Abstract: In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the position. This will be called horizon risk. We clarify that dynamic risk measures are subject to horizon risk, so we propose to use the fully-dynamic version. To quan- tify the horizon risk we introduce the h-longevity as an indicator. We investigate these concepts together with other properties of risk mea- sures as normalization, restriction property and different formulations of time-consistency. We also consider these concepts for fully-dynamic risk measures generated by backward stochastic differential equations (BSDEs), backward stochastic Volterra integral equations (BSVIEs) and families of these. Within this study we provide new results for BSVIEs: a converse comparison theorem and the dual representation of the associated risk measures.