Are there any possible risks of exercising (body weight, calisthenics only) at high altitudes? I'm talking of altitudes above 4500m.

Background: I'll be trekking in the Himalayan region for a couple of months this year. Most of the treks are in the range of 4500m-5900m. Since I'll be on many long hikes, I do not want to lose the muscle mass by not doing my regular workouts (all calisthenics, no weights/machines involved).

Please assume that I will have a good source of proteins. The question is purely on the any possible risks of high altitude workouts.