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Can two companies own stock in each other?
I was looking at NAT and NAO, NAT owns 20% of NAO.  They trade opposite each other on the price of oil, low is good for NAT, bad for NAO.  In bad times the other company's stock would probably rise, so they could trim excess shares to keep a stable monetary holding.  This would create cash in bad times, in good times they could buy more, creating a floor as well for the other.