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Critical price impact and the intrinsic fragility of financial markets
(Capital Fund Management (Paris) and Ecole Polytechnique)
How does the very fact of buying (or selling) an asset modify its price? This is a fundamental question, not only to understand how financial markets operate and whether they are stable, but also to shed light on the still active debate on market "efficiency" (as highlighted by the split 2013 Nobel Prize in Economics).
One can measure, as for a physical system, the "response" of the price to a small perturbation, for example buying a total of Q shares where Q is small compared to the market turnover. The surprise is that the average impact of such a transaction is not linear in Q (as one would naively guess) but behaves as the square-root of Q. This implies a formal divergence of the linear response, as for a critical system. Interestingly, the square-root behaviour is universal, i.e. independent of the market and the epoch.
We will present a consistent theory for such a non-trivial observation, confirmed by numerical simulations and further experimental observations. Our scenario suggests that markets are intrinsically fragile and turbulent.