Converse trading strategies, intrinsic noise and the stylized facts of financial markets

Abstract

This paper proposes a simple asset pricing model with three groups of traders: chartists who believe in the persistence of bull and bear markets, fundamentalists who bet on a reduction of the observed mispricing, and investors who follow a buy-and-hold strategy. The innovative feature of the model concerns the frequency of trading: rather than remaining constant over time, each agent in a group is only assumed to become active with a certain probability over a given market period. Depending on the trading strategy, part of this elementary kind of intrinsic noise is additive and another part is multiplicative. Using bootstrap and Monte Carlo methods, it is demonstrated that this combination can contribute to explaining the stylized facts of the daily returns on financial markets, such as volatility clustering, fat tails, and the autocorrelation patterns.

Keywords:

• Fundamentalist and technical trading
• Model validation
• Volatility clustering
• Daily returns
• Autocorrelation patterns

Acknowledgement

Detailed comments by two anonymous referees are gratefully acknowledged.

Notes

†For recent surveys of this burgeoning field of research, see Chiarella et al. (2009), Hommes and Wagener (2009), Lux (2009a) and Westerhoff (2009), among others.

†The same version of technical trading or trend chasing has also been employed in models by Day and Huang (1990), Brock and Hommes (1998), and Boswijk et al. (2007). In the latter two cases this becomes obvious if their price expectations are combined with the market maker scenario below. If one feels that the term ‘chartists’ is a slight abuse of language, these agents may also be referred to as anti-fundamentalists; or, more generally, the strategies of the two groups may be described as mean-reverting and mean-fleeing, respectively. We prefer ‘chartists’ since it reads more fluently.

‡Although we are concerned with daily prices and Boswijk et al. (2007) deal with annual data, it is interesting to note that their paper finds some empirical support for equations (1) and (2). They, moreover, report that the market impact of the two opposing groups is time-varying, which will actually be a key feature of our model.

†We also abstain from randomizing these switches, as this would only blow up the notation.

‡The alternative stylized modeling of price determination by a Walrasian auctioneer, who sets the price such that the expression in square brackets in (6) vanishes, is a different mechanism and does not seem very suitable here since it removes the momentum from the equation. See also Chiarella et al. (2009), who provide a nice overview of the implications of different price setting mechanisms.

†In this respect, the modeling architecture is different from many other asset pricing models, where the deterministic dynamics (perhaps those of an unstable equilibrium point, for example) or their inherent nonlinearities may play a greater role for the properties of the stochastic system.

‡Detailed descriptions of the statistical properties of asset prices can be found in Cont (2001), Lux and Ausloos (2002) and Lux (2009b).

§This means that the entire series covers 6867 days, of which the first 100 days are set aside to allow the computation of autocorrelations up to a lag of 100 days from t = 1 onward.

†Since it reduces the overall computational effort by roughly two-thirds, this and the simulations to follow have approximated the binomial deviates with random draws from the corresponding normal distribution; see Press et al. (1986, section 7.3) for the computational background.

†To be precise, the event was specified by J > 150 for the objective function outlined above.

†These numbers and the other statistics discussed here are documented in table A1 in the appendix. In addition, the table reports two (representative) autocorrelation coefficients for the raw returns to confirm their overall insignificance.

‡The density functions have been estimated by means of the Epanechnikov kernel (Davidson and MacKinnon 2004, pp. 678–683).

†The much wider bootstrap distribution of the volatility could be explained by the different noise levels of the S&P 500 returns over longer periods of time, which we have already touched on in the discussion of figure 1. Normally, there are multiple random draws of the same block at the cost of other blocks that do not appear at all in the bootstrap series. This causes a certain dispersion of the volatility measure across the 5000 samples. In contrast, as has also been noted in the discussion of figure 1, the model's noise over the (relatively) tranquil periods is more homogeneous.

‡While there are far more traders on the FX than on the stock markets, when considering the absolute number of agents in the model the ceteris paribus condition of the fixed market impact coefficient μ should be taken into account. A more scrupulous modeling approach might scale it in some way with the overall number of agents, but the problem of how precisely this should be specified seems to be terra incognita in all models where the market prices are assumed to respond to total excess demand (since the number of traders is usually fixed). Empirical evidence on the price impact of orders in different markets, which has recently been provided by Bouchaud et al. (2009), has not been taken into account so far.

†Franke (2010) discusses two other, structurally very appealing models from the literature which reveals that, in their present specification, they cannot reasonably keep their promise of matching the stylized facts. According to the explicit method-of-simulated-moments estimation of Franke (2009), the threshold switching model of Manzan and Westerhoff (2005) appears to be somewhat superior to the results in this paper. As a most recent contribution, the concept of ‘structural stochastic volatility’, the basic idea of which bears some resemblance to our intrinsic noise, has been shown to succeed in meeting similar standards to the present model (or even stronger ones) (Franke and Westerhoff 2009, 2010).