Abstract
Market microstructure is the subfield of finance and econophysics1 which studies how prices result from the process of trading securities. Large trades move prices2 and incur trading costs. Here we combine dimensional analysis, leverage neutrality, and a principle of market microstructure invariance to derive scaling laws which express transaction costs functions, bid-ask spreads, bet sizes, number of bets, and other financial variables in terms of trading volume and volatility. For example, market liquidity is proportional to the cube root of the ratio of dollar volume to return variance. We illustrate the scaling by showing that bid-ask spreads in Russian stocks indeed scale with the cube root. In addition to being of interest to risk managers and traders, these scaling laws provide scientific benchmarks for evaluating controversial issues related to high frequency trading, market crashes, and liquidity measurement as well as guidelines for designing policies in the aftermath of financial crisis.
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