It's actually possible to lose 4 pounds of fat per week. My PR is 9 fat pounds dropped in 2 weeks, and my bodyfat went from 12% to 7.5% over the course of those 2 weeks, but what I did to do that was rather extreme. Currently I'm dropping around 2 pounds of fat per week, and I'm using a bit more of a sane approach

P.S. I'm not losing any muscle in the process, and in fact I'm adding a bit of muscle to myself as witnessed by my steady strength increases. Case in point, wide grip chins bodyweight for 6 reps 2 weeks ago, and now bodyweight plus 25 pounds added for 8 reps.