Dynamic Strategic Arbitrage∗

Dynamic Strategic Arbitrage∗ Vincent Fardeauy Frankfurt School of Finance and Managment This version: June 11, 2014 Abstract Asset prices do not adjust instantaneously following uninformative demand or supply shocks. This paper offers a theory based on arbitrageurs' price impact to explain these slow-moving capital dynamics. Arbitrageurs recognizing their price impact break up trades, leading to gradual price adjustments. When shocks are anticipated, prices exhibit a V-shaped pattern, with a peak at the realization of the shocks. The dynamics of market depth and price adjustments depend on the degree of competition between arbitrageurs. When shocks are uncertain, price dynamics depend on the interaction between arbitrageurs' competition and the total risk-bearing capacity of the market. JEL codes: G12, G20, L12; Keywords: Strategic arbitrage, liquidity, price impact, limits of arbitrage. ∗I benefited from comments from Miguel Antón,Bruno Biais, Maria-Cecilia Bustamante, Amil Dasgupta, Michael Gordy, Martin Oehmke (discussant), Matt Pritsker, Jean-Charles Rochet, Yuki Sato, Kostas Zachariadis, Jean-Pierre Zigrand and seminar and conference participants at LSE, INSEAD, FRB, the University of Zurich and the 2013 AFA meetings in San Diego. I am grateful to Dimitri Vayanos and Denis Gromb for supervision and insights. Jay Im provided excellent research assistance. This paper is the first part of a paper previously circulated as \Strategic Arbitrage with Entry". All remaining errors are my own. yDepartment of Finance, Frankfurt School of Finance and Management, Sonnemannstrasse 9-11, 60314 Frankfurt am Main, Germany. Email: [email protected]. 1 1 Introduction Empirical evidence shows that prices recover slowly from demand or supply shocks that are unre- lated to future earnings and that these patterns are due to imperfections in the supply of capital. Patterns of slow price adjustments due to these sluggish capital responses have been documented, for instance, in the catastrophe reinsurance markets (Froot and O'Connell, 1999), and in numerous popular arbitrage strategies used by hedge funds such as convertible debt and merger arbitrage (Mitchell, Pedersen and Pulvino, 2007).1 These price patterns present a challenge for models of efficient capital markets based on competitive, rational investors, which predict that the supply of capital is perfectly elastic. This paper proposes a theory based on arbitrageurs' price impact to explain why capital appears to be slow-moving. There is widespread evidence that maket depth is limited, even in actively traded markets, and that investors develop strategies to minimize their price impact.2 Arbitrage in particular typically involves setting up positions in relatively illiquid markets that are often dominated by a few highly specialized sophisticated investors.3 I consider a model in which supply shocks and market segmentation generate price discrepancies between two identical assets. I show that when arbitrageurs recognize their price impact, these price discrepancies are not eliminated instantaneously. Strategic arbitrageurs break up their trades to minimize price impact and exploit price discrepancies longer, which results in gradual price convergence. The interesting feature of the model is that arbitrageurs' price impact and the quantity they trade are both endogenous. The model generates additional predictions which match well-documented empirical findings, such as V-shaped price patterns around anticipated (and uninformative) supply shocks, time- varying market depth, and changes in the sign of basis between identical or closely-related assets. Moreover, the model is extended to analyze arbitrageur's behaviour when the supply shocks are 1See Duffie (2010) for additional examples. 2See Chan and Lakonishok (1993, 1995) and additional references in Section 2. 3Anecdotal evidence reveals that some strategies can be dominated by a one or a handful of arbitrageurs. For instance, LTCM was nicknamed the central bank of volatility (Lowenstein, 2000) as it was selling large amounts of out-of-the-money put options and hedging in the underlying securities. Recently, JP Morgan was put under the spotlight after one of it's traders in the Chief Investment Office accumulated large positions in the CDS markets. The trader, who was called the 'London Whale' by the press and other market participants, was reportedly involved in yield curve arbitrage. See `London Whale' Rattles Debt Market", Wall Street Journal, April 6, 2012. 