Archive for May 16th, 2009
A few days ago (May, 14th) Rama Cont from Columbia gave a very interesting talk at the Frankfurt School of Finance & Management about contagious default and systemic risk in financial networks. From the abstract:
The ongoing financial crisis has simultaneously underlined the importance of systemic risk and the lack of adequate indicators for measuring and monitoring it. After describing some important structural features of banking networks, we propose an indicator for measuring the systemic impact of the failure of a financial institution –the Systemic Risk Index– which combines a traditional factor-based modeling of financial risks with network contagion effects resulting from mutual exposures. Simulation studies on networks with realistic structures -in particular using data from the Brazilian interbank network- underline the importance of network structure in assessing financial stability and point to the importance of leverage and liquidity ratios of financial institutions as tools for monitoring and controling systemic risk. In particular, we investigate the role played by credit default swap contracts and their impact on financial stability and systemic risk. Out study leads to some policy implications for a more efficient monitoring of systemic risk and financial stability.
He presented pretty remarkable results of a simulation study he conducted together with two of his students. The main goal was to introduce a “systemic risk index” (SRI) that quantifies the impact of an institution’s default on the financial systems through direct connection (i.e. counterparty credit risk) or indirect connection (i.e. seller of CDS). Based on that he compared the effect of risk mitigating techniques (i.e. limits on leverage, capital requirements) on the SRI. The simulation was based on random graphs constructed via preferential attachment, i.e., new nodes in the sytem tend to connect to the better connected ones – the Matthew principle. The constructed graphs were structurally similar to the structure observed in real-world networks in Brazil and Austria. Running the risk of oversimplifying, the key insights were:
- The main message: It is not about being “too big to fail” but about being “too interconnected to fail”. In the presented study size was completely uncorrelated to the potential impact given default. That is especially interesting given that in the current discussion about the financial crisis, one prominent argumentation demands the split up of large financial institution. Assuming that the results are realistic, this would provide only minimal systemic risk mitigation but might increase the administrative overhead to monitor all these smaller units. Another consequence that might be even a bit more critical is the implied moral hazard. Whereas gaining a certain size in order to be “too big to fail” is a rather hard task, being “too interconnected to fail” is rather simple: Given the later described large impact of only a few CDSs it might suffice to buy and sell a lot of CDSs (or other structures) back-to-back (i.e. you are long and short the same position and thus net flat) in order to insure yourself against failure by weaving or implanting yourself deep into the financial network. (see also 2. below)
- Based on the real-world network that were studied, only a few hubs in the network constitute the largest proportion of potential damage. These are the ones that are highly connected. Thus a monitoring focused on these particular nodes that could be identified using the proposed SRI might already lead to a considerable mitigation of systemic risk.
- It does make a difference if you have a limit on leverage compared to capital requirements only. The impact of the worst nodes in the network considerable dropped in presence of limits on leverage (as for example in Canada employed).
- Comparing the situation with and without CDSs, the presence of only a few CDSs can change the dynamics of the default propagation dramatically by introducing “shortcuts” to the network – effects similar to the small world phenomenon.
- In the model at hand, it didn’t make a difference if CDS contracts were speculative or hedging instruments. Note, that was under the assumption that the overall number of contracts in the simulation remained constant and only the proportion were altered – otherwise under the mainstream assumption that more than 50% of all CDSs are speculative, removing those would reduce the number of contracts present by more than 50% and thus considerably reducing the risk through “shortcuts”.
Wolfram|Alpha, the computational search engine, is online now. Check it out yourself - it is definitely worth it.
A few examples that I tried:
- 3-cross polytope or the n-cross polytope
- another polytope example
- you can also solve equation
- or calculate recurrence relations
More examples are available here.