Network Modeling 101 - Applications to the banking industry
- 1. Network Modeling 101 For Financial Interlinkages By Prajakta Kharkar-Nigam (pkharkar@gmail.com) Financial Stability Dept. Bank of Uganda 22 March 2013 Acknowledgement: The presenter would like to thank Dr. Giorgos Cheliotis’ for inputs drawn from his social network analysis course at National University of Singapore
- 2. Key Question: Interconnectedness If one bank were to face an adverse shock, how would the rest of the system be affected? Potential Solution: Analysis using network modeling tools 2
- 3. What does a network model look like? 3
- 4. Where are network models used? • Intelligence agencies identify criminal and terrorist networks from traces of communication that they collect; and then identify key players in these networks • Social Networking websites like Facebook identify and recommend potential friends based on friends- of-friends • Epidemiologists track spread of diseases • Central Banks for mapping interlinkages between FIs 4
- 5. Why Networks? • Among central banks, who is using them? – Bank of England , Deutsche Bundesbank, European Central Bank, Reserve Bank of India, South African Reserve Bank, Bank of Uganda etc. • Most central banks favour network analysis because – Networks make ‘big things visible to the naked eye’ • Uncover patterns in relationships or interactions which may not be readily clear in the numbers – • Follow the paths that information (liquidity, panic) follows in financial systems – Once data is mapped as a network, it is easy to simulate systemic shocks, contagion and crises. 5
- 6. Key attributes of a network Network map • How to represent interlinkages in a visual map? Tie strength (link • How to identify strong/weak interlinkages? • How much liquidity/information is being carried perspective) through each link? • Which nodes are critical to the network? Key players • Which banks are systemically important? Cohesion (cluster • How close knit is the network? • Who is likely to help/hurt who in a crisis or in the perspective) event of a bank resolution? 6
- 7. Nodes, Links and Adjacency 7
- 8. Adding magnitudes to linkages Edges represent : • Volume, frequency or value of actual transactions •flows of information or money, •ownership affiliations Weights (for linkages) can be based on: •Volume, frequency or value of transactions supplied by a bank •Perceptions of bank’s risk in the market •Combination 8
- 9. Paths, shortest paths, longest distance • Path: A path between any two nodes is any sequence of non-repeating nodes that connects the two nodes. • Shortest Path: The shortest path or distance between two nodes is the path that connects the two nodes with the shortest number of edges. • Longest distance: The longest shortest path or distance between any two nodes is a useful measure of the reach of the network. It also indicates how long it will take at most to reach any node in the network. 9
- 10. Tie strength and its measures • Once a network is mapped, to find out which link(s) matters the most or is ‘central’ • Four measures of centrality: 1. Degree Degree – For identifying which banks are most connected directly and hence, central for spreading liquidity – Measured by number of links leading in or out of the node 2. Betweeness – For identifying which bank is systemically important enough (well connected directly and indirectly) that if it fails, the network may either break down or will face severe delays in transferring funds – Likewise it also tells us which banks will lead to Betweeness fastest transmission of contagion risk – Measured by number of shortest paths that pass through the given node divided by all shortest paths in the network 10
- 11. Tie strength and its measures (cont’d) 3. Closeness (double edged sword) – For identifying if we were to add liquidity in the system, through which banks will it spread the fastest Closeness – Likewise, if there were a panic, through which banks might it spread the fastest – Measured by mean length of all shortest paths from a node to all other nodes in the network, that is how many hops on average does it take to reach every other node in the network 4. Eigenvector – For identifying which banks are directly connected to the most connected banks. First round of banks to fail if a shock were to hit the well-connected node. Eigenvector – Measured as proportional to sum of all the eigenvector centralities of all nodes directly connected to it. – This is similar to how Google ranks web pages, those linked to other highly linked pages come out higher in the search results. 11
- 12. Interpretation of tie strength measures for banking industry • How many banks can this particular bank Degree affect directly? • How likely is this bank to be systemically Betweeness important to the network? • How quickly on average can problems at this Closeness bank spread to other banks in the network? • How well is this bank connected to other Eigenvector systemically important banks? 12
