Identifying Trading Opportunities by using Correlation Matrices to reduce the latency of response time through a nodal Credit Structure.

Premise No company exists in the Credit System in isolation. There are a large number of interconnections between any company and a variety of others in its vertical market. For instance, Visteon, the auto parts manufacturer, derives a large part of its income from the Ford Motor company, thus a significant credit event affecting Ford, will have non-trivial implications for Visteon. This paper deals with the fundamental identification of the problem as a direct corollary of a mass-spring system in structural dynamics. This idea can be extended to a series of companies in a credit “cascade”. The whole notion of a company existing by itself in isolation is not commensurate with the reality of the market. Three things become apparent on closer examination of the problem at hand.

• Every company is connected to an arbitrary number of other companies and this can be modelled in the same way route matrices are constructed. These sub-matrices can be combined in the same way as the sub-matrices representing nodes are modelled in finite element analysis.

• Any arbitrary matrix representing these routes between each node is constructed and each entry is marked to show the number of routes between any node and its neighbouring nodes.

• The amount of time which elapses between a credit event occurring and the “ripples” spreading out to the satellite companies is certainly not instantaneous. This is where the opportunity lies. This paper aims to demonstrate how a properly constructed system can model the invisible links and allow a market actor to obtain significant advantage by looking for trades in the “wash” of the credit cascade.

How to construct a mechanical analogue of the Credit System In Engineering, there is a concept called dualism. In short, dualism provides a mechanism for engineers from one discipline to identify a set of processes which may have well defined sets of equations and well known solutions in another discipline. Electrical and Mechanical engineering disciplines share a remarkable variety of applied mathematical methods despite the problem-space being apparently radically different.

The Electrical-Mechanical Analogue: The LCR (inductance, capacitance, resistance) Series Circuit This is obviously NOT a mass-spring-damper system, yet it is of great interest to those concerned with mass-spring-damper systems, as one will see.

Here it is necessary to know that the potential drop across a capacitor is given by where q is the charge on the capacitor with capacitance, C. R is electrical resistance, L is inductance and e(t) is the applied voltage. i(t) is the current that results (it is the output from the system). It is also necessary to know that

The differential of both sides of this leads to

(The rate of change of charge across a capacitor is equal to the current in the circuit) and hence

Applying Kirchhoff’s 2nd Law (the sum of the potential drops across all elements in a circuit equals the applied potential)

Unfortunately, this differential equations involves TWO time-dependent output variables i(t) and q(t). However as seen above, they are related, so the equation can be totally written in terms of q (or indeed of i) leading to a second-order differential equation in q, or differentiating equation (A) with respect to time and replacing

with i, gives

Note the similarity between the two equations marked # (the other is on page 3.)

Here they are again.

These two equations are fundamentally identical and constitute an electrical- mechanical analogue. Notice the analogy between corresponding parameters and variables. In the electrical circuit: L behaves like mass, M R behaves like mechanical resistance, R

i(t), the output from the electrical system, corresponds to displacement, y(t), the output from the mechanical system.

, the rate of change of applied voltage, behaves like the applied force, f(t). These analogies form the basis of analogue computers, aircraft simulators, etc. in which real-world mass-spring-damper type systems can be simulated with the equivalent electrical analogue circuit. In any such system, if you know the values of M, R and k then you can simulate that system electronically.

Now back to the Credit System We can represent the companies as nodes in a system that we model in a similar way to the nodes in a mass-spring system. The aim of this study is to find the Credit Analogues for the mass-spring system. The reasoning behind this is that there exists a comprehensive toolbox in engineering mathematics for solving mass matrix problems. There are results from any system known as eigenpairs which allow us to find resonant frequency responses for a system and thus predict the behavior of any node. The fundamental error being committed in the Credit System today is how analysts work out the behaviour of companies following a credit event. There will be repercussions and thus trading opportunities since the price of corresponding equities and credit default swaps will not change immediately.

Analogy with Currency Trading Let us consider 3 currency pairs, Pound Sterling, Dollar and Chinese Renminbi. Today, the crosses are as follows, GBPUSD = 2.06 GBPCNY = 15.94 USDCNY = 7.74 Now for an efficient market, we notice that there is no benefit to be had by holding any one currency cross in relation to another. But now let us imagine that for some reason that we are holding GBP30,000 in 159400 CNY, 20600 USD and 10000 GBP. Let us now say that the USD against the GBP weakens to 2.12, with the other 2 crosses remaining the same. We can make money risklessly by selling our 10000 GBP to buy 21200 USD. We can then convert the 21200 USD to buy 164,088 CNY. The extra CNY now converts into 10,294 GBP. So for doing nothing except identifying the conversion discrepancy, we have made a riskless 294GBP. Of course by doing this trade, we will change the crosses immediately. By selling GBP we will change the exchange rate of the cross between USD and GBP, driving it down from 2.12 to something lower. By selling CNY we will drive down the number of USD we get for each CNY. This is the same basis behind Capital Structure Arbitrage. We use the relative imputed valuations between the equity, bonds and credit default swaps of the same company. As the equity price of a company changes, its CDS and bonds ought to reflect this change, but in reality there are delays in the price movements. Using different models for working out Credit Default Swaps (CDS) prices we can make money by simply buying or selling CDS based on the movement on stock prices and bonds. In effect, we have transformed the Capital Structure equilibrium problem to the Currency problem space and thus apply the same money making methods from Currency trading to Capital Structure. Both are forms of arbitrage.

Optimisation Methods We can never be certain of the reality of the reported cash reserves, liabilities or assets of any firm. What we can do instead is build a nodal picture of the connections a firm has with others. This will be achieved by talking to analysts and also following the movement of suspected realtives.