These historical distributions can be compared with a normal curve calibrated to the same data. In each case, there is strong evidence of non-normality in the empirical distribution. Specifically, the tails of the historical distribution are often significantly higher than normality would imply. For real variables like GDP, around 18% of the data across the UK, US, Germany and Japan fall outside the ‘bell’ curve described by a best-fit normal distribution. For financial variables like equity prices, around 10% of that data fall outside the normal distribution. In both cases, there is evidence of out-sized dislocations in variables, which occur with far-higher frequency than normality would imply. This evidence is consistent with, if not proof of, complex system dynamics. Chart 6: Long-run distributions of economic and financial variables  UK House Prices: 1846-2015, Annual  Oil Prices: 1862-2015, Annual  M4 Credit Growth: 1881-2015, Annual  CPI inflation: 1662-2015, Annual  25  All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx  25  World GDP growth (across the UK, US,  UK GDP growth: 1701-2015, Annual  Germany, Japan): 1871-2015, Annual  UK wage growth: 1751-2015, Annual  Equity prices: 1709-2016, Monthly  Corporate bond spreads: 1854-2016, Monthly  Dollar-Sterling Exchange rate: 1791-2016, monthly  Source: Hills, Thomas and Dimsdale (2016); Bank calculations. Notes: For each empirical distribution f(x), a Gaussian fit to f(x) of the (𝑥−𝜇)2  form 𝑔(𝑥) = 𝐴exp (− ) is sought in which A, 𝜇 and 𝜎 are varied and optimised using the Levenberg–Marquardt non-linear least 2𝜎2 squares fitting algorithm.

Because of the additional stress that central bank balance sheets have undergone, in terms of the size and the number and magnitude of new risk factors that must be managed, as I have already mentioned, there is a need to revisit the tools we have used to assess the resilience of our portfolios. To this end, a session will be held to discuss the design of stress tests for balance sheets and how this tool helps institutions to articulate risk tolerance and to assess the capacity of portfolios to deal with different negative scenarios, ensuring that banks maintain the capacity to manage policy measures if necessary. We will also be discussing risk governance, as it is essential to have a solid structure that clearly defines roles and responsibilities. Since the risk management governance structure may differ from one country to another, we want to learn about the construction and implementation of the models, the institutional arrangements within the organization that allow the dissemination of financial risk management objectives and the role played by the lines of communication with the bank authorities in order to specify guidelines and directives to address this issue. Finally, issues related to sustainability and climate change have been incorporated into the balance sheet risk management framework of some central banks. We therefore want to review and understand how central banks' risk is affected by climate change through channels that include the credit risk of their own assets and through their impact on the real economy.