- 13. (Sets of) Key Players •Node 10 is the most central according to degree, but nodes 3 and 5 together will reach more nodes due to closeness. •Moreover the tie between them is critical; if severed, the network will break into two isolated sub-networks •So other things being equal, banks 3 and 5 together are more ‘key’ to this network than bank 10 •Thinking about sets of key players is necessary 13
- 14. Cohesion (cluster) and its measures • Four measures of cohesion: 1. Reciprocity: • For identifying which banks are transacting with each other and where the relations are unilateral. Reciprocity • Insight into distribution of power and dependence. • The ratio of the number of relations which are reciprocated (i.e. there is an edge in both directions) over the total number of relations in the network 2. Density • It is a common measure of how well connected Density a network is (not a specific node). A perfectly connected network is called a clique and has density=1 • Measured by the ratio of the number of edges in the network over the total number of possible edges between all pairs of nodes 14
- 15. Cohesion and its measures (cont’d) 3. Clustering – Clustering indicative of the presence of different smaller networks within a large network of banks. Clustering – Indicates if certain group of banks transact or interact within themselves, and more importantly how that changes over time. – A node’s clustering coefficient is measured as the density of its neighborhood. 4. Average distance – For identifying how quickly on average would any shock spread through the entire banking network. – The average of all shortest paths in a network indicates how far apart any two nodes will be Avg. distance on average 15
- 16. Interpretation of cohesion measures for banking industry • Which banks are transacting with each other Reciprocity on both sides of transactions? • How close knit the banking industry is? This Density can cause risks to become systemic in no time. • Is a certain group of banks transacting Clustering amongst themselves, and more importantly how is that changing over time? Average • How quickly on average would any shock spread through the entire banking network? distance 16
- 17. Further food for thought • Network models can be used for stress testing, crisis simulation and for surveillance • Network maps give us a framework to dissect interconnectedness with the full big picture in view. • Key insights for macroprudential policy – Interconnectedness is a double edged sword – What is good in normal times is precisely what leads to crises in stressed times – Optimal level of network measures is required, an excess in either direction would be undesirable. 17
Editor's Notes
- #2: Bundesbank TA – Dr Co Pierre Georg – 15th-19th April (TA and training)Over the next few weeks, we will have presentations to bring everybody abreast of basics of network theory and the work which has been done on it within the dept. This is the first of those presentations, so my objective today is mainly to give you a ‘teaser’ to tickle your thoughts, make you curious about this stuff and hungry to know more.
- #4: Looks like chaos but it is not. The network model is not a hierarchy- it is not like our organisational structure. Instead of focusing on individual financial institutions and their attributes, or on macroscopic conglomerate structures, it centers on relations between institutions and groups.AXA (insurer) linked to almost 5 bank groups directly and almost all indirectly, there is no way it would be come unscathed from a ‘banking’ crisis.
- #5: Network models have several practical applications but their origins are in social sciences for studying social networks. But the quantitative analysis of networks has been made possible by mathematicians and computer scientists. Six degrees of separation – rings a bell?A new perspective.
- #7: Each attribute enables us to analyse the network to get different insights
- #10: Longest distance, not longest pathKnowing upto here, we can construct a network map but we can’t analyse it.
- #11: Nodes 3 and 5 have highest degree (4) – there’s an in-degree and an out-degree, to be used for the respective purposesNode 5 has higher betweeness centrality than 3
- #12: Nodes 3 and 5 have lowest closeness, while node 2 fares almost as well. Node 3 has highest eigenvector centrality, closely followed by 2 and 5.
- #13: Sometimes it seems they are all tell us the same thing but no, the insights are nuanced. Systemic importance, probability, speed etc.
- #14: This is where judgment comes into play. So by employing quantitative network analysis, we cannot discard judgement, quite the opposite. We need judgment to make sense out of network measures.
- #15: Density is useful in comparing networks against each other, or in doing the same for different regions within a single network
- #16: Clustering is Density 2.0
- #17: These measures should be observed over time because changes matter more than absolute state of the network at a point in time. Is the network moving towards a structure that leads to greater and quicker amplification of risks?