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«Björn-Christopher Witte Working Paper No. 64 April 2009 b B A M B AMBERG E CONOMIC R ESEARCH GROUP k k* BERG Working Paper Series on Government and ...»

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Temporal information gaps and market efficiency:

a dynamic behavioral analysis

Björn-Christopher Witte

Working Paper No. 64

April 2009











BERG Working Paper Series

on Government and Growth Bamberg Economic Research Group on Government and Growth Bamberg University Feldkirchenstraße 21 D-96045 Bamberg Telefax: (0951) 863 5547 Telephone: (0951) 863 2547 E-mail: public-finance@sowi.uni-bamberg.de http://www.uni-bamberg.de/vwl-fiwi/forschung/berg/ ISBN 978-3-931052-71-3 Reihenherausgeber: BERG Heinz-Dieter Wenzel Redaktion Felix Stübben∗ ∗ felix.stuebben@uni-bamberg.de Temporal information gaps and market efficiency: a dynamic behavioral analysis Björn-Christopher Witte University of Bamberg Department of Economics Feldkirchenstrasse 21 D-96045 Bamberg Abstract: This study seeks to explore, how market efficiency changes, if ordinary traders receive fundamental news more or less often. We show that longer temporal information gaps lead to fewer but larger shocks and a reduction of the average noise level on the dynamics. The consequences of these effects for market efficiency are ambiguous. Longer temporal information gaps can deteriorate or improve market efficiency. The concrete result depends on the stability of the market together with the interval in which the length of the gap is incremented.

Keywords: Temporal information gaps, market efficiency, disclosure policy, agentbased financial market models, technical and fundamental analysis.

JEL classification: G12; G14.

1. INTRODUCTION Conceived in the 1960s the Efficient Market Hypothesis (EMH) has become one of the most famous economic paradigms. It states that security prices fully reflect all available fundamental information. Fama (1970) has differentiated three interpretations of such

efficiency. The following formulation rests partly on Jensen (1978):

In general a market is efficient with respect to information set if is properly reflected in prices.

– In the weak form comprises solely the information contained in the past price history of the market as of time t.

– In the semistrong form comprises all information publicly available at time t.

– In the strong form comprises all information known to anyone at time t.

In the past thirty years lots of empirical (e.g. Shiller 1981, Cutler et al. 1989, Lev 1989, Mitchel and Mulherin 1994) as well as some analytical findings (Grossmann and Stieglitz 1980, Shleifer and Vishny 1997) have challenged the EMH. The flourishing field of behavioral finance (see, e.g. Shleifer 2000, Hirshleifer 2001, Shiller 2003, or Lo 2004) has proposed some explanations of its failing. The central insight is that agents do not process information fully rationally but follow sentiments and commit systematic errors. Still, this view simplifies the reality of financial markets. Due to publicity laws and corporate disclosure policies, for instance, traders do not even receive fundamental information currently. Our analysis focuses on this fact and its consequences for market efficiency.

The underlying question of our research is: How does market efficiency change, if ordinary traders receive fundamental information more or less often? In this context, the term “temporal information gap” will denote the span of time in which traders do not receive any

–  –  –

conceptualize the process of value discovery as a complex process. The computation of the

proper fundamental value necessities three conditions:

I. Fundamental data must be available. In reality disclosure regulations obligate firms to disseminate fundamental data only at discrete steps of time.

II. Fundamental data must be complete, correct and definite. In reality disclosure regulations do not prescribe to publish all value-relevant information and give considerable leeway to creative accounting.

III. Agents must know the exact relationship between fundamental information and value. Not every real trader is an expert and uses rational methods to compute the true value out of the bulk of data. Additionally, the methods themselves are

–  –  –

Figure 1 illustrates the process of value discovery. The process implicates the possibility of information gaps on the side of traders. The term “information gap” is originated in agency theory where it is used synonymously for the deficit of information of the agent relative to the principal. Regarding the process of value discovery two causes of such an information deficit become apparent. First, agents have not received the latest information and second, agents have received the latest information, but the information lack of content. Accordingly, we denominate the first form of information gap as “temporal” and the second as “substantive”.

Temporal as well as substantive information gaps can arise in various extents. The extent of a temporal information gap (TIG) is determined by the time that agents lack of current information. We specify the TIG as the number of periods in which agents do not get any For an overview of common methods see Brealey et al. (2006).

–  –  –

assume that once the information is public, the true fundamental value is known to traders, that is, condition II and III are fulfilled.2 To conduct our analyses we construct an agent-based model of a financial security market.

The chartist-fundamentalist approach has proven to be a powerful tool in this area (for recent surveys see Hommes 2006, LeBaron 2006, Lux 2006, Westerhoff 2008 and Westerhoff 2009.

The behavioral approach is based on the observation that financial traders use two main strategies: fundamental and technical analysis. Fundamentalists fix their orders to economic fundamentals, whereas chartists try to predict prices by simple technical trading rules based upon patterns in past prices, such as trends. The interplay of both strategies creates model dynamics that replicate some stylized facts of real financial markets.

