level with regard to each bank ’ s capital needs. this effect is critical now that qualifying banks choosing an advanced approach to credit or operational risk will be allowed to apply some of their own assessments of risk in the calculations of their minimum capital requirements. we might view the entire three - pillar structure of basel ii as a series of built - in reality checks for management ’ s decision - making. in this regard, the three pillars of basel ii are intended to make sure that management assesses and controls its risks carefully and that it takes the steps necessary to allocate the appropriate capital. as you know, in the first pillar, the minimum capital requirements focus management ’ s attention on identifying, assessing and quantifying risk within a specified framework. this puts the onus of analysis and decision - making on the right set of shoulders : bank managers are in the best position to evaluate their risks and are ultimately responsible for responding to them. when banks consider their risks more comprehensively and work to evaluate rigorously the magnitude of losses that they may face, they are improving the quality of the information at their disposal. that, in turn, should improve their ability to arrive at sound decisions regarding the amount of capital that they may need to weather potential losses in the future. considerable attention has been paid to some of the formulas and techniques that we have adopted in pillar 1 to help quantify the potential for losses related to credit and operational risk exposures. we must remember that these formulas are not revolutionary. in fact - in one of many examples of how basel ii seeks to reflect reality - the new framework draws on the tremendous advances that many firms have already achieved in quantifying their exposures to credit and operational risk. this reflects as well one of the committee ’ s goals to build the new framework on sound risk management practices in use today and to provide sufficient flexibility for it to evolve with advances in the future. at the same time, the committee knows that mathematical formulas and financial models are only as good as the assumptions they make. at best, therefore, they serve as supplements to our insight : they do not replace our need for expertise and judgement. even einstein warned of the dangers of confusing mathematical certainty with reality. he said once that, “ as far as the laws of mathematics refer to reality, they are not certain ; and as far as they are certain, they do not refer to reality. ” reasonable supervisors and bankers know that we cannot rely purely on the apparent mathematical certainty of models and formulas

of the european union but is still sizable, which is more bewildering in the case of the currency union. a departure from perfect capital mobility has important economic implications, as it might be leading to lower aggregate investment, a higher home bias in investment decisions and a lack of portfolio diversification. the capital markets union project has received a stronger push over the last few months. most of the work in terms of harmonising investment products across the eu has already been agreed. progress on savings products has also been achieved. in particular, the development of the market for the pan - european pension product is particularly relevant considering the situation of public finances in many eu countries and the challenges posed by population ageing. but, looking ahead, greater headway is needed over the coming years. in particular, allow me to highlight three dimensions. first, the legal framework : insolvency regimes vary widely across jurisdictions for financial and non - financial corporations, as a result of cultural traditions and legal frameworks. this is a major obstacle for cross - country investments and, i would add, a very difficult one indeed to overcome. second, the strengthening of european regulators. as european markets become more integrated and technologically complex, this is becoming a more essential element that policy - makers need to address. it will be even more important since, depending on the final outcome of negotiations, brexit might increase the risk of fragmentation, as some companies and transactions may be reallocated to various possible destinations, while others may remain in the uk. 8 / 11 third, more needs to be done in terms of making capital taxation more consistent. the debate has stalled in this regard. for example, the various regimes for withholding taxes, with more than 90 types of forms in different languages, are often cited as a huge obstacle for investment by market participants. moreover, the favorable tax treatment of debt compared to that of equity has significant economic implications. a well - functioning capital markets union will have major ramifications as it will attract institutional investors, improving the allocation of resources and strengthening the international role of the euro. crucially, it will help reshape capital markets in europe after brexit. i believe that this project is essential for the single market, for the economic and monetary union and a resilient euro, and, ultimately, for the eu ’ s global competitiveness. i am certain that these and other matters will be raised and discussed during the following panel of this conference. the case