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Macquarie applies Benford’s law to identify firms which may be manipulating their accounting data, or perhaps even engaging in outright fraud. According to this law, there is a natural frequency of 1 to 9 occurring as the first digit in a number, with the chance of 1 for instance being around 30%, and the chance of 9 less than 5%.
If the figures in the financial statements of a company show a large deviation from Benford’s law, this could be a reason for suspicion. They find a Sharpe ratio of about 0.5 for a sector neutral top-minus-bottom quintile strategy based on this idea. The correlation with traditional quantitative factors is found to be low, which suggests it could be a nice diversifier in multi-factor models.
Our main concern is whether it is really strong enough to improve upon a traditional multi-factor model. The robustness across different markets would also need to be investigated further.
* Macquarie, “Japan Dynamics: Quant Strategy – Red Flag Reporting”, 16 July 2014