Appendix I. International Banking Activity
Appendix II. Calculating the Distance-to-Default
Appendix III. The Binomial LOGIT Model
Appendix IV. Data Details
Appendix V. Examples of Binomial LOGIT Results Output
Appendix VI. Stock Market Capitalization
Appendix VII. Binomial LOGIT Results for 24-Bank Sample
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The authors wish to thank Arabinda Basistha, Paul Mills, Jason Mitchell, James Morsink, Peter Wilding, and seminar participants at the Bank of England and HM Treasury for their helpful comments. All mistakes remain the responsibility of the authors.
The U.K. stock market is the world’s third largest by capitalization (8 percent), behind New York and Tokyo. London is second only to New York in terms of foreign listings, with 330 foreign companies listed on the London Stock Exchange as at January 2006. The U.K. insurance industry is the largest in Europe and the third largest in the world. Moreover, London is the only center where each of the 20 largest international insurance and reinsurance in the world operates.
Commodities are traded on the London Metal Exchange, the International Petroleum Exchange, and the London International Financial Futures and Options Exchange, which incorporates the London Commodity Exchange.
They include: releveraging in parts of the corporate sector globally and the implications of underpriced risk; high U.K. household sector indebtedness and rising personal insolvencies; rising systemic importance of large, complex financial institution and their increasing links to U.K. banks; dependence of U.K. financial institutions on market infrastructures and utilities, and potential lack of preparedness for any disruption to these services.
For example, Duggar and Mitra (2006) demonstrate that the major Irish banks are also vulnerable to shocks emanating from the Netherlands and the United States, contrary to the focus of the Irish supervisory authorities largely on the United Kingdom.
Generally, empirical studies have shown that the distance-to-default is a good predictor of corporate defaults (Moody’s KMV), and is able to predict banks’ downgrades in developed and emerging market countries (Gropp, Vesala and Vulpes, 2004; and Chan-Lau, Jobert, and Kong, 2004).
The DD measure represents the number of standard deviations away from the point where the book value of a bank’s liabilities is equal to the market value of its assets. The DD is an attractive measure in that it measures the solvency risk of a bank by combining information from stock returns with information from leverage and volatility in asset values—key determinants of default risk. It does not require specification of a particular channel of contagion, that is, the channel through which the transmission of shocks occurs. It should be noted that DDs are risk-neutral, that is, they do not take into account that risk preferences may be different between volatile and benign periods.
We calculate weekly ADDs—on a daily basis—for the following reasons: (i) extreme events are more significant if they are prolonged; events that last for only a day are of little concern; (ii) the use of weekly changes reduces “noise” in the data. For instance, stock price returns exhibit day-of the-week effects (Chang, Pinegar, and Ravichandran, 1993; French, 1980; Jaffe and Westerfield, 1985; Keim and Stambaugh, 1984; and Lakonishok and Smidt, 1988), while non-synchronous trading effects related to the overnight or weekend non- trading periods impact the calculation of daily close-to-close returns (Rogalski, 1984), effects of which could be “smoothed” using weekly data.
Figure A.7, Appendix 3 presents the 10th percentile left tail (extreme values or co-exceedances) of the common distribution of the ADDs for individual banks. Ideally, a first or even fifth percentile left tail would capture the very extreme events; however, either cut-off would have resulted in much too few observations for this period of data.
Gropp, Lo Duca, and Vesala (2005) and Gropp and Moerman (2004) incorporate most listed banks in the EU, in their respective papers, including banks that are also nonsystemic. This could have the effect of overestimating the impact of certain banking systems on others. Indeed, Gropp and Moerman (2004) observe that “an unreasonable number of very small banks” appear to have systemic importance in their results.
Gropp, Lo Duca, and Vesala (2005) and Gropp and Moerman (2004) only examine the inter-relationships among banks in the EU, potentially omitting important linkages with other major banking centers.
We originally selected the top 35 largest banks in the world, but subsequently refined the sample to the 24 largest exchange-listed banks for which good quality and sufficient data are available. The list of banks in our dataset is presented in Table A.1, Appendix 4.
The number of lags is arbitrary; the larger the number of lags, the better. In this instance, we choose 30 lags to incorporate daily movements over a one-month period.
The number of lags is arbitrary and the larger the better. We choose 30 lags to incorporate movements in the past month.
In the United Kingdom, the split of fixed/floating rate new loans to households averaged 66 percent fixed and 34 percent floating in the year to November 2006, while the stock of fixed rate loans is estimated at around 40–45 percent. Although some lenders have reportedly increased their maximum LTV ratios quite aggressively (up to 125 percent) for new mortgage loans, the average LTV ratio for the stock of mortgages remains much lower than during the early-1990s. This is largely because the LTVs for older loans may have declined with the continuing rise in associated property prices. The stock of LTVs averaged an extremely favorable 40-50 percent in 2005, and is slightly higher than 50 percent for most banks currently.
The 10th percentile left tail for each sample, expanded by one bank at a time, remains at -0.018.
We test for robustness by omitting the local stock market variable and rerunning the binomial LOGIT model. Our results show that the contagion effects remain largely the same; some of the local market effects are captured by the global market variable. However, the McFadden R2 is slightly stronger for the existing model.
See BoE (2006) for a discussion of work that is under way and new work that may be required in this area.
We initially calculate the 5 percent tail, but there are too few observations for estimation purposes.
This operation adjusts for any serial correlation in the residuals, which may be induced by our use of overlapping weekly ΔDDs.
The results are not significantly different when we apply the GOMPIT distribution, instead of the LOGIT distribution.