Ebook Price Impact and Portfolio Impact
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.
We show that Friedman’s original intuition is in fact correct, but with a small modification: price impact is indeed equivalent to survival, but under the risk-neutral rather than the physical measure. Namely, an agent has a long-run price impact if, and only if, the long-run share of the aggregate wealth that he owns has a non negligible market value.
A similar result holds for portfolio impact. We show that the long-run impact of agent j on the portfolio of agent i is equivalent to the survival of agent j, but under agent i’s wealth-forward measure. This measure has a density proportional to that of the risk-neutral measure, but it is multiplied with agent i’s wealth. This is very intuitive: the agent, j, who bets on the realization of states in which agent i’s wealth is the largest, will have the most significant impact on state prices in those states and, consequently, on agent i’s optimal portfolio.
We consider an economy populated by an arbitrary number of agents with arbitrary heterogeneous risk aversions and beliefs, maximizing utility from terminal consumption. We derive closed-form asymptotic expressions for equilibrium quantities and study how price impact, portfolio impact and survival depend on the cross-sectional distribution of agents’ characteristics. We show that allowing for more than two agents can lead to new, surprising phenomena that cannot occur in two-agent economies. In particular, we show that even a non surviving agent with no price impact may have long-run impact on other agent’s equilibrium optimal portfolios. In contrast to the findings of KRWW (2006), we show that non surviving irrational agents can have both price and portfolio impact even if they are optimistic, as
long as the preferences are heterogeneous across agents. As we show, the presence of such overoptimistic irrational traders is crucial for generating the empirically observed U-shaped pattern for the equilibrium state price density. Finally, when the economy is populated by a large number of agents, both price impact and portfolio impact can be permanent: they may not vanish even for periods arbitrarily close to the terminal time horizon. This behavior is completely different from that in a two-agent economy in which both price and portfolio impact always vanish for periods sufficiently close to the terminal time horizon.
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