Based on historical experience, that assumption cannot be taken for granted when it comes to estimating financial risks. As discussed by Aikman et al (2014), there are at least three reasons for this. 19  All speeches are available online at www.bankofengland.co.uk/speeches  19  First, assigning probabilities is particularly difficult with rare, high-impact events, such as financial crises or the failure of a large financial institution. Degrees of freedom are small in number, historical precedents rarely exact and causal mechanisms imperfectly understood. This means estimated default probabilities, and losses given default, are often highly imprecise. Indeed, that is (one reason) why model-based estimates of the same underlying risks can differ so significantly across banks (BCBS (2014a)). Second, the behaviour of complex, interconnected financial systems can be very sensitive to small changes in initial conditions and shocks. That might be because these systems exhibit multiple equilibria, with path-dependency or hysteresis. Or it may reflect network feedback effects propagating financial contagion. Complex systems exhibit tipping points, with small changes in parameter values capable of moving the system from stability to collapse (Anderson and May (1992), Gai and Kapadia (2010), Gai, Haldane and Kapadia (2011)). In complex webs, the failure of two identical-looking banks can have very different implications for financial system stability. The radical uncertainty in such complex webs generates emergent behaviour which can be near-impossible to predict, model and estimate (Haldane (2016)). Third, because they contain human actors whose beliefs about the future shape their behaviour today, financial systems are particularly prone to instabilities and sunspots.

With that in mind, we conclude with some thoughts on issues which might be fruitful for future research on regulatory policy. International Regulatory Reform  There are already a number of detailed accounts of the regulatory reforms undertaken by international policymakers over the past decade (Carney (2017b), Duffie (2017), FSB (2017a), Greenwood et al (2017), Sarin and Summers (2017), Yellen (2017)). The following is a summarised and simplified account of the state of play. It partitions reform efforts into their microprudential and macroprudential components, recognising that the two often overlap and are usually mutually reinforcing in their impact. We focus here squarely on international banking regulation. We do not cover insurance regulation or international accounting standards. We do not discuss regulatory reforms undertaken nationally, such as the “Volcker Rule” in the US (Financial Stability Oversight Council (2011)) and the “Vickers proposals” in the UK (Independent Commission on Banking (2011)). Nor do we discuss international reforms of market infrastructure – for example, clearing – and financial market instruments (FSB (2017b)). Finally, we do not cover changes to banks’ large exposures regime and a range of pay and governance reforms. Microprudential Reform  Under the umbrella of Basel III, international reform of microprudential regulation has focused on four key areas: capital, leverage, liquidity and resolution. Taking these in turn:  Reform of risk-based capital standards has focused on increasing the quantity and quality of capital held by banks against their asset exposures.