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