Monday, December 27, 2010

Complexity economics and the global financial system

Andrew Haldane of the Bank of England has an excellent speech highlighting the complex and adaptive nature of the global financial markets. He compares the reaction of global financial market to market events as similar to the "flap of a butterfly’s wing in New York or Guangdong generates a hurricane for the world economy". He writes,

"Complex because these networks are a cat’s-cradle of interconnections, financial and non-financial. Adaptive because behaviour in these networks are driven by interactions between optimising, but confused, agents. Seizures in the electricity grid, degradation of ecosystems, the spread of epidemics and the disintegration of the financial system – each is essentially a different branch of the same network family tree."

Conventional wisdom on complex systems like eco-systems and financial markets was that they were self-regulating and self-repairing. It was though that complex systems tended to exhibit greater stability, and complexity strengthened self-regulatory forces in systems, so improving robustness. However, the events of the past 18 months have revealed a financial system which has shown itself to be neither self-regulating nor self-repairing. He uses four mechanisms to explain complex adaptive systems

1. Connectivity and stability - robust-yet-fragile character

Interconnected networks exhibit a knife-edge, or tipping point, property. Within a certain range, connections serve as a shock-absorber. The system acts as a mutual insurance device with disturbances dispersed and dissipated. Connectivity engenders robustness. Risk-sharing – diversification – prevails. But beyond a certain range, the system can flip the wrong side of the knife-edge. Interconnections serve as shock-amplifiers, not dampeners, as losses cascade. The system acts not as a mutual insurance device but as a mutual incendiary device. Risk-spreading – fragility - prevails. The extent of the systemic dislocation is often disproportionate to the size of the initial shock.

Another feature of connected networks is their 'long-tailed distribution' - the histogram formed by the number of links to each node. Unlike the randomly configured network with its symmetric and bell-shaped distribution, many real-world networks do have a thin middle and long, fat tails. There is a larger than expected number of nodes with both a smaller and a larger number of links than average.

Long-tailed distributions have been shown to be more robust to random disturbances, but more susceptible to targeted attacks. Therefore, long periods of apparent robustness, where peripheral nodes are subject to random shocks, offers little comfort or assurance of network health. It is only when the hub – a large or connected financial institution - is subject to stress that network dynamics will be properly unearthed.

Another feature of connected networks is their 'small world' property. In his famous chain letter experiment, Stanley Milgram showed that the average path length (number of links) between any two individuals was around six – hence 'six degrees of separation'. He found that certain key nodes can introduce short-cuts connecting otherwise detached local communities. This property will tend to increase the likelihood of local disturbances having global effects – so-called 'long hops'. A local problem quickly turns into a global one.

Haldane examines the global financial system and finds several interesting changes over the past two decades. First, the scale and interconnectivity of the international financial network has increased significantly - nodes have ballooned, increasing roughly 14-fold, and links have become both fatter and more frequent, increasing roughly 6-fold. Second, the international financial network exhibits a long-tail. Measures of skew and kurtosis suggest significant asymmetry in the network’s degree distribution. Third, the average path length of the international financial network has also shrunk - between the largest nation states, there are fewer than 1.4 degrees of separation.

2. Feedback and stability

The sub-prime crisis generated panic hoarding of liabilities (counterparty risk meant that banks hoarded liquidity rather than on-lend it) and distress sales of assets (to meet margin calls or reduce exposures). Individually-rational actions generated a collectively worse funding position for all. These rational responses by banks to fear of infection added to the fragility of an already robust-yet-fragile financial network.

3. Uncertainty and Stability

Through widespread counterparty uncertainty, networks have important consequences for the dynamics and pricing in financial markets. Given the multiple levels of splicing and dicing of derivative instruments, it was impossible to even trace back counterparties, leave accurately alone pricing those risks. Links in the chain are unknown and determining your true risk position is thereby problematic. The network chain was so complex that spotting the weakest link became impossible.

4. Innovation and stability

Another dimension of network stability was the role of complex financial instruments. Financial engineering unleashed into the markets an alphabet soup of instruments whose range of real risks were often impossible to assess with any reasonable degree of certainty.

He draws insights from network theory in areas like ecology, epidemiology, biology and engineering, to explain the emergence over the past decade of a financial network characterized by complexity and homogeneity (pro-cyclical and exposure to similar types of instruments and areas). The trend towards slicing and dicing risk and diversifying them through securitization and derivative instruments dramatically increased the system inter-connectedness and complexity. he says,

"Follow-the-leader became blind-man’s buff. In short, diversification strategies by individual firms generated heightened uncertainty across the system as a whole... a strategy of changing the way they had looked in the past led to many firms looking the same as each other in the present. Banks’ balance sheets, like Tolstoy’s happy families, grew all alike. So too did their risk management strategies. Financial firms looked alike and responded alike. In short, diversification strategies by individual firms generated a lack of diversity across the system as a whole. So what emerged during this century was a financial system exhibiting both greater complexity and less diversity. Up until 2007... complexity plus homogeneity equalled stability."

The impact of these trends was that the financial network,

"... was at the same time both robust and fragile – a property exhibited by other complex adaptive networks, such as tropical rain forests; whose feedback effects under stress (hoarding of liabilities and fire-sales of assets) added to these fragilities – as has been found to be the case in the spread of certain diseases; whose dimensionality and hence complexity amplified materially Knightian uncertainties in the pricing of assets – causing seizures in certain financial markets; where financial innovation, in the form of structured products, increased further network dimensionality, complexity and uncertainty; and whose diversity was gradually eroded by institutions’ business and risk management strategies, making the whole system less resistant to disturbance – mirroring the fortunes of marine eco-systems whose diversity has been steadily eroded and whose susceptibility to collapse has thereby increased."

He then draws on the experience of other network disciplines and provides some tentative policy prescriptions to manage the financial network and avert systemic dislocations. He discusses three areas,

"1. Data and Communications: to allow a better understanding of network dynamics following a shock and thereby inform public communications. For example, learning from epidemiological experience in dealing with SARs, or from macroeconomic experience after the Great Depression, putting in place a system to map the global financial network and communicate to the public about its dynamics... Part of the answer lies in improved data, part in improved analysis of that data, and part in improved communication of the results;

2. Regulation: to ensure appropriate control of the damaging network consequences of the failure of large, interconnected institutions. For example learning from experience in epidemiology by seeking actively to vaccinate the 'super-spreaders' to avert financial contagion; and

3. Restructuring: to ensure the financial network is structured so as to reduce the chances of future systemic collapse. For example, learning from experience with engineering networks through more widespread implementation of central counterparties and intra-system netting arrangements, which reduce the financial network’s dimensionality and complexity."

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