Consider first a portfolio of three commodities using monthly data from 1890. 18  Specifically, we generate 100,000 random series of data from the underlying process. We use these series to forecast conditional volatilities and then compare these with actual conditional volatilities. BIS central bankers’ speeches  13  Determining the risk of this portfolio in a Value-at-Risk (VaR) framework involves estimates of asset volatilities and correlations. We consider three models to estimate the variance-covariance matrix of returns which vary in complexity from the simple (a sample average covariance matrix (MA)) to the relatively simple (an exponentially-weighted covariance matrix (EWMA)) to the complex (a multivariate GARCH(1,1)). Using historical samples of different sizes, these models are used to generate forecasts of VaR over the period 1970–2010. These VaR estimates can be compared with actual losses over this period. We report the ratio of actual to expected VaR violations – the “violation ratio” – at the 95% confidence interval. The closer this ratio is to unity, the better the performance of the model. The violation ratios are shown in Chart 18. The simpler moving-average models materially outperform the complex GARCH model when samples are around 20–30 years. The performance of the complex models improves as the sample size is increased. But even with a sample size of three-quarters of a century, the simple models perform at least as well as the complex one. Another dimension to complexity is the number of assets in a portfolio. So consider a different portfolio of 200 equities since 1973.
The UK, Sweden and Denmark have so far chosen to remain outside EMU. Sweden and the UK have inflation targets and floating exchange rates, while Denmark’s monetary policy is oriented towards a fixed exchange rate against the euro. These three countries are important to Norway, both because of their geographical proximity and because they account for close to 40 per cent of Norway’s foreign trade. If these countries join EMU some time in the future, it is possible that the use of the euro by Norwegian households and businesses will increase somewhat. However, extensive use of the euro as a means of settling domestic payment transactions is unlikely. In those cases where we have seen partial or total currency substitution, such as in some countries in Eastern Europe and Latin America, it has usually been a result of strongly deteriorating confidence in the local currency. Confidence can deteriorate when inflation is high and variable or when government finances are on the verge of collapse. By influencing the volume of NOK in circulation, Norges Bank will always be able to ensure that the internal value of the Norwegian krone is maintained in line with the guidelines for monetary policy. If the introduction of the euro increases efficiency and economic growth in the participating countries, this will have positive spillover effects on the Norwegian economy. Stable economic developments in the euro area are also very important for the Norwegian economy. Thank you for your attention. 8  BIS Review 90/2001