It depends on what timeframe you are talking about. On a day to day timeframe there can be some pressure on all stocks if there is a big sell off that day. The opposite is also true on big days in the market.
However, from my research I couldn't find an absolute correlation with the week to month timeframe. Stocks can easy buck market trends for various reasons like blowout earnings, new product announcement, etc.
I do believe that on a longer term scale like month to years there is a correlation. Two perfect examples are the late 90's dot com rally, which most stocks were going up rapidly not even based on valid reasons. The other great example is the busting of that that same bubble from 2000 through 2002. The majority of stocks lost significant value with the general market pressure.
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