Synthetic pairs

Trading Discussion
1

I have been wondering if it’s possible to create or synthesize pairs such as the following

  1. EURUSD - GBPUSD
  2. EURUSD + GBPUSD
  3. EURUSD ÷ GBPUSD
  4. EURUSD × GBPUSD

I am actually curious to know if there is a possibility of synthesizing a pair or instrument that is bounded above and below such the following
(EURUSD - GBPUSD)/(EURUSD + GBPUSD) which is bounded between -1 & 1. This is just one example in many.
Given the possibility of such a virtual instrument one would just buy it when it’s close to the lower bound (in this case -1) and sell close to the upper bound (in this case +1).