It is often argued that the increasingly complex and inter-connected nature of the global financial system makes it safer and more robust. In our view this is often, but not necessarily always the case.

In fact, it might be that, in the most serious circumstances this complexity, and even our attempts to manage risk itself, can make things worse.

It is often argued that the financial system is now 'safer' than it has been in the past. This is partly because of the wide range of financial tools available to institutions. Risk can be diffused and 'spread out' - thus reducing individual exposures.

From the portfolio risk perspective, one way of looking at this is to think of their being 'active overlaps' between the risk portfolios of different institutions, generating a quasi super-portfolio. This can then benefit from a very large degree of portfolio diversification - thus dramatically reducing the overall risk, and consequently the individual risks of its participating components.

However, in our view, complexity is itself a source of risk. I believe this to be a fundamental truth, but we can illustrate it using three particular points.

Firstly: complexity causes a lack of transparency. This means that, even given all of the necessary facts - which are usually not available - it is hard to understand what is really going on, and difficult to make proper objective judgements.

This effect manifests itself both at the level of individual market participants and observers (including regulators and governments), and also at the level of the market itself. It is hard to argue that a market can be 'efficient' in the technical sense, when it is so difficult to interpret the information that it provides.

Secondly, no matter how diligent and detailed is our risk analysis, in the face of such complexity, there is always likely to be something that we have missed, tucked away in some dark corner of risk phase-space.

A classic example of this effect is the Space Shuttle. This is, we are told, the most complex machine ever built, and it is extremely impressive. However, from the risk perspective, this complexity results in great fragility - there are enormous numbers of things that can (and do) go wrong, both individually and in complex combinations. This makes flight risk management a Herculean task.

Thirdly, which is the main trust of this article; it is possible to generate 'leveraged risk circulation', without even realising it, which can result in systemic instability. This requires some explanation.

If you lend money to a counterparty, then your risk is that they won't pay you back - this is a straightforward 'credit risk' - and if you are a bank lending this money, you will estimate the chance of this happening, use risk-adjusted pricing to 'price it in', and ensure you have enough capital to cover your exposure.

Now, suppose that you are a bank, and you have made many such loans, and you are managing a risk portfolio - if your analysis shows that your risk is larger than you would like, either for the whole portfolio, or perhaps for a given sector, you might chose to do something about it.

In finance speak, you might choose to 'hedge' your risk - and one way of doing this would be effectively to buy an 'insurance policy' that protected you against the risks you were concerned about. Of course these are not normally referred to as insurance policies, but one particular variant is called a 'credit derivative'. This might, for example, take the form of a 'policy' that paid you if a certain number of counterparties in a given sector defaulted.

When you include the effect of this risk management tool in you analysis, you would see that your risk profile was now healthy again. At this point, you might correctly anticipate a 'But'.

We will use an extreme case to illustrate a point. Lets suppose that you are a bank, and you have worrying exposures to the banking sector, so you put in place credit protection (in this case a credit derivative), that you have bought from ... a bank. There is obviously a flaw in your master plan.

The flaw is that the circumstances under which you need to 'cash in' your credit protection are likely to be those under which your insurance is worthless - because the bank that sold it to you has gone bust.

What this means is that, when analysing the real risk of your portfolio, you not only need to take account of the effect of your credit protection, but also the credit risk associated with that protection itself - and for various technical reasons, this is far from straightforward.

At this point, we draw on the experiences of 'Lloyds of London' in the not too distant past.

In the late eighties and early nineties Lloyds found itself in some difficulties, because it had accidentally built up a large portfolio risk. It is important to understand what this means. Lloyds had a large portfolio, containing many large risks - this wasn't the crux of the problem. The problem was that the risk of their overall portfolio was much worse than they had thought, and when things started to go wrong, the proverbial pigeons came home to roost, and many 'Names' were hit very hard - so how did this happen ?

