(a)  (b)  Out-of-sample performance is measured by the mean squared prediction error. A lower number implies better performance. 32  GARCH innovations are normally-distributed. BIS central bankers’ speeches  Charts 12–17: Mean Squared Prediction Errors (MSPE) and Decomposition(a)(b) Chart 12: Sample size = 20  Chart 13: Sample size = 500  Chart 14: Sample size = 2500  Chart 15: Sample size = 25,000  Chart 16: Sample size = 100,000  Chart 17: Sample size = 250,000  Source: Bank calculations. (a) MSPE equals the sum of the squared bias and variance. (b) Data generating process: GARCH (3,3) with normally-distributed innovations. BIS central bankers’ speeches  33  Chart 18: VaR violation ratios for portfolio of (a) commodities  Chart 19: VaR violation ratios for portfolios of (a) equities  Source: Global Financial Data and Bank calculations. Source: Global Financial Data and Bank calculations. (a)  Equally-weighted portfolio of silver, wheat and hogs. Validation period starts in 1970. 95% VaR using monthly returns. (a)  (b)  EWMA: lambda = 0.94. (b)  For each k-sized portfolio, the result shown is the average of 100 random k-sized combinations of equities out of a universe of 210 stocks in the S&P 500. Validation period starts in 2005. 95% VaR using daily returns. EWMA: lambda = 0.94. Chart 20: Evolution of bank price to book ratios, (a)(b) historical and present day  Source: Thomson Reuters Datastream, Calomiris and Wilson (2004) and Bank calculations.

Unlike covered bonds, the latter are backed by packages or specific groups of foreign trade financing operations. These new bonds may contribute to reducing exporting firms’ financial costs and to increasing the total volume of financing. Along with providing financing, banks also extend coverage for export risks, relating for instance to the recipient country’s economic or political situation, so-called “country risk”; the risk that products may be damaged in transit or withheld at borders; collection difficulties in the event of non-payment, associated with different jurisdictional frameworks; and greater uncertainty in the relationship between the supplier and acquiring company. Banks have used various instruments to extend guarantees on international trade flows. The classic instrument is, of course, the documentary credit. The importer’s bank guarantees the exporter’s bank that payment will be made once it has been confirmed, through presentation of the pertinent documentation, that the transaction has been correctly completed. In this way, exporters notably reduce their risks. Naturally, the demand for coverage of credit risk is higher for trade flows with countries with which there are fewer historical ties and with those trade partners for which greater risk is perceived. Accordingly, this may prove important in the opening-up of new markets and in flows to emerging economies. As regards the medium and long term, the nature and functioning of transactions differ from those for short-term transactions. The financial services provided by banks for longer-dated terms are, essentially, financing and the extension of guarantees and bonds needed to participate in international tender procedures.