The race to zero may have contributed to those abnormalities, adding liquidity during a monsoon and absorbing it during a drought. This fattens tail risk. Understanding and correcting those tail events is a systemic issue. It may call for new rules of the road for trading. Grit in the wheels, like grit on the roads, could help forestall the next crash. 14  BIS central bankers’ speeches  References Aldridge, I (2010), “High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems”, Wiley Publications. Arestis, P and Demetriades, P (1997), “Financial Development and Economic Growth: Assessing the Evidence,” The Economic Journal, Vol. 107, No. 442 (May, 1997), pp. 783–799, Blackwell Publishing for the Royal Economic Society. Automated Trader Magazine (2010), “What just happened?”, Issue 18(3), available at: http://www.automatedtrader.net/articles/risk/50335/what-just-happened. Bouchaud, J, Farmery, J D and Lill, F (2009), “How markets slowly digest changes in supply and demand,” Santa Fe Institute working paper. Blackledge, J (2008), “Application of the fractal market hypothesis for macroeconomic time series analysis,” ISAST Transactions on Electronics and Signal Processing, Vol. 1(2), pp. 89–110. Brogaard, J (2010), “High frequency trading and its impact on market quality”, mimeo. CFTC-SEC (2010), “Findings regarding the market events of May 6, 2010”, Report of the staffs of the CFTC and SEC to the joint advisory committee on emerging regulatory issues, September 30. CFTC-SEC Advisory Committee on Emerging Regulatory Issues (2011), “Recommendations regarding regulation to the market events of May 6, 2010”, available at: http://www.cftc.gov/ucm/groups/public/@aboutcftc/documents/file/jacreport_021811.pdf.

That is what we appear, increasingly, to find in financial market prices in practice, whether in volatility and correlation or in fat tails and persistence. This change in price dynamics will in turn influence market-making behaviour. Consider the problem facing an HFT market-maker. They face inventory risk from market fluctuations and information risk from adverse selection. Pricing these risks means forming a guess about the future path of prices. The greater the potential range of future prices, the larger the insurance premium they will demand. The future price range (maximum – minimum) for a price series at some future date T, R(T), can be written generically as: 20 (1) where κ is a constant and σT is the standard deviation of the process up to time T. H is our old friend the Hurst coefficient, dredged up from the Nile; it can be thought to summarise the degree of fat-tailedness and persistence in prices. When the holding period is short (say T=1), as with HFT, the future price range is the volatility of the series magnified by the Hurst coefficient. In other words, the fatter and more persistent the tails (H), the greater the market risk and the wider the bid-ask spread of the HFT. This has implications for the dynamics of bid-ask spreads, and hence liquidity, among HFT firms. During a market crash, the volatility of prices (σ) is likely to spike. From equation (1), fractality heightens the risk-sensitivity of HFT bid-ask spreads to such a volatility event.