Are you projecting from the patio (rear projection) or the yard (front projection)? Rear projection retractable screens are fairly expensive. If you are doing front projection, you can get a 150", 16:9 retractable by Elite from Amazon for about $210+ shipping. http://www.amazon.com/Elite-Screens-M150UWH-Manual-Projection/dp/B000BFW6RO
I toyed with buying this for my outdoor screen, but my wife wanted the screen in another area. I hate to say it, but she was right. I went with Spandex in a 120" screen and it works pretty well. The beauty of Spandex is that it does both front & rear projection. (Mine is solely front projection) If you want to go rear projection, you could just build a frame, install a couple of "j" hooks under the patio roof and hang the screen from them. Whatever you decide to do, you will need some sort of downward tension to keep the screen from blowing in the wind. If you're interested in the Spandex, PM me and I'll give the info on where I bought mine. I attached a couple of pics of my screen for an FYI kind of thing. Good luck.
PS - I use an Epson MovieMate 60 for outdoor movies. It's only 540p, but it's 2000 lumens, 3000:1, HDMI w/a built in dvd player. The 5020 will look much better.