What might be a reasonable assumption about the relationship of TIGs and market efficiency?

Consider that the forces of arbitrage tend to adjust prices to the value which arbitrageurs assume to be proper. TIGs make possible that this estimation is already misaligned in reference to the true fundamental value. Clearly, the misalignment tends to be heavier, the less often arbitrageurs receive fundamental information, i.e., the longer the TIG. One may conclude that longer TIGs should lead to a fall of market efficiency, at least in the strong form. Market efficiency in the semistrong form might not be influenced by TIGs, since the concept merely measures the difference between true prices and arbitrageurs’ subjective fundamental perception while ignoring the objective misalignment of the latter.

The results of our study run counter to these intuitions. Longer TIGs do not always mean a fall of market efficiency. The explanation lies in the complex effects of TIGs on price One may wonder why we do not simply speak of information lags instead of temporal information gaps. The reason is that the term “information lag” suggests that all information is disclosed with the same delay. This does not apply to our model since we assume information of different periods to be released in a bundle.

–  –  –

dynamics, which in turn improves efficiency. Thus, even if longer TIGs increase the bias between the true fundamental value and the perception of traders, market efficiency, in each form, improves if the volatility effect is strong enough. The analysis will show that the overall effect of larger TIGs on market efficiency depends on the endogenous stability of the market and on the interval in which the TIG is incremented.

The paper is organized as follows: Section two is dedicated to a deeper theoretical foundation of our project. We recapitulate the state of efficiency research and conceptualize the process of value discovery. Section three derives the relationships between TIGs and the noise affecting the market. In section four we introduce the chartist-fundamentalist approach and develop a dynamic behavioral model accordingly. Section five presents the model simulations, resumes the complex results, and intends to provide interpretations. Section six underscores the relevance of the results in the context of corporate disclosure policy and institutional regulation. Finally, in section 7 we summarize the most important findings.


This section is dedicated to TIGs, noise and the relationship between both. Economics refer to noise in many contexts and use the term with different connotations.3 In the context of our study we define noise as an exogenously driven influence on the dynamics of prices. Shocks are understood as singular occurrences of noise.

In general, exogenous influences on the dynamics of prices arise from changes of the fundamental data. If fundamentals change, traders will compute a new fundamental value, reformulate their orders respectively, and prices will adjust to the new demand. Clearly, this Black (1986) provides an overview of different fields and senses in which noise affects market efficiency.

–  –  –

fundamentals. As long as fundamental movements are not communicated to traders, they will not manipulate the dynamics of prices. During the TIG, therefore, no shocks will appear. This observation enables us to specify the initial definition of shocks: Shocks consist in the recognition of fundamental changes from one observation step to another. Let the parameter denote the length of a TIG. It follows that a shock will arise every ℎ

period. Formally:

–  –  –

where ℎ is any period in which a shock affects the dynamics of prices.

What can be said about the relationship between gap and the average “size” of the shocks? If the true fundamental price follows a random walk, it will tend to drift apart from an initial value over time. Accordingly, as long as traders are not informed about fundamental movements, the deviance between their subjective pricing of the fundamental value and its true level tends to rise. Thus, when traders finally learn the relevant data, the perceived change of the fundamental value will on average be heavier, the longer the preceding TIG.

We conclude that the shocks on price dynamics will be stronger, the higher the gap.

The exact quantitative relationship is easy to derive. Assume that the evolution of the fundamental value () is defined by

–  –  –

where is the change of fundamentals in period t. is a normally distributed, independent variable with mean 0 and variance 2. For the normal distribution holds that if and are independent normal random variables with ~(, 2 ) and ~(, 2 ), then their sum is normally distributed with = + ~Ν( + , 2 + 2 ).

–  –  –

2 ~(0, 2 ), …, and ~(0, 2 ), then their sum is normally distributed with = ~Ν(0, 2 ).

This means that if traders learn the fundamental value every ℎ period, the variance of the perceived changes, and therefore the size of the shocks, will be -times the variance of the

periodical change of fundamentals. Formally:

–  –  –

Let ℎ denote the occurrences of shocks, then due to (5) the following relationship must

be valid:

ℎ 2 = [ℎ 2 ], with ℎ = ∗ . (6)

From (6) results:

–  –  –

where ℎ is the average absolute shock and the average absolute periodical change of fundamentals. Accordingly, the average size of the shock after periods of zero

–  –  –

of fundamentals.

In summary, we could detect two effects of TIGs on noise:

A. The higher the TIG, the less often shocks hit the dynamics of prices.

B. The higher the TIG, the heavier the shocks will be.

As exogenous shocks are generally known to destabilize dynamics, the two effects must be rivaling: When TIGs grow, the effect of fewer shocks (A) tends to stabilize the dynamics, whereas the effect of heavier shocks (B) works destabilizing.

Which of the two effects prevails with respect to the average noise level? We define the average noise level as the mean shock averaged over all transaction periods, no matter if a

shock appears or not. Formally:

–  –  –

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