I think that everyone has a mischievous elf living in their house! I have twice bought new prescription sunglasses for visiting the family in Australia. Both times they disappeared en route. I am certain that I packed them, but they have never been seen again, either here or in Oz.
The only other thing that ever disappeared was a Terry Pratchett book called Pyramids. I bought it as a gift, and put it in my wardrobe until it was needed, and it vanished! I had to buy another copy, and the original has never surfaced, in many years.
I blame the elf! I hope he relents and returns your coat!