A "cheap" MHL cable will probably be MHL 1.0, which won't support 1080p (1080i @ 30Hz max rather than the 1080p @ 60Hz that MHL 2.0 supports)
Most MHL cables are also designed for use with recent Samsung devices, which use a proprietary MHL implementation, which is NOT compatible with non-Samsung devices.
The MHL "standard" is almost totally useless, mostly thanks to Samsung creating this confusion, plus the fact that almost no-one ever categorically states what version of the format (1.0, 2.0 and now 3.0) their devices are.
The new Sony devices support MHL 3.0, if they use a standard implementation then their adapters might be the way to go, assuming they eventually turn up and don't cost an arm and a leg.
1) There is NO SUCH WORD as "alot" - It's "a lot"
2) The shortened form of You are is You're - NOT Your
3) Loosing & Loose have completely different meanings to Losing & Lose.