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Let's say I buy 1000 shares of ABC for 10$ each. Avg. Cost : 10$
Six months later I sell 500 shares for 12$ each. Total earnings: 1000$
Question: should I include the earnings in the formula of the avg. cost in order to drive the avg. share cost lower?
You bought 1,000 shares at $10 and sold 500 shares at $12. That's a $1,000 gain.
When you sell the remaining 500 shares, what will you put on your taxes as the cost basis? It will be what you paid for them which is $10.
If you like, you can calculate other stats regarding your trades but the cost basis is what you paid for the shares.
