I saw some intraday price spiking today on the SPY at around 10:20 and it was similarly mirrored across a variety of instruments including AAPL, MSFT and quite a few others. Considering so many instruments are algorithmically traded an instantly aware of what is taking place elsewhere it seems almost impossible at times to avoid these type of correlated movements, even though the initial trigger may or may-not have been of any fundamental importance to most of the effected. This got me thinking... Are there any instruments that are not as predisposed to this type of correlated price movement just due to the nature of their makeup? This could be because their value is based off an abstracted calculation, they don't correlated to the broader market in general, or maybe its due to something else altogether.
You need to study intermarket analysis. For example, if the equity market rises so does the US Dollar. If the Dollar rises, then the Euro must fall. Hence, if SPX climbs then the Euro will sell off. Bond market also moves, for the most part, inversely to the equity. So does Gold. I could go on and on, but I'll stop here for now.
The overall stock market exercises a very significant gravitational pull on all the individual components. I've read statistic studies showing that over time, as much as 80% of a stock's movement can be attributed to market movement. And I've found that to be true in my experience. If that's a concern to you, then look into other areas, or give into the force and embrace indexes and their derivatives.
If something is causing a volatility spike like that in correlated and none correlated trading instruments...its almost always news related. In fact, I've been involved in the markets for a long time and whenever I've seen a volatility spike that hits all markets at the same time... Its news related...big news that all financial networks are talking about around the world. In contrast, if a volatility spike like that only hits correlated markets and doesn't hit none correlated markets...it may or may not be news related but whatever the reason...its being ignored by none correlated markets. Thus, not important overall to all markets but only important to those correlated markets. If you're not in a trade when such occurs...problem solved. If you're in a trade when such occurs...hopefully you're not one of those people that doesn't like to use stops. If you're in a trade when such occurs and you get stopped out...shit happens and start preparing for your next trade.
This is the entire basis of modern portfolio theory, which it looks like you're independently discovering on your own. Every stock's variance is made up of idiosyncratic variance inherent in that stock alone and systemic variance related to the market as a whole. That systemic variance has a name, beta, which roughly speaking is how much a stock moves in response to an overall move in the market. A stock with a beta of 1, for example, moves 1:1 with the market, where a beta of -1 means it moves opposite the market, while 0 would be that it moves independent of the market. To answer your original question then, look for low beta stocks, something you can screen for in most screeners. However I'd also highly recommend one of the free MOOC finance courses. I think you'd love it and really get a lot out of it given that you're clearly intellectually curious and have already independently figured out part of the picture.
the idea isn't to get non correlated, the idea is to get inversely correlated. But it's out of the fire and into the frying pan, then you still need to decide what and how much insurance to buy (or sell.) and yes I agree, the best non correlated instrument is usually cash
Sigs answer is great because I thought "oh yeah, thats beta" . I wonder if you could bucket news into sectors. The effect of energy news on SP500 high beta energy components is likely to exceed that low beta healthcare components. So play XOM/SPY against MDT/SPY in theory, which is XOM/MDT in practice. Dont think people would give these away (assuming they exist) till the opportunity has closed. it would be tough to discover possibly millions of possibilities here considering the amount of company, sector,market, intra-market, global news effecting 500 stocks daily.