This paper considers a multi-way massive multiple-input multiple-output relaying system, where single-antenna users exchange their information-bearing signals with the help of one relay station equipped with unconventionally many antennas. The relay first estimates the channels to all users through the pilot signals transmitted from them. Then, the relay uses maximum-ratio processing (i.e. maximum-ratio combining in the multiple-access phase and maximum-ratio transmission in the broadcast phase) to process the signals. A rigorous closed-form expression for the spectral efficiency is derived. The effects of the channel estimation error, the channel estimation overhead, the length of the training duration, and the randomness of the user locations are analyzed. We show that by deploying massive antenna arrays at the relay and simple maximum-ratio processing, we can serve many users in the same time-frequency resource, while maintaining a given quality-of-service for each user.