Lower Bounds on Asset Return Comovement

Abstract

Under standard assumptions from dynamic asset pricing theory (value additivity, complete markets, rational expectations, and strict stationarity and ergodicity) and absence of arbitrage, lower bounds on the conditional and unconditional cross-moments of the returns on two assets a.re derived. They a.re expressed in terms of the second moment of a linear combination of option premia. The restrictions a.re probed with data from the foreign exchange market covering the period 1983-1991. Assuming that the value of the economy's benchmark payoff never exceeds one, and substituting linear projection for conditional expectation, several violations of the conditional lower bounds are discovered. The violations are attributed to unit roots in the data.