SHORT-HORIZON TRADING AND MARKET MOVEMENT. 18 February Jeremy Large St Hugh s College, University of Oxford Tudor Investment Corp

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1 SHORT-HORIZON TRADING AND MARKET MOVEMENT 18 February 2013 Jeremy Large St Hugh s College, University of Oxford Tudor Investment Corp - 0 -

2 OVERVIEW Cover some material I prepared for the Bank of England in 2006 (pre-crunch!) Focus on economic effects rather than mathematical formalism Topics: How markets crash ( dislocate, in the BoE jargon of the time) Crashing upwards or sideways - 1 -

3 HOW MARKETS CRASH : FOUR MAIN INGREDIENTS Funding constraints Loss limits Market dislocation Turbulent markets - 2 -

4 HOW MARKETS CRASH : FOUR MAIN INGREDIENTS Funding constraints Loss limits Lower limits on traders funds when marked-to-market Even in the face of riskless arbitrage Stem from ex ante agency problems When broached: forced liquidation, perhaps insolvency Examples Stop-loss levels / circuit breakers Haircuts Margin calls VaR targets Balance sheet leverage ratio targets (ratings) Market dislocation Turbulent markets - 3 -

5 HOW MARKETS CRASH : FOUR MAIN INGREDIENTS Funding constraints Loss limits Lower limits on traders funds If broached, forced liquidation Price on a market where a trader s funding constraint binds Typically a lower limit but not necessarily Market dislocation Turbulent markets - 4 -

6 HOW MARKETS CRASH : FOUR MAIN INGREDIENTS Funding constraints Loss limits Market dislocation Lower limits on traders funds If broached, forced liquidation Price on a market where a trader s funding constraint binds Typically a lower limit but not necessarily Can happen before prices reach loss limits due to coordination failure Unlike loss limits, the dislocation is a common shock Turbulent markets - 5 -

7 HOW MARKETS CRASH : FOUR MAIN INGREDIENTS Funding constraints Loss limits Market dislocation Turbulent markets Lower limits on traders funds If broached, forced liquidation Price on a market where a trader s funding constraint binds Typically a lower limit but not necessarily Can happen before prices reach loss limits due to coordination failure Unlike loss limits, the dislocation is common Period before a dislocation Funding constraints are close Traders are braced for dislocation - 6 -

8 AGENDA How markets crash Overview Literature review A simple model - 7 -

9 FOUR PREDICTIONS 1. Any given market dislocation and the preceding turbulence, is likely to involve many assets simultaneously. 2. In turbulent markets prices can fall due to attacks by predatory traders. 3. In turbulent markets prices can fall, as a greater return is required by short-horizon traders who have heightened and/or less precise expectations of future undiversifiable illiquidity. 4. In turbulent markets volatility can rise and the histogram of returns can become more negatively skewed

10 FOUR PREDICTIONS 1. Any given market dislocation and the preceding turbulence, is likely to involve many assets simultaneously. Brunnermeier and Pedersen (2005a) 2. In turbulent markets prices can fall due to attacks by predatory traders Brunnermeier and Pedersen (2005b) 3. In turbulent markets prices can fall, as a greater return is required by short-horizon traders who have heightened and/or less precise expectations of future undiversifiable illiquidity Acharya and Pedersen (2005); Vayanos (2004); Kyle and Xiong (2001); Danielsson and Zigrand (2006) 4. In turbulent markets volatility can rise and the histogram of returns can become more negatively skewed. Vayanos (2004); Xiong (2001); Danielsson and Zigrand (2006) - 9 -

11 FOUR PREDICTIONS Assumption: The average positions of short-horizon investors are positive 1. Any given market dislocation and the preceding turbulence, is likely to involve many assets simultaneously. Brunnermeier and Pedersen (2005a) 2. In turbulent markets prices can fall due to attacks by predatory traders Brunnermeier and Pedersen (2005b) 3. In turbulent markets prices can fall, as a greater return is required by short-horizon traders who have heightened and/or less precise expectations of future undiversifiable illiquidity Acharya and Pedersen (2005); Vayanos (2004); Kyle and Xiong (2001); Danielsson and Zigrand (2006) 4. In turbulent markets volatility can rise and the histogram of returns can become more negatively skewed. Vayanos (2004); Xiong (2001); Danielsson and Zigrand (2006)

12 AGENDA How markets crash Overview Literature review A simple model How markets price (il)liquidity, and how they price the risk of illiquidity

13 A BENCHMARK MODEL OF AN EFFICIENT MARKET Financial asset in zero net supply Many competitive patient risk-neutral traders A delta transactions cost so no trading unless strictly wanted Traded at periods 0, 1 and 2 Ultimately delivers a cash flow of v, v = v 0 + s 1 + s 2, 12 - v 0 =10 at time 0, 11 - Public signal s 1 at time 1, Public signal s 2 at time 2, - s i = ± 1 (50:50), s 2 s price = E [ v ]

14 ADDING INGREDIENTS FOR HORIZON IMBALANCES (1) Assumption 1 Funding constraints Traders face identical funding constraints so that at any time they may own or short no more than a single unit of the asset. Assumption 2 Loss limits Traders all have the same loss limit, which can bind if, when marked to market, the value of their position falls by more than 2. (so fundamentals not quite enough in themselves to hit loss limits)

15 ADDING INGREDIENTS FOR HORIZON IMBALANCES (2) Divide traders into two types: the majority are long-horizon traders, and a minority are short-horizon traders. Assumption 3 Long-horizon traders as passive counterparties Long-horizon traders are indifferent to holding the asset at any price and shorthorizon traders compete in such a way that price equals the cash flow they expect from owning it (if this exists). Assumption 4 Short-horizon traders Only short-horizon traders' positions are marked to market over the duration of the model. This happens at time 2 with probability μ in (0,1]

16 A BENCHMARK MODEL OF AN EFFICIENT MARKET (3) Assumption 5 Forced liquidation If a short-horizon trader is marked to market and broaches loss limits at time 2, then he is forced into liquidation, unless he pays an agency-related deadweight-loss, c>0, for every unit of the asset he owns or shorts. For concreteness, assume c*µ = 2. v 0 v 0 + s 1 v Prob. μ of forced liquidation c

17 HORIZON IMBALANCES CUT BOTH WAYS Assumption 6 Negative horizon imbalances All short-horizon traders are initially long +1 in the asset Assumption 7 Positive horizon imbalances All short-horizon traders are initially short -1 in the asset 9½ loss limit loss limit 10½

18 PROPERTIES OF INEFFICIENT EQUILIBRIA Loss Limits Loom (not too) Large Proposition : Initial price is drawn towards the loss limit Proposition : Even before loss limits bind, volatility rises A signal of +1 is news about fundamentals, and about liquidation risk Both contribute to volatility Proposition : Even before loss limits bind, returns are skewed in their direction Correlation between returns and volatility 9½ loss limit 10½ loss limit

19 SOME COMMENTS ON THIS MODEL Started from a very simple efficient market Introduced just enough assumptions to get Horizon imbalances: when short-horizon traders 1) Gather on the same side of the market 2 ) Seriously risk broaching loss limits and having to liquidate This makes returns biased and skewed towards these loss limits more volatile Emphasised that horizon imbalances can cut both ways

20 THE YEN ANTI-CRASH IN AUTUMN 1998 Turbulent market Market dislocation /01/93 15/06/94 28/10/95 11/03/97 24/07/98 06/12/99 19/04/01 01/09/02 14/01/04 28/05/ Yen per dollar