I'd say it depends very much on the size of the correction.
If you look at what's happened with major corrections over the past 35 years:
1. '87 Crash. All stocks were affected, big and small. I was working in a broking house on 20 Oct (Australia followed US lead on Oct 19) and on that day there were NO blue slips (buy orders). And screens were lopsided, just sell orders, no buyers. Even the largest companies were affected. I had guys ringing up asking me to sell at any price on many companies, and you could sell anything! I doubt that will happen ever again in my lifetime ( and I don't plan to get hit by a bus at all touch wood).
2. Tech wreck, early 2000's. All tech stocks affected big and small. Most other sectors affected to some degree, big and small. And the fallout continues beyond the initial drops.
3. 2008. A time when many believed the banks were going to fail altogether. Another time when all sectors, and big and small were affected.
4. March 2021. When economic ramifications of the virus finally sunk in. Again all sectors affected, big and small.
With the amount of money being created by central banks, the minimalistic interest rates in most economies, the likelihood of another major crash is less likely for a while - DESPITE many small businesses going under, and lots of unemployment and underemployment in many countries. It seems strange how quick most share markets have recovered, despite the virus and its impact on economies still affected - of course those sectors most affected have continued to wallow eg travel related stocks etc.
There will always be the odd 2 - 3% odd falls, on a 1 - 3 day basis, but nothing that most economic commentators consider likely. If that remains then you will note that on down days perhaps a majority of shares might fall, but even on those days there will be stocks that buck the trend - just consider this. That even on real bad trading days, the RELATIVE value of most stocks remain intact. ie a recognition by the market that a company has its perceived value. And when a stock announces something that adds value, it is likely to outperform.
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