Extreme returns: The case of currencies Carol Osler a,⇑ , Tanseli Savaser b a Brandeis University, Waltham, MA, USA b Williams College, Williamstown, MA, USA article info Article history: Received 12 February 2010 Accepted 22 March 2011 Available online 12 April 2011 JEL classification: G1 F3 Keywords: Crash risk Fat tails Exchange rates High frequency Microstructure Jump process Value-at-risk abstract Financial market crashes can occur even in the absence of news. This paper highlights four properties of price-contingent trading that increase the frequency of such events. Price-contingent trading is common across financial market, since it includes algorithmic trading, technical trading, and dynamic option hedg- ing. The four properties we consider are: (1) high kurtosis in the distribution of order sizes; (2) clustering of trades within the day; (3) clustering of trades at certain prices; and (4) feedback between trading and returns. The paper estimates the relative importance of these factors using data from the foreign exchange market. Calibrated simulations indicate that interactions among these factors are at least as important as any single one. Among individual factors, the orders’ size distribution and feedback effects have the strongest influence. Overall, price-contingent trading could account for half of realized excess kurtosis. The paper suggests that extreme returns unaccompanied by news are statistically inevitable in the presence of price-contingent trading. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction This paper analyzes the triggers for financial-market crashes. According to standard models, the trigger for extreme returns can only be new information. In reality, however, extreme returns are often unaccompanied by news (Covrig and Melvin, 2005; Cutler et al., 1991). There was no news of obvious relevance, for example, to trigger the flash crash of May 2010, the stock-market crash of 1987 (Shiller, 1989), or the 15% drop in dollar-yen in October 1998 (Covrig and Melvin, 2005). Eye-popping financial returns happen much more frequently than predicted by the normal distribution. Fat-tailed returns and, more generally, high return kurtosis have been documented for equities (Fama, 1965), bonds (Roll, 1970), and currencies (Westerfield, 1977). Standard analysis predicts that returns should be normally distributed, since they assume normally dis- tributed shocks and a linear relation between returns and funda- mentals. Even without such assumptions, however, one might infer normally distributed returns in light of the central limit theorem coupled with the frequency and variety of financial mar- ket shocks. This paper investigates how the frequency of extreme ex- change-rate returns is influenced by price-contingent trading – meaning trading that is triggered when the price arrives at a spe- cific level. Price-contingent trading is common in most financial markets because it arises from algorithmic trading, technical trad- ing, and dynamic option hedging. We highlight four properties of price-contingent trading that raise the likelihood of extreme re- turns: (1) fat tails in the distribution of order sizes; (2) clustering of order executions at certain times of day; (3) clustering of order executions at certain price levels (Osler, 2003); and (4) feedback between trading and returns (Genotte and Leland, 1990; Morris and Shin, 2004; Osler, 2005). We also show that interactions among these factors, which cannot be measured in any straightfor- ward way, also contribute to fat tails. While some of these factors have been mentioned previously in the literature, we are the first to evaluate their relative importance and to point out the importance of their interactions. We do this using simulations calibrated to match the properties of the com- plete record of stop-loss and take-profit orders processed by the Royal Bank of Scotland, the world’s fifth largest foreign exchange dealing bank (Euromoney, 2007). We focus on the three major 0378-4266/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2011.03.016 ⇑ Corresponding author. Tel.: +1 781 736 4826; fax: +1 781 736 2269. E-mail addresses: cosler@brandeis.edu (C. Osler), tsavaser@williams.edu (T. Savaser). Journal of Banking & Finance 35 (2011) 2868–2880 Contents lists available at ScienceDirect Journal of Banking & Finance journal homepage: www.elsevier.com/locate/jbf