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We develop a general multivariate aggregation property which encompasses thedistinct versions of the property that were introduced by Neuberger [2012] andBondarenko [2014] independently. This way, we classify new types of model-freerealised characteristics for which risk premia may be estimated without bias.We focus on the aggregation property for multivariate martingales and logmartingales, and then define realised third and fourth moments which allowlong-term higher-moment risk premia to be measured, efficiently and withoutbias, using high-frequency returns.

The Aggregation Property and its Applications to Realised Higher Moments