Agglomerative hierarchical cluster analysis & Dendograms to club LFCIs

We found an interesting article on the Large Complex Financial Insitutions (LCFIs) and the common factors that influence their asset price behavious. The write-up talks about how various large complex financial institutions show the same behaviour of CDS premia due to exposure to the same macro-economical variables. It uses agglomerative hierarchical cluster analysis approach & correlation matrix to prove how the financial institutions can be clustered on the basis of equity returns and credit default swap premia.

The key points summarising the write-up are:

· - It seeks to determine the extent to which LCFIs are influenced by common factors. Knowledge of these common factors is important for the assessment of risks to financial stability emanating from LCFIs.

· -When compared with institution-specific factors, systemic risks arising through ‘common exposures to macroeconomic risk factors across institutions’ carry the ‘more significant and longer-lasting real costs’ to the financial system.

· -This article takes a complementary approach and examines the asset price behaviour of LCFIs on the assumption that sophisticated market participants are able to see through the veil of accounting (and possibly incorporate information not published incorporate accounts) when pricing assets. In particular, correlation matrices are computed for equity returns and changes in credit default swap (CDS) premia. Several techniques are used to summarise the essential features of these two correlation matrices, many of which simply provide graphical or numerical summaries of a subset of the correlations.

-· - To the extent that equity prices reflect discounted future income streams, a high correlation between equity returns of LCFIs may indicate exposures to common return factors. Similarly, if CDS premia are taken as indicative of the risk of the institutions, similar behaviour of CDS premia may suggest exposure to common risk factors. The analysis of common factors influencing LFCIs’ asset prices encompasses both perceptions of direct exposures between LCFIs and exposures to similar external factors.

· -Empirical techniques are applied that summarise the key features of these LCFIs’ equity returns and CDS premia changes.

· -A number of methods are used to investigate the essential features of the correlations of these returns, imposing no assumptions on what is driving the correlations. Results from this analysis are then used to build a factor model of LCFI asset prices, to investigate the extent to which LCFIs’ asset prices are driven by common factors.

· CORRELATION:

*data used: Equity prices denominated in US dollars for the LCFI group are taken from Datastream for the period 30 May 1994 through 6 October 2003.

-Weekly equity returns are calculated as percentage changes using Monday closing prices.

- As a comparison, equity return correlations for a control group of non-financial companies matched to the LCFI group by market capitalisation and country were also computed. These correlations are on average much lower than those between LCFIs

· Cluster analysis:

Cluster analysis attempts to determine the natural grouping of observations and is best viewed as an exploratory data analysis technique. It is applied here to determine groups of LCFIs whose equity prices or CDS premia behave in similar ways. These companies can then be considered to be similar institutions whose equity returns or CDS premia changes are probably driven by common factors.

· Case uses: agglomerative hierarchical cluster analysis

1. This approach combines LCFIs into groups of similar institutions. The algorithm initially views each observation (LCFI) as a separate group (giving N groups each of size 1). The closest two groups in terms of the Euclidean distance are then combined (giving N-2 groups of 1, and one group of 2). This process continues until all observations are combined into one group (of N LCFIs).

2. The clustering results of the equity returns of the fourteen LCFIs are shown in a dendrogram. Two major clusters are apparent, since the LCFIs cleanly divide into US and European groups.

3. Within these regional groups, sub-groups can also be identified. The North American bloc consists of two sub-groups: (i) the three large banking groups (Citigroup, JP Morgan Chase and Bank of America), and (ii) the three brokerage houses (Merrill Lynch, Morgan Stanley and Lehman Brothers). The European bloc contains sub-groups made up largely of national clusters. Thus the Swiss banks join together, as do the two British banks and the two French banks. The six continental banks form a single cluster before the UK banks are added. The first LCFIs to join the two French banks do so a long way from the bottom of the dendrogram, indicating relatively high levels of idiosyncrasies

4. The clustering of LCFIs according to changes in CDS premia is similar. Again, the European LCFIs are grouped together first along regional/national boundaries and then to form a large group, while the US banks broadly group as for equity returns.

5. Exceptions:

i) JP Morgan Chase now clusters with the brokerage houses rather than the banks.

ii) Lehman Brothers forms an outlier, only joining the rest of the LCFIs when the European and US groups have combined.

· Variables: regression= r = α + βW + δL + r *

where the dependent variable, r, is the equity return for the LCFI at time t, W represents the return on the world equity index and L represents the return on the relevant local equity index. Cluster analysis is then performed on the residuals of the regression, r*, which are free from world and local market effects.

· Importantly the writeup suggests that the three US brokerage houses are different from all of the banking-oriented LCFIs once market effects are removed. The US banks cluster with a large group of European banks, then the two French banks, before finally clustering with the three US brokerage houses. Sectoral segmentation is then an important dimension to the degree of heterogeneity of the LCFI group in addition to geographical splits.

· Conclusion: The dendrograms suggest which LCFIs are similar to other LCFIs, and which groups of LCFIs are similar to other groups of LCFIs. But not all institutions are equally important. Some are closely related to many others, possibly spread across several groups. These LCFIs are important nodes in a network.

· The results also highlight that the LCFIs cannot be viewed as a homogeneous group. Despite the emergence of these globally focused LCFIs, there are still noticeable divisions between sub-groups of LCFIs, according to both geography and whether the LCFI is primarily a bank or a brokerage.

Posted by: Akhil Parekh

Roll no.12066

Finance Batch

SIBM Bangalore

Source: "Large complex financial Instituions - common influence on asset price behaviour?" by Ian W Marsh and Ibrahim Stevens, G10 Financial Surveillance Division, and Christian Hawkesby, Financial Industry and Regulation Division, Bank of England

S