The price dynamics of common trading strategies

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Abstract

A deterministic trading strategy can be regarded as a signal processing element that uses external information and past prices as inputs and incorporates them into future prices. This paper uses a market maker based method of price formation to study the price dynamics induced by several commonly used financial trading strategies, showing how they amplify noise, induce structure in prices, and cause phenomena such as excess and clustered volatility.

Introduction

Under the efficient market hypothesis prices should instantly and correctly adjust to reflect new information. There is evidence, however, that this may not be the case: the largest price movements often occur with little or no news (Cutler et al., 1989), price volatility is strongly temporally correlated (Engle, 1982), short-term price fluctuations are non-normal,1 and prices may not accurately reflect rational valuations (Campbell and Shiller, 1988). This suggests that markets have non-trivial internal dynamics. Traders may be thought of as signal processing elements, that process external information and incorporate it into future prices. Insofar as individual traders use deterministic decision rules, they act as signal filters and transducers, converting random information shocks into temporal patterns in prices. Through their interaction they can amplify incoming noisy information, alter its distribution, and induce temporal correlations in volatility and volume.

This paper2 investigates a simple behavioral model for the price dynamics of a few, common archetypal trading strategies. The goal is to understand how these strategies affect prices. There are three groups of agents: value investors (or fundamentalists) who hold an asset when they think it is undervalued and short it when it is overvalued; trend followers (a particular kind of technical trader, or chartist), who hold an asset when the price has been going up and sell it when it has been going down; and market makers, who absorb fluctuations in excess demand, lowering the price when they have to buy and raising it when they have to sell. These are of course only a few of the strategies actually used in real markets. But they are known to be widely used (Keim and Madhaven, 1995, Menkhoff, 1998), and understanding their influence on prices provides a starting point for more realistic behavioral models.

The first behavioral model that treats the dynamics of trend followers and value investors that we are aware of is due to Beja and Goldman (1980). Assuming linear trading rules for each type of trading, they showed that equilibrium is unstable when the fraction of trend followers is sufficiently high. A related model using non-linear investment rules was introduced by Day and Huang (1990), who added market makers, modified the strategies, and demonstrated chaotic dynamics for prices. The Beja and Goldman model was extended by Chiarella (1992), who made the trend following rule non-linear. When the fraction of trend followers is sufficiently low, the equilibrium is stable, but when it exceeds a critical value it becomes unstable, and is replaced by a limit cycle. The excess demand of each trader type oscillates as the cycle is traversed, causing sustained deviations from the equilibrium price. This model was further enhanced by Sethi (1996), who studied inventory accumulation, cash flow, and the cost of information acquisition. He showed that for certain parameter settings the money of trend followers and value investors oscillates, and when trend followers dominate there are periods where the amplitude of price oscillations is large. Except for some remarks by Chiarella, this work is done in a purely deterministic setting.

Studies along somewhat different lines have been made by Lux, 1997, Lux, 1998, Lux and Marchesi (1999), and also by Brock and Hommes, 1997, Brock and Hommes, 1998, Brock and Hommes, 1999. Both study the effect of switching between trend following and value investing behavior. Brock and Hommes assume market clearing, and focus their work on the bifurcation structure and conditions under which the dynamics are chaotic. The Lux et al. papers use a disequilibrium method of price formation, and focus their work on demonstrating agreement with more realistic price series. They also assume a stochastic value process, and stress the role of the market as a signal processor. Bouchaud and Cont (1998) introduced a “Langevin model”, which is closely related to the work presented here.3 These are not the only studies along these lines; for example, see Goldbaum (1999), or for brief reviews see LeBaron (in press) or Farmer (1999).

The model discussed here was developed independently, and takes this study in a somewhat different direction. Like Day and Huang (1990) and Day (1994), we explicitly include a market maker.4 We modify their model by assuming a simpler price formation rule, explore several different fundamentalist investment strategies, study a more general trend following strategy, and most importantly, we study stochastic information shocks and fundamental values. The use of a market maker allows us to study the price dynamics of each trading strategy individually, i.e. in a setting that includes only that strategy, the market maker, and noisy inputs. We characterize the noise amplification and price autocorrelations caused by each strategy. We investigate simple linear strategies analytically, and also present some numerical results for a heterogeneous market with more complicated non-linear strategies.

Section snippets

Price formation model

In most real markets changes in the demand of individual agents are expressed in terms of orders. To keep things simple, we assume market orders, which are requests to transact immediately at the best available price. The fill price for small market orders is often quoted, so that it is known in advance, but for large market orders the fill price is unknown. This implies that transactions occur out of equilibrium.

Agent behaviors

We now describe some trading strategies in more detail and study their price dynamics. Since the market maker is in a sense a “neutral” agent, we can begin by studying each strategy trading against the market maker. Each strategy induces characteristic price dynamics which can be characterized by its autocorrelation and noise amplification.

One approach to classifying financial trading strategies is based on their information inputs. Decision rules that depend only on the price history are

Concluding remarks

These results illustrate how commonly used trading strategies affect prices. Trend following strategies act as signal filters, amplifying high frequency noise and inducing short-term positive autocorrelations. Value investing strategies act as signal transducers, incorporating information about value into prices, and inducing negative short-term autocorrelations. The fact that prices in real markets have very small autocorrelations suggests that value investors cannot be the only group

Acknowledgements

We would like to thank Paul Melby for contributing Fig. 3, and John Geanakoplos for helpful discussions. We also thank the McKinsey Corporation for their generous support.

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