Relative-entropy tests of market efficiency
Symbolic benchmarks, finite alphabets, and attainable log-growth
Jan Vecer · Quantitative Finance · Forthcoming
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Publisher DOI: 10.1080/14697688.2026.2749693 · Download BibTeX
What the paper asks
How can we express departures from a market-efficiency benchmark in units of information, test them statistically, and distinguish that information from what a specified trading strategy can attain?
The paper studies symbolic and finite-alphabet representations of market data. It connects conditional relative entropy, likelihood-ratio inference, and expected logarithmic growth while keeping the information set and available trading opportunities explicit.
Main connections
- A statistical benchmark: conditional relative entropy measures departure from the chosen reference law. Finite-alphabet likelihood-ratio statistics give this population quantity a statistical counterpart.
- The effect of coarsening: a simpler observation alphabet can discard population information. Its effect on statistical power also depends on the test and sampling problem.
- Attainable growth: information and trading gains agree under the appropriate payoff and trading assumptions. A restricted strategy set can implement only part of the available information.
Empirical illustration
A daily S&P 500 illustration uses a bounded cash/index allocation. It finds no statistically significant improvement for that tested allocation. The framework therefore separates an information measure, evidence against a benchmark, and a demonstrated trading advantage.
Citation and manuscript
Jan Vecer. “Relative-entropy tests of market efficiency: symbolic benchmarks, finite alphabets, and attainable log-growth.” Quantitative Finance, forthcoming. DOI: 10.1080/14697688.2026.2749693.
The linked PDF is the supplied author manuscript, with its original title and contents. It is not the publisher’s version of record. Use the DOI for the journal record and final bibliographic details as they become available.
Explore the ideas
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