;rel=1″>YouTube Video</a> </b> <b> Check also <a href=””></a&gt; </b> </para> </sec><sec><heading></heading><para><br></para> <para> A consensus is building worldwide <a href=”#references”>[1]</a> that financial trading institutions should be subjected to mandatory centralized clearing of all derivatives trades. The argument has so far focused on the transparency benefits of such a rule. The emphasis is on preventing any further systemic perils. </para> <para> <br> One assumption of regulatory advocates and foes alike is that it would become just one more financial burden on trading institutions. The disagreement is often only as to whether the systemic benefits outweigh the private costs. However, closer scrutiny reveals that the contrary of the base assumption might be true. Generalized centralized clearing would reduce trading institutions’ operational costs. Here is why. <br> <br> Suppose we have 10 financial institutions all trading derivatives contracts with one another. <br> <br> In a non-centralized clearing system, each financial institution has a cost center whose job is to manage and approve trading limits on all derivatives contracts with counterparts as part of each institution’s counterparty credit risk management function. Since each institution has nine counterparts and there are ten such institutions, that means there are 90 counterparty credit risk positions to monitor. <br> <br> In a centralized clearing system, the central clearing authority is the counterparty on all trades. Its counterparty credit risk management cost center manages the credit risk of the ten trading institutions. If the central counterparty entity is backed by the government so as to be default free, none of the trading institutions has to monitor the credit risk of the clearing institution. In any case, each counterparty has to worry at most about the solvency of the central counterparty and not that of the other trading institutions, a role that a single third party can effectively fill for all parties. Hence we would be reduced to a single cost center monitoring 10 counterparty credit risk positions. <br> <br> A centralized counterparty system in this example thus reduces the overall number of counterparties credit risks to monitor from 90 to a mere 10. More generally, with a centralized clearing system, if there are p counterparties, there are p(p-1) counterparty risks to estimate while a central counterparty only has p (or 2p if the clearing counterparty may default) counterparty risks to estimate. Put differently, overall counterparty risk management costs grow linearly with the number of participants while in a bilateral counterparty system, those costs grow quadratically. Hence, the structure of these benefits is similar to what is known in communication economics as “network effects”. If the number of counterparties exceeds 2 (or 3 if the clearing counterparty may default) and the cost of estimating a counterparty credit risk is constant, a central counterparty system results in less overall costs. In this sense, this organizational structure is “optimally informationally efficient” and this result may be stated as a holistic theorem <a href=”#references”>[2]</a> . Figures 1 and 2 summarize this analysis. <br> <br> It is then clear that the marginal fee paid to a clearing institution for counterparty risk management will become insignificant as the number of counterparties increase compared to the cost to each party if they were managing such a risk internally. Indeed, if setting up a clearing system entails a setup cost s in units of costs needed to manage or estimate a counterparty risk, a central counterparty system is more cost efficient once the number of counterparties becomes larger than c = 3(1+√(1+4s/9))/2. c is obtained by solving x(x-1)-x-s=0. Figure 3 shows how c is a concave function of s. <br> <br> Furthermore, in a clearing system, counterparty credit risk is better accounted for since the clearing organization maintains a consolidated tabulation of each party’s net positions. According to the 4th quarter of 2008 report of the Office of the Comptroller of the Currency <a href=”#references”>[3]</a> , the leading financial institutions still do more than 90% of their trading over the counter. <br> <br> In the best of worlds, there would be a single central and default free clearing entity who would keep netting all trades and granting trading limits. The practical hurdle to such an arrangement is that the only viable pretender – a default free sovereign government backed entity, would most likely lack the internal expertise to timely and cost effectively value and assess the risks of all potential contracts with its various counterparts. That is why a transparent inter-connected layered structure as described in our <a href=””>powerpoint presentation</a> would act as an effective substitute. This structure somehow implements the <a href=””>subsidiarity principle</a> that is used in the catholic church to enable a highly centralized institution to effectively function. <br> <br> Smart regulation would thus further come into