2 stochastic, i.e. when the arbitrage is risky, and study whether arbitrageurs \lean against the wind". I consider a multiperiod model in which arbitrageurs exploit price differences between two identical assets traded in segmented markets (e.g. Siamese twin stocks, a derivative and the equivalent security based on the underlying, etc.). In each local market, competitive investors receive endowment shocks that are correlated with the asset payoff. Correlations to the asset payoff are (for simplicity) opposite across local investors, thus market segmentation causes prices to diverge. Stronger hedging needs from local investors create a larger arbitrage \supply" and thus larger price differences. Arbitrageurs can trade in both markets and act as middlemen until assets mature and pay off the same dividend.4 Arbitrageurs are imperfectly competitive. While intermediating trades, they understand that they face downward-sloping demand curves in each market and take into ac- count the impact of their trades on market-clearing prices. This setting with complete information is suitable to analzye cleanly the effects of uninformative supply shocks on price dynamics.5 If arbitrageurs take prices as given, the spread between the prices of the two assets drops instantaneously to zero. Since arbitrageurs are perfectly hedged across markets A and B, they are effectively risk-neutral, and eliminate any mispricing immediately, resulting in perfect risk-sharing and liquidity. By contrast, imperfectly competitive arbitrageurs intermediate only a limited amount between the two markets to keep the spread open and maximize capital gains. Further, as trades have a permanent effect on prices, arbitrageurs break up their trades to exploit the arbitrage as long as possible. When there is a constant arbitrage supply, arbitrageurs reallocate the asset slowly from one market to the other, giving rise to slow-moving capital. A similar mechanism implies that when unanticipated supply shocks occur at some stage, their effects on prices die out only gradually. In both cases, the equilibrium speed of arbitrage increases as more arbitrageurs compete in the trade. This predictable price pattern arises in equilibrium even though all investors have perfect 4The assumptions of market segmentation and identical assets emphasize arbitrageurs' role as intermediaries but are not essential for the results. 5Apart from hedging needs, supply shocks can arise from portfolio rebalancing of passive investors (e.g. index funds or ETFs) around index recompositions, forced liquidations of market participants following shocks to their portfolios (e.g. LTCM unwound its convertible arbitrage activity following losses on other convergence trades), etc. Gromb and Vayanos (2010) provide additional examples. 3 foresight. What induces local investors in, say, market A, to sell today given that in that market the price of the asset will (on average) increase tomorrow? Local investors are willing to sell today because waiting is risky. New information about the fundamental accrues between today and tomorrow and will affect tomorrow's actual price.6 Nevertheless, the anticipation of a more favorable price reduces local investors' willingness to sell today. Hence local investors' perfect foresight erodes arbitrageurs' market power, as in the classical durable goods monopoly problem. The slow-moving dynamics rely crucially on the discreteness of trading and the finiteness of the horizon. The discreteness implies that receiving liquidity today is not exactly equivalent to receiving liquidity tomorrow, while the finite horizon provides arbitrageurs a means to commit to provide only limited liquidity in the future. The model generates additional predictions, including V-shaped price effects around the realization of anticipated shocks, time-varying market depth, and sign changes of price differences in case of negative decreasing supply. V-shaped price patterns have been documented around corpo- rate or Treasury bond issuances, and around pre-announced index recompositions, which trigger shifts in uninformed demand for stocks (e.g. from passive investors such as index funds and ETFs), resulting in changes in the net supply.7 These patterns have proven hard to reconcile with rational behavior of market participants because price decreases and reversals are gradual and predictable. This type of price patterns emerges in the model around the realization of pre-announced shocks, even though all market participants are rational. After the realization of the shocks, prices adjust gradually as in the case of surprise shocks. Indeed, arbitrageurs avoid providing any additional liquidity ahead of the shock, so that much of the shock absorption occurs after realization. The anticipation of this behavior by local investors generates an increasing spread up to the realization. The striking feature of this result is that, between the announcement and the realization 6Vayanos and Woolley (2008) have a similar effect, which they term a bird-in-the-hand effect. 7Keloharju, Malkmaki,

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