Chart 19: ROC curves for individual and combined regulatory tools (96 bank sample with LTD)  Hit rate  1 0.8 0.6 0.4 0.2 0 0  0.2  LR  0.4 0.6 False alarm rate RWCR  LTD  0.8  1  LR + RWCR + LTD  Sources: Buckmann, M., Kapadia, S., Kothiyal, A. and Bank calculations. 50  All speeches are available online at www.bankofengland.co.uk/speeches  50  Table 5: Current international macroprudential tools (taken from Grace, Hallissey and Woods (2015))  Country Poland  Instrument used Series of measures to limit FX-lending incl. higher DSTI ratios for FX-loans, higher risk weights for FX-loans. Borrowers can only borrow same currency as income (Jan 14). 80% LTV cap with mandatory mortgage insurance, capped 25 year loan term, maximum total debt service ratio  Canada  of 44%. Time varying. Canada has taken four macroprudential policy measures since 2008 to tighten to these requirements. New Zealand Sweden  UK Australia Norway  Proportionate LTV cap at 80% (2013), temporary restriction. Core funding ratio of 75% in 2010. 85% LTV cap (2010). Higher capital for mortgages (2013). 1% CCB on domestic exposures (2015). 3% SRB and 2% Pillar 2 for 4 systemic banks (2015) Proportionate LTI cap at 4.5 times. 0.5% counter-cyclical capital buffer from June 2017, with expectation of increasing to 1%. Increase in risk weights for self-verified mortgages and non-prime home loans in 2004. LTV cap of 90% (Mar 2010), reduced to 85% (Dec 2011). Countercyclical capital buffer of 1% from June 2015.

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.