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Suppose I have an individual brokerage account with a number of positions. As far as I found, the taxation takes place per position, i.e. I can be forced to pay tax even if the portfolio loses money.

Did I get that right and if yes, is there a way to pay the tax on the entire portfolio instead?

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    If the portfolio has realized losses, those would offset any realized gains. If the portfolio has unrealized losses, you always have the option of realizing those losses in order to offset any realized gains. Beyond that, I'm not sure what you'd be looking for. Are you trying to pay taxes on all the unrealized gains (or losses) every year? – Justin Cave Mar 2 at 16:38
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    Does your broker withhold taxes or are you assuming that brokers withhold taxes? – D Stanley Mar 2 at 16:48
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    To further Justin's comment - gains and losses across portfolios can offset each other - when you file, the main distinction is only between long- and short-term gains. – D Stanley Mar 2 at 16:50
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There is a logical error in your conclusion - although each position produces taxable income (or loss) by itself, the amounts are totaled up, and your tax is calculated from the totals (across all your accounts). So they are considered as a portfolio.

In more detail, there are slight asymmetries introduced by the IRS: there are two different flavors of gains/losses - short term and long term - and they get accumulated separately, and at the end taxed differently. Long term gains even out with short term losses, and remaining losses can only be deducted up to 3k$, the rest to be used next year.
Overall, that doesn't change the concept of 'portfolio' taxation, it just limits a bit how you can use losses.

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In a non sheltered account in the US, individual closing transactions result in realized gains or losses that are taxable events. As noted by D Stanley, the distinction between them is long and short term gains. However, there is a variation that might address your question.

Professional traders, including retail traders who meet the requirements (heavy consistent trading), can apply for Tax Trader Status. If approved by the IRS, you'll do Mark-to-Market accounting which means no long term capital gains or losses and purchases and sales won't have to be reported. Securities are considered sold on the last business day of the year even if they are not actually sold (market value is determined by the market price on the last trading day of the year and a gain or loss is recognized based upon that price). On January 1, the stock is deemed to have a new cost basis which is the price at which the position was deemed sold.

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