Suppose I buy one share of stock in AAPL.
6 months later I buy another share.
6 months later AAPL does a 2:1 reverse split and I sell the resulting share.
Would I pay short term or long term capital gains on that sale?
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In the US you would split the sale back to 1/2 a share each and also halve the net amount received from the sale. Then, you'd pair them off.
So if the holding period is 6 months for the first purchase then it would be a short term gain (or loss) and the second purchase would be a long term gain (or loss).
It's the same process as when a stock does a traditional 2:1 stock split except it's now done in reverse (1:2).
Each transaction stands on its own. The reverse split changed your first 1 share into 1/2 share, and it changed your second 1 share into 1/2 share. In both cases, the basis didn't change -- you paid what you paid, and it's the excess over what you paid that gets taxed. And the holding period didn't change -- you bought it when you bought it. If you sell both 1/2 shares at the same time it doesn't change things; each 1/2 share is taxed based on when you bought it and your basis is the amount that you paid for it.
It might be easier to picture this with bigger numbers, so that you aren't dealing with half shares. If you bought ten shares and later bought another ten shares, the reverse split would leave you with a total of ten shares, five from the first purchase and five from the second. If you sell the first five shares you have a 1 year holding period, so a long-term capital gain. If you sell the second five shares you have a six month holding period, so a short-term capital gain. If you sell all ten shares at the same time you still, conceptually, have two sales: five shares with a long-term capital gain and five shares with a short-term capital gain.