Arbitrage and the expectations hypothesis.pdf

ARBITRAGE AND THE EXPECTATIONS HYPOTHESIS Francis A. Longsta?¤ ¤Professor of Finance, The Anderson School at UCLA, Box 951481, Los Angeles, CA 90095-1481. I am grateful for the comments of Pedro Santa-Clara, Olivier Ledoit, Eduardo Schwartz, two anonymous referees, and the editor, Ren?e Stulz. All errors are my responsibility. 1 ABSTRACT This paper shows that all traditional forms of the expectations hypothesis can be consistent with the absence of arbitrage if markets are incomplete. A key implication is that the validity of the expectations hypothesis is purely an empirical issue; the expectations hypothesis cannot be ruled out on a priori theoretical grounds. 2 One of the oldest and best-known models in ˉnance is the expectations hypothesis of the term structure. Introduced by Fisher (1896) more than a century ago, the expectations hypothesis has become a standard framework for explaining how yields of di?erent maturities are related and provides an important empirical benchmark. From a theoretical perspective, however, the expectations hypothesis is not gen- erally viewed as a viable model of the term structure. In particular, Cox, Ingersoll and Ross (1981) show that the traditional expectations hypothesis is actually a set of mutually exclusive propositions and o?er a proof that most forms of the expec- tations hypothesis admit arbitrage. Recently, McCulloch (1993) and Fisher and Gilles (1998) present counterexamples to the Cox, Ingersoll, and Ross proof, show- ing that the traditional forms of the expectations hypothesis can be consistent with the absence of arbitrage. They acknowledge, however, that their counterexamples are somewhat contrived and view them as economically implausible. These results leave the impression that the expectations hypothesis is only consistent with the absence of arbitrage in pathological cases of little practical interest. In this paper, we argue that the expectations hypothesis is much more theo- retically defensible than commonl