文档介绍：Statistical Arbitrage and Securities Prices
Oleg Bondarenko
University of Illinois at Chicago
This article introduces the concept of a statistical arbitrage opportunity (SAO). In a
finite-horizon economy, a SAO is a zero-cost trading strategy for which (i) the
expected payoff is positive, and (ii) the conditional expected payoff in each final
state of the economy is nonnegative. Unlike a pure arbitrage opportunity, a SAO can
have negative payoffs provided that the average payoff in each final state is non-
negative. If the pricing kernel in the economy is path independent, then no SAOs can
exist. Furthermore, ruling out SAOs imposes a novel martingale-type restriction on
the dynamics of securities prices. The important properties of the restriction are that
it (1) is model-free, in the sense that it requires no parametric assumptions about the
true equilibrium model, (2) can be tested in samples affected by selection biases, such
as the peso problem, and (3) continues to hold when investors' beliefs are mistaken.
The article argues that one can use the new restriction to empirically resolve the joint
hypothesis problem present in the traditional tests of the efficient market hypothesis.
In a fairly general environment, this article proposes a novel martingale-
type restriction on the dynamics of securities prices. This restriction has a
number of important properties. Most notably, the restriction may be
viewed as model-free because it requires no parametric assumptions about
the true equilibrium model. To derive the restriction, we rely on the
concept of statistical arbitrage, a generalization of pure arbitrage.
A pure arbitrage opportunity (PAO) is a zero-cost trading strategy that
offers the possibility of a gain with no possibility of a loss. As is well
known, the existence of PAOs is patible with petitive equili-
brium in asset markets. The fundamental theorem of the financial theory
establishes a link between the absence