The EXOplanet high resolution SPECtrograph (EXOhSPEC) instrument is an echelle spectrograph dedicated to the detection of exoplanets by using the radial velocity method using 2m class telescopes. This spectrograph is specified to provide spectra with a spectral resolution R < 70, 000 over the spectral range from 400 to 700 nm and to reach a shortterm radial velocity precision of 3 m/s. To achieve this the separation between two adjacent spectral orders is specified to be greater than 30 pixels and to enable a wide range of targets the throughput of the instrument is specified to be higher than 4%. We present the results of the optimization of the spectrograph collimator performed and initial tests of its optical performance. First, we consider the spectrograph design and we estimate its theoretical performance. We show that the theoretical image quality is close to the diffraction limit. Second, we describe the method used to perform the tolerancing analyzes using ZEMAX software to estimate the optical performance of the instrument after manufacturing, assembly and alignment. We present the results of the performance budget and we show that the estimated image quality performance of EXOhSPEC are in line with the specifications. Third, we present the results of the stray light analysis and we show that the minimum ratio between the scientific signal and the stray light halo signal is higher than 1,000. Finally, we provide a status on the progress of the EXOhSPEC project and we show the first results obtained with a preliminary version of the prototype.