Electrohelicity arises in molecules such as allene and spiropentadiene when their symmetry is reduced and helical frontier molecular orbitals (MOs) appear. Such molecules are optically active and electrohelicity has been suggested as a possible design principle for increasing the chiroptical response. Here we examine the fundamental link between electrohelicity and optical activity by studying the origin of the electric and magnetic transition dipole moments of the pi-pi* transitions. We show that the helical character of the MOs drives the optical activity in allene, and we use this knowledge to design allenic molecules with increased chiroptical response. We further examine longer carbyne-like molecules. While the MO helicity also contributes to the optical activity in non-planar butatriene, the simplest cumulene, we show there is no relation between the chiroptical response and the helical pi-MOs of tolane, a simple polyyne. Finally, we demonstrate that the optical activity of spiropentadiene is inherently linked to mixing of its two pi-systems rather than the helical shape of its occupied pi-MOs. We thus find that the fundamental connection between electrohelicity and optical activity is very molecule dependent. Although electrohelicity is not the underlying principle, we show that the chiroptical response can be enhanced through insight into the helical nature of electronic transitions.