The traditional view of financial markets, rewarded in 2013 with a particularly ambiguous Nobel price, is that of efficiency: at any time, the price is assumed to be a reliable and unbiased indication of the fundamental value of each company, raw material, currency, rate or risk. It should therefore be impossible, with a strategy based on public information only, to make systematic profits. Financial markets should be perfect measuring instruments, with no influence on the price they seek to “discover” (in reference to the usual expression of “price discovery” in the economics literature, which seems uncannily linked to the allegory of Plato’s cave). Markets should offer investors fair betting opportunities on the future performances of companies, without introducing any informational bias that would systematically benefit to experts, nor any bubble that would attract gullible investors in a smokescreen.

Efficient markets should thus – at least theoretically – remain fundamentally stable. Any deviation from the “fair price” would immediately be corrected by informed agents, leading to a price continuously and optimally reflecting all the relevant information available. In this context, sudden price changes and violent market moves should be entirely explained by exogenous causes. Yet, empirically, price variations show some surprising statistical regularities (detailed in Section 2): fat-tailed distributions (or “Pareto tails”), and intermittent price dynamics (flushes of stress interrupting calm periods with varying lengths of time). How to reconcile the efficient markets theory with these universal and non-trivial statistical properties, observed on any market and at any point in time? Admittedly, a significant number of variables, that can impact financial markets or not, are themselves fat-tailed distributed, such as the wealth of individuals, the size of mutual funds or companies, the scale of natural disasters, etc. This could be enough to explain the fat-tailed distribution of price moves, but not the excessive, intermittent, long-term memory volatility of financial markets.

Jean-Philippe Bouchaud & Damien Challet

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