Theoretically, if you design an automated trading system for one market, could you move it to another market say, from the S and P to say, the bovespa or the Forex markets and expect similar returns?
A strategy typically performs a given way in a specific market because of the typical price action in that market. And typical price action arises because of the activities of the specific participants typically acting in that market. From a theoretical standpoint therefore, if the participants acting in the other market are typically generally the same, and their behaviour in that market is generally the same, then the strategy might perform the same in the second market. Otherwise, it is more likely to perform differently. Other structural factors like minimum tick size, commissions, etc can also make a difference too. Test to find the answer ...
Only if the strategy is flexible enough to be tunable (optimized) to the different behaving instrument.
I don't go live with strategies which are not (more or less) stable for different markets (of same equity class) ...