Andrew Lo in his book, Adaptive Markets, advocates an investment product that he names a “dynamic index.” He has facilitated the operation of a variant of this dynamic indexation, “dynamic allocation,” by founding a company, AlphaSimplex. Another dynamic investment is GMO’s Benchmark...

We propose a new decomposition of the realized covariance matrix into components based on the signs of the underlying high-frequency returns. Under an asymptotic setting in which the sampling interval goes to zero, we derive the asymptotic properties of the resulting realized semicovariance...