Dimensional Analysis, Leverage Neutrality, and Market Microstructure Invariance

This paper combines dimensional analysis, leverage neutrality, and a principle of market microstructure invariance to derive scaling laws.
• Scaling laws relate transaction costs functions, bid-ask spreads, bet sizes, number of bets, and other financial variables in terms of dollar trading volume and volatility.
• These laws are tested using a data set of trades in the Russian and U.S. stock markets and find a strong support in the data.
• These scaling laws provide useful metrics for risk managers and traders; scientific benchmarks for evaluating issues related to high frequency trading, market crashes, and liquidity measurement; and guidelines for designing policies.

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