We can calculate the expected stock return (under the measure $Q$) from at-the-money ($K=S_t$) option prices as:
$$E\left(\frac{S_T-S_t}{S_t}\right)=\frac{e^{rT}}{S_t}(C_t-P_t)$$
The result is mainly based on the fact that $$(S_T-S_t)^+-(S_t-S_T)^+=S_T-S_t$$ and $C_t=e^{-rT}E((S_T-K)^+)$.
I am looking for an expression of stock return using options with $K\neq S_t$.
My first approach was to equate the two sides and determine the difference:
$$(S_T-K)^+-(K-S_T)^+\stackrel{!}{=} S_T-S_t+\left[(S_T-S_t)^+-(S_t-S_T)^+-((S_T-K)^+-(K-S_T)^+)\right]$$
Maybe it would be possible to rearrange this term to get a sum of option payoffs plus a deterministic part (i.e. a bond).
Please let me know if you find a solution.