We present an analysis of medium-resolution optical spectra and long-term V band photometry of four cool stars, BD+13 5000, BD+11 3024, TYC 3557-919-1, and TYC 5163-1764-1. Our spectroscopic analysis demonstrates that the stars are giant or subgiant from K0 or K1 spectral type, and all of them exhibit emission features in their Ca ii H& K lines. These features appear to be modulated with the rotation of the stars. Except for BD+11 3024, we observe that the radial velocities of the target stars are not stable, which suggests that each of them might be a member of a binary system. Global analysis of photometric data indicates a clear cyclic variation for BD+13 5000 and TYC 5163-1764-1, with a period of 8.0 +/- 0.3 and 5.04 +/- 0.04 year, respectively. Besides that, we observe a dramatic increase (approximate to 07) in the mean brightness of BD+11 3024, accompanied with a 2.87 +/- 0.12 cyclic variation, embedded into the global brightening trend, which indicates possible multiple cycles on this star.