EMPIRICAL EVIDENCE OF KNIGHTIAN UNCERTAINTY IN EQUITY MARKETS
Schoening, Julie Li
Market microstructure theory builds on the assumption that the arrival of new information induces trading, because it alters market participants’ expectations of the true price. The bid-ask spread, which represents microstructure frictions, should straddle the expected true price (Madhavan, 1992). In empirical studies, the bid-ask midpoint is a generally accepted and frequently used proxy for the expected true price of the asset (Hasbrouck, 2007; Huang & Stoll, 1997). In this paradigm, price discovery occurs through trading, with the expected true price unvarying between two adjacent trades.I consider, on the contrary, that it is not only possible but also common for the expected true price to be outside the bid-ask interval in a modern equity market. I provide empirical evidence of quote movements within time periods of no trade using tick-by-tick equity market data. To explain such previously undocumented evidence, I suggest a Knightian uncertainty model from Easley and O’Hara (2010a), which models liquidity freeze in the fixed-income market. I form hypotheses to test potential causes of the instances where quotation prices clearly deviate from the expected true price of the security. I build a Monte Carlo simulation of the limit order book with order entries, cancellations, and executions following separate Poisson processes, and use the simulation results as a benchmark to test the significance of the empirically observed deviations: they are statistically significant in both frequency and magnitude. Since Knightian uncertainty cannot be quantified by definition, I take a process-of-elimination approach to test competing hypotheses on valuation risk, microstructure risk, and time of the day effects. I find the empirical evidence of Knightian uncertainty consistent with theoretical prediction, although market risk factors also contribute significantly.These findings challenge the classical assumption of the relationship between the theoretical construct of true price and the empirically observed quotation prices in a microstructure setting; extend a new approach led by Easley and O’Hara (2010a) and Routledge and Zin (2009) to consider Knightian uncertainty—differentiated from risk—to interpret new market data; and contribute to the empirical literature on Knightian uncertainty.
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