Temporal aggregation and risk–return relation

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The function form of a linear intertemporal relation between risk and return is suggested by Merton's [1973. Econometrica 41, 867–887] analytical work for instantaneous returns, whereas empirical studies have examined the nature of this relation using temporally aggregated data, i.e., daily, monthly, quarterly, or even yearly returns. Our paper carefully examines the temporal aggregation effect on the validity of the linear specification of the risk–return relation at discrete horizons, and on its implications on the reliability of the resulting inference about the risk–return relation based on different observation intervals. Surprisingly, we show that, based on the standard Heston's [1993. Review of Financial Studies 6, 327–343] dynamics, the linear relation between risk and return will not be distorted by the temporal aggregation at all. Neither will the sign of this relation be flipped by the temporal aggregation, even at the yearly horizon. This finding excludes the temporal aggregation issue as a potential source for the conflicting empirical evidence about the risk–return relation in the earlier studies.