I had a long term capital gain of 3000$ this year from sale of one stock. If I take a long term loss of 50$ on another long term holding, can I reduce capital gain tax on the my profits?
Is this a good strategy?
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Tax questions require that you specify a jurisdiction.
Assuming that this is the US, you owe Federal income tax (at the special long-term capital gains tax rate) on the net long-term capital gains (total long-term capital gains minus total long-term capital losses) and so, yes, if these two were your only transactions involving long-term holdings, you would pay long-term capital gains tax on $3000-$50 = $2950. Many States in the US don't tax long-term capital gains at special rates the way the Federal Government does, but you still pay taxes on the net long-term capital gains. I suspect that other countries have similar rules.
As Dilip said, if you want actual concrete, based in tax law, answers, please add the country (and if applicable, state) where you pay income tax. Also, knowing what tax bracket you're in would help as well, although I certainly understand if you're not comfortable sharing that. So, assuming the US...
If you're in the 10% or 15% tax bracket, then you're already not paying any federal tax on the $3k long term gain, so purposely taking losses is pointless, and given that there's probably a cost to taking the loss (commission, SEC fee), you'd be losing money by doing so. Also, you won't be able to buy back the loser for 31 days without having the loss postponed due to the wash sale that would result.
State tax is another matter, but (going by the table in this article), even using the highest low end tax rate (Tennessee at 6%), the $50 loss would only save you $3, which is probably less than the commission to sell the loser, so again you'd be losing money. And if you're in a state with no state income tax, then the loss wouldn't save you anything on taxes at the state level, but of course you'll still be paying to be able to take the loss.
On the high end, you'd be saving 20% federal tax and 13.3% state tax (using the highest high end tax state, California, and ignoring (because I don't know :-) ) whether they tax long-term capital gains at the same rate as regular income or not), you'd be saving $50 * (20% + 13.3%) = $50 * 33.3% = $16.65.
So for taxes, you're looking at saving between nothing and $16.65. And then you have to subtract from that the cost to achieve the loss, so even on the high end (which means (assuming a single filer)) you're making >$1 million), you're only saving about $10, and you're probably actually losing money.
So I personally don't think taking a $50 loss to try to decrease taxes makes sense. However, if you really meant $500 or $5000, then it might (although if you're in the 10-15% brackets in a no income tax state, even then it wouldn't). So the answer to your final question is, "It depends." The only way to say for sure is, based on the country and state you're in, calculate what it will save you (if anything).
As a general rule, you want to avoid letting the tax tail wag the dog. That is, your financial goal should be to end up with the most money, not to pay the least taxes. So while looking at the tax consequences of a transaction is a good idea, don't look at just the tax consequences, look at the consequences for your overall net worth.
No, if you are taking a loss solely and purely to reduce the tax you have to pay, then it is not a good strategy, in fact it is a very bad strategy, no matter what country you are in.
No investment choice should be made solely due to your tax consequeses. If you are paying tax that means you made a profit, if you made a loss just to save some tax then you are loosing money. The whole point of investing is to make money not lose it.