Lloyds was organised into 'syndicates', these syndicates sold insurance policies and managed their own individual risk profiles. When a syndicate judged that their risk profile was unacceptable, they would 're-insure' some of their risk - effectively taking out an insurance policy with another syndicate. Taking into account these risk mitigation measures, the syndicate would then look at their remaining 'Net' risk, which would then fall back within their acceptable risk limits.

So, given that the individual syndicates were all actively risk managed - what went wrong ? As it turned out, the syndicate's 'gross' risk levels were progressively increasing, and so they were doing more and more risk mitigation. As more and more re-insurance was done, a complex web of 'netting' effects came into existence. 'Circularities' developed in the re-insurance between the syndicates. In effect, syndicates were re-insuring themselves.

While this problem was building up, the overall risk - as measured by the sum of all of the Net risks of the individual syndicates was not obviously excessive.

This problem came to light when the system was 'shocked', claims were made on policies, which triggered re-insurance claims, which set of a vicious circle of risk realisation. It became clear that the overall risk was far greater than had previously been supposed.

Lloyds is actually a relatively simple case, because of the circumstances described, it can be seen why attempts at risk mitigation failed - and why the Net risk measures used were not appropriate.

For more complex systems, the analysis is not so straightforward. In particular, where we have complex webs of risk inter-dependency and netting effects, we can create the same problem, without the 'self insurance' effect being at all obvious. The author refers to this effect as 'Leveraged Risk Circulation'. So how does this relate to the financial system of today ?

The way a regulator would judge a bank, and set capital requirements, is at least partially, according to the risk the bank had taken on. This is often estimated using portfolio risk models. It is important to emphasise at this point that this is not done naively, and there are 'safety margins' built in, and rules about the kinds of netting that are allowable in these calculations.

However, this raises the possibility that there is a significant hidden systemic risk in the financial system, which arises from a combination of its complexity taken together with the ways that risk is measured and reported.

If we take a large-scale portfolio view, then in the authors opinion, the overall effect of much of this complexity is to reduce the levels of 'intermediate' and 'large' risks, but also possibly to increase some 'extreme' risks. We can look at this in several ways.

One aspect is the problematic issue of 'risk circulation', described above. This is a 'conditional' effect, and just as in the case of Lloyds, can lie hidden and unnoticed, until a 'shock' to the system occurs.

Secondly, we can draw another parallel from portfolio analysis. Credit risk profiles, like others, benefit from diversification. Statistics works in our favour, and the probability distribution for losses tend to become more concentrated around 'Expected' values, and extreme events become progressively less likely - but there is a catch

If we do this analysis properly (in the authors view), then we find that the benefits of diversification do not always turn out quite as expected. These benefits are significant for intermediate levels of risk, but are (in relative terms) less for larger and extreme risks. In statistical terms these distributions are 'fat tailed'. I would argue that many models underestimate the fatness of the tails for the more extreme risks.

If we temporarily delve into some of the underlying mathematics, there is a simple explanation for this. The distribution function can be thought of as being, in some sense a weighted average of a series of conditional distributions - each of these being for a particular set of governing circumstances. However, for a small number of these, which correspond to particularly severe environments, much of the benefit of diversification is lost, and extreme losses can occur.

Another way to look at this is to consider the analogy with a simple spider's web.

The web consists of an interconnected set of threads, which re-enforce one another. When a small, light object hits the web, the effect of the impact is quickly spread out and absorbed by the web, which stays intact. However, if a heavier object impacts the web, then the threads around the impact site break, but the rest of the web stays intact.

The silk from which these webs are made is incredibly strong, but if nature were able to have made it even stronger, would it have done so ? Probably not - because there would come a point where if a heavier object were to impact the web, then instead of failing locally, the web would take the full force of the impact, and either become detached or be destroyed.

This simple example shows how the web's inter-connectedness increases its strength and effectiveness, making it more robust and reducing the risk of failure. However, if the inter-connections are made too strong, then, for extreme events, the risk of total failure is actually increased.