I had to reread your question. The answer is a solid no. If you purchased stock then you purchased it from someone and they no longer have a tie to that stock. The fact that the price has gone up means that other people were willing to buy that stock and other people who used to own that stock were willing to sell it for the higher price.
Now, the people that sold the stock to you are certainly missing out on the extra gains they would have received if they had just continued to hold it, but they are not losing money while the stock goes up. You lose money if you buy stock, the price goes down, and then you decide to sell it.
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