Samuelson Hypothesis and Carry Arbitrage

The relationship between the Samuelson hypothesis and carry arbitrage is examined. The empirically based Samuelson hypothesis states that futures price volatility will increase with approaching expiration. The existing empirical evidence related to the Samuelson hypothesis is mixed. The theory-based carry arbitrage is not feasible in many futures markets for a variety of reasons, including the inability to short sell the underlying instrument. The important link between the empirical Samuelson hypothesis and the theoretical carry arbitrage is identified and explored. The degree to which carry arbitrage is empirically validated is associated with the degree to which the Samuelson hypothesis is not supported. The empirical evidence here supports this claim as well as identifying which futures markets are consistent with the Samuelson hypothesis and which futures markets are not. Fifty futures markets are examined between June 1, 1993, and March 8, 2012, and empirical support for the link between carry arbitrage and the Samuelson hypothesis is documented. Empirical evidence is provided of carry arbitrage activities in some metals, debt, stock indices, and foreign-exchange futures markets. Those same futures markets fail to support the Samuelson hypothesis. The results are important as an improved understanding of futures price volatility provides numerous benefits to a host of constituencies.