The principal motivation for studying survival of irrational traders and their long-run price impact comes from the theory of efficient financial markets. If irrational traders do have long-run impact on asset prices, there will be persistent market inefficiencies, and prices will constantly deviate from fundamental values and give rise to inefficient allocations.

Starting with Friedman (1953), it has long been argued that irrational traders cannot survive in a competitive market, as they will constantly lose money betting on the realization of very unlikely states of the economy. Basing on this intuition, Friedman argued that irrational traders cannot influence long-run asset prices. In a recent seminal contribution, Kogan, Ross, Wang and Westerfield (2006) (henceforth, KRWW (2006)) demonstrated that survival and price impact are two independent concepts: even if irrational traders do not survive, they can still have a substantial long-run impact on asset prices. They also show that irrational traders portfolio policies can deviate significantly from what the asymptotic moments of stock returns suggest. KRWW (2006) suggest the following intuitive explanation of these surprising phenomena: “Under incorrect beliefs, irrational traders express their views by taking positions (bets) on extremely unlikely states of the economy. As a result, the state prices of these extreme states can be significantly affected by the beliefs of the irrational traders, even with negligible wealth. In turn, these states, even though highly unlikely, can have a large contribution to current asset prices.” This intuition naturally gives rise to the following questions: what, precisely, are the extremely unlikely states responsible for the price impact, and what is the exact economic mechanism by which these states generate price impact? In this paper, we provide detailed answers to these questions.