Roman Kozhan

Execution Risk in High-Frequency Arbitrage

In this paper, we investigate the role of execution risk in high-frequency trading through arbitrage strategies. We show that if rational agents face uncertainty about completing their arbitrage portfolios, then arbitrage is limited even in markets with perfect substitutes and convertibility. Using a simple model, we demonstrate that this risk arises from the crowding effect of competing arbitrageurs entering the same trade and inflicting negative externalities on each other. Our empirical results provide evidence that support the relevance of execution risk in high-frequency arbitrage. This paper was accepted by Wei Xiong, finance.

Asset allocation with distorted beliefs and transaction costs

In this paper we study the problem of the optimal portfolio selection with transaction costs for a decision-maker who is faced with Knightian uncertainty. The decision-makers portfolio consists of one risky and one risk-free asset, and we assume that the transaction costs are proportional to the traded volume of the risky asset. The attitude to uncertainty is modeled by the Choquet expected utility. We derive optimal strategies and bounds of the no-transaction region for both optimistic and pessimistic decision-makers. The no-transaction region of a pessimistic investor is narrower and its bounds lie closer to the origin than that of an optimistic trader. Moreover, under the Choquet expected utility the structure of the no-transaction region is not necessarily a closed interval as it is under the standard expected utility model.

Firms' Investment under Financial Constraints: A Euro Area Investigation

In this article we describe a model of optimal investment of various types of financially constrained firms. We show that the resulting relationship between internal funds and investment is nonmonotonic. In particular, the magnitude of Cash Flow (CF) sensitivity of the investment is lower for the firms with credit rationing compared to the firms that are able to obtain short-term external financing. The inverse relationship is driven by the leverage multiplier effect. A positive CF shock increases the short-term borrowing capacity of the firm, which in turn has a positive effect on investment and the firms growth. Moreover, the leverage multiplier effect is the highest for firms relying on short-term credits and it is lower for firms that are able to obtain long-term financing. Analysing a large euro area data set we find strong empirical support for our theoretical predictions. The results also help to explain some contrasting findings in the financial constraints literature.

Optimal Insurance Under Adverse Selection and Ambiguity Aversion

We consider a model of competitive insurance markets under asymmetric information with ambiguity-averse agents who maximize their maxmin expected utility. The interaction between asymmetric information and ambiguity aversion gives rise to some interesting results. First, for some parameter values, there exists a unique pooling equilibrium where both types of insurees buy full insurance. Second, in separating equilibria where the low risks are underinsured their equilibrium contract involves more coverage than under standard expected utility. Due to the endogeneity of commitment to the contracts offered by insurers, our model has always an equilibrium which is unique and interim incentive efficient (second-best).

Non-additive anonymous games

This paper introduces a class of non-additive anonymous games where agents are assumed to be uncertain (in the sense of Knight) about opponents’ strategies and about the initial distribution over players’ characteristics in the game. We model uncertainty by non-additive measures or capacities and prove the Cournot–Nash equilibrium existence theorem for this class of games. Equilibrium distribution can be symmetrized under milder conditions than in the case of additive games. In particular, it is not required for the space characteristics to be atomless under capacities. The set-valued map of the Cournot–Nash equilibria is upper-semicontinuous as a function of initial beliefs of the players for non-additive anonymous games.

On Uncertainty, Market Timing and the Predictability of Tick by Tick Exchange Rates

This paper examines the predictability of exchange rates on a transaction level basis using both past transaction prices and the structure of the order book. In contrast to the existing literature we also recognise that the trader may be subject to (Knightian) uncertainty as opposed to risk regarding the structure by which exchange rates are determined and hence regarding both the model he employs to make predictions and the reliability of any conditioning information. The trader is faced with a two stage decision problem due to this uncertainty; first he needs to resolve a question of market timing as to when to enter the market and then secondly how to trade. We provide a formalisation for this two stage decision problem. Statistical tests indicate the significance of out of sample ability to predict directional changes and the economic value of predictability using one week of tick-by-tick data on the USD-DM exchange rate drawn from Reuters DM2002 electronic trading system. These conclusions rest critically on the frequency of trading which is controlled by an inertia parameter reflecting the degree of uncertainty; trading too frequently significantly reduces profitability taking account of transaction costs.

Market Order Flows, Limit Order Flows and Exchange Rate Dynamics

We study the relation between limit order flow, market order flow and returns. We develop a model where market-makers face inventory risk and adverse selection and show how prices depend on market and limit order flows. In the model, market-makers receive information through trade with customers and optimally split their subsequent trading between market and limit orders so as to exploit this information while controlling risk. Both types of order convey information and impact prices. Empirically, we show that adding limit order flows to regressions of (FX and equity) returns on market order flows greatly improves explanatory power. The price impact of limit orders is positive and smaller than that of market orders. Omitting limit order flows from the regression causes a large downward bias in the price impact of market orders. Thus there is evidence that traders speculate using a combination of limit orders and market orders.

Uncertainty Aversion in an Agent-Based Model of Foreign Exchange Rate Formation

In this paper we test whether investors are uncertainty averse during a real-life trading process in the foreign exchange market. We do this through an agent-based model in which fundamentalist and chartist beliefs of the exchange rate are allowed to be either uncertainty neutral or uncertainty averse. The uncertainty aversion is modelled via the maxmin expected utility approach. We find that traders are uncertainty averse in the FX market. The estimation results show that the inclusion of uncertainty averse agents improves the performance of the model and the uncertainty aversion parameter is significantly different from zero. Fundamentalists are found to be uncertainty neutral and chartists - mainly uncertainty averse.

Spurious Regressions of Stationary AR(p) Processes with Structural Breaks

When a pair of independent series is highly persistent, there is a spurious regression bias in a regression between these series, closely related to the classic studies of Granger and Newbold (1974). Although this is well known to occur with independent I(1) processes, this paper provides theoretical and numerical evidence that the phenomenon of spurious regression also arises in regressions between stationary AR(p) processes with structural breaks, which occur at different points in time, in the means and the trends. The intuition behind this is that structural breaks can increase the persistence levels in the processes (e.g., Granger and Hyung (2004)), which then leads to spurious regressions. These phenomena occur for general distributions and serial dependence of the innovation terms.

How Riskless is 'Riskless' Arbitrage?

In this paper, we challenge the notion that exploiting “riskless” arbitrage is riskless. We show that if rational agents face uncertainty about completing their arbitrage portfolios, then arbitrage is limited even in markets with perfect substitutes and convertibility. We call this phenomenon “execution risk” in arbitrage exploitation. Using a simple model, we demonstrate that this risk arises from the crowding effect of competing arbitrageurs entering the same trade and inflicting negative externalities on each other. We argue that the cost of illiquidity and holding inventory are potential negative externalities. Our empirical results provide evidence that support the relevance of execution risk in arbitrage.