play in the form of capital reserves requirements each such clearing entity would have to maintain in return for FDIC-type guarantees that ensure default free status. In addition, regulators should mandate that all clearing entities share among themselves the net positions of all counterparties in real time. Such a step would facilitate effective credit risk management by making available to all who need to know, up to date aggregate balance sheets of all trading parties. <br> <br> This last requirement plays an essential role to prevent the sometimes fateful delays in recognizing the parties’ true risk positions. The recent AIG, Lehman and Bear Stearns cases are a prime example. We could metaphorically call it a two-timing or multiple-timing credit arbitrage. It is a practice that takes advantage of counterparties delayed awareness of each other’s true credit position. It is an important factor explaining how neither regulators nor credit agencies could provide timely warnings on financial institutions true credit profile up until just before they collapsed. It is that sudden realization that caused many institutions to stop trading with one another in September when Lehman failed. </para> <para><br></para> </sec><sec><heading>Re-examining the “Government is the problem” mantra in light of the holistic theorem</heading><para></para> <para> Another application of the holistic theorem to debunk the economic theory that is the basis for Reagan’s famous assertion that Government is the problem. In <i>Constitution of Liberty</i> <a href=”#references”>[4]</a> , Friedrich Hayek, the conservative economists’ hero stated, “Probably nothing has done so much harm to the liberal cause as the wooden insistence of some liberals on certain rules of thumb, above all of the principle of laissez-faire capitalism” . The intellectual backbone of modern hostility towards central authority intervention that came to power in the early eighties with Reaganomics and Margaret Thatcher is grounded in Ronald Coase’s article “The Problem of Social Cost” <a href=”#references”>[5]</a> where the argument is made that it is often better for two parties to reach a negotiated solution when one party operate a plant that pollutes the environment that the other uses for their livelihood if the value created by the plant is greater than that lost earnings to the other party. Therefore, the argument goes, intervention by the government causes more harm than good because its cost subtract from the financial ability of the polluting plant to viably compensate the other party and result in less value created overall. As our analysis of critical mass levels in figure 3 shows, once there are more than 2 players involved, the cumulative benefits of a central authority of reference to all parties start far outweighing any cost such an authority may impose while getting started. In addition to systemic failure evidenced in this financial crisis, going forward, the advents of the internet and the ever cheaper internet technologies will increasingly reduce the cost of setting up and managing any centralized counterparty system. </para> <para>Yes, sometimes government really is the solution. Stimulating and effective regulations that demonstrate comprehensive understanding of the intricate forces at play and convincingly explain how the best interests of all the major stakeholders are being served ensure their sustained success.</para> </sec><sec><heading><br></heading></sec><sec><heading>Conclusion</heading><para><br> The applications of this application are numerous and the above are just a few examples. Often humans converge to its prescription without the mathematical rationale outlined above because it just seems commonsensical. In that sense this “Holistic Theorem” compares to other statistic models of social organization such as <a href=””>Zipf Law</a> . </para> <para>The mathematically inclined would also note that the failure to have a central counterparty of reference is as inefficient as doing geometry n a system without origin or point of reference and trying to locate the position of a myriad of points with respect to one another in a multi-dimensional (risks) space.</para> <para> My blog on May 11 below further uses the holistic theorem to explain how high density population tend to prefer a strong role for a central government. <br></para> <para><a href=””></a&gt; </para> <para> This explains the Blue Vs. Red states divide in the US, the Hamiltonian Vs. Jeffersonians’ viewpoints as perfectly rational from each subjective viewpoint (urban, densely populated Vs. rural, sparsely populated) <br></para> <para><br></para> </sec><sec><heading>Wolfram Demonstration</heading><para> This presentation is also illustrated as a peer-reviewed publication in the Wolfram demonstrations project <br></para> <para><a href=””>Holistic Theorem</a> </para> <para><br><a href=””&gt; <img alt='”Holistic Theorem” from the Wolfram Demonstrations Project’ src=””></a&gt; </para> <para> This knol tinyurl: <b></b&gt; </para> </sec>

Appendix 1

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