To reduce the risk that the results are portfolio-specific, we construct the maximum number of combinations of portfolios of different sizes (ranging between two and 100 assets per portfolio) using daily returns. For each of these sets of portfolios, we forecast VaRs for the period 2005–2012 using the EWMA and GARCH models. To keep things simple, these models are all estimated over a common sample period. The expected losses can then be compared with actual losses, allowing “violation ratios” for portfolios of differing sizes to be calculated. The results are summarised in Chart 19. For very simple portfolios of two or three assets, the performance of the simple and complex models is not so different. As the number of assets increases, however, the simple model progressively out-performs the complex one. That is a direct result of the uncertainties associated with over-fitting the complex model relative to the simple one. The message from these experiments is clear and consistent. Complexity of models or portfolios generates robustness problems when understanding a complex financial system over plausible sample sizes. More than that, simplicity rather than complexity may be better capable of solving these robustness problems. (7)  Public policy – more or less? In forgone output, financial crises can be as costly as wars. The public policy issue, then, is whether the war on crises is best waged with the weapons of the past. Einstein wrote that: “The problems that exist in the world today cannot be solved by the level of thinking that created them”.
Against that background the Bank is continuing to work constructively with the ECB though its membership of the General Council, while at the same time we are working with the Government and the financial sector to ensure that we are technically prepared for transition to the euro if and when that is what the Government, Parliament and the people of this country decide. The build-up to the euro roughly coincided with the accelerating advance of information and communications technology that is sweeping across the global economy. This development, too, can give rise to technical concerns - the Bank and FSA cooperated, for example, in helping to ensure that the financial sector was properly prepared to combat the Millennium bug. But its ramifications go very much wider. We are having to monitor very closely the potential impact of the “new economy” on productivity growth and what that may mean for monetary stability; and we are having to keep a very close eye on financial market volatility as investors struggle to assess its impact on relative stock values for its effect on financial stability. In the financial sector in particular the new technology is perhaps the main driver of innovation and change. It makes possible the introduction of new services and products, and is radically altering the way in which existing services are delivered - often at a fraction of the initial cost and, potentially, at lower risk.