Storing Spare Tubular

I just started using tubulars this year. When I am not riding is it ok to keep the spare all rolled up and tied to the back seat or should I let it hang unfolded? Thanks.

I use an old ratty looking tire for a spare. And some say all my tires are ratty ! And I just keep it under my seat. Tufo makes a neat bag for that purpose. I do keep my new and or like new tires on rims inflated. No sun light.
Thanks Dirtball!