Measuring the Value of Extra Information for Statistical Arbitrage

Summary

This document presents an asymmetric information model in which ordinary market participants observe noisy information about an asset’s future cash flow, while one trader also receives a separate, noisy signal. The extra signal may share noise with the market’s information. The informed trader uses it to identify statistical arbitrage opportunities while accounting for the added risk.

The model measures ordinary information using mutual information between price and cash flow, then values the trader’s added signal by comparing that measure for informed and general participants. The difference is nonnegative when the signal-to-noise ratio is known in advance. The authors also construct trading strategies to show how the extra information can be used for profit. The document gives a theoretical framework and strategy constructions, but does not provide empirical validation, implementation details, or evidence about performance under real trading costs and market conditions.

Key ideas

• The model gives one trader an additional noisy information source alongside the market’s shared signal.
• Mutual information between price and cash flow measures the information available to general participants.
• The value of the extra signal is defined by its increase in mutual information for the informed trader.
• The information-value difference is nonnegative when the signal-to-noise ratio is known beforehand.
• Constructed strategies illustrate how the signal may support statistical arbitrage, subject to added risk.

Tags

# Informed Traders


# Informed Traders









An asymmetric information model is introduced for the situation in which there is a small agent who is more susceptible to the flow of information in the market than the general market participant, and who tries to implement strategies based on the additional information. In this model market participants have access to a stream of noisy information concerning the future return of an asset, whereas the informed trader has access to a further information source which is obscured by an additional noise that may be correlated with the market noise. The informed trader uses the extraneous information source to seek statistical arbitrage opportunities, while at the same time accommodating the additional risk. The amount of information available to the general market participant concerning the asset return is measured by the mutual information of the asset price and the associated cash flow. The worth of the additional information source is then measured in terms of the difference of mutual information between the general market participant and the informed trader. This difference is shown to be nonnegative when the signal-to-noise ratio of the information flow is known in advance. Explicit trading strategies leading to statistical arbitrage opportunities, taking advantage of the additional information, are constructed, illustrating how excess information can be translated into profit.

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