Question on Hedge Fund Investors' taxation

I have a question about how investors in hedge funds get taxed on their short-term capital gains. With mutual funds, I understand that short-term gains are returned in distributions for tax purposes, making them effectively the same as normal income. I'm also operating under the assumption that an investor cannot bypass short-term capital gains tax by not withdrawing their money from the firm for a period greater than one year, while the manager makes short-term investments.

Assume hedge fund WSO Capital is a $2 billion fund that only holds investments for a few weeks or months at a time. A wealthy client gives the firm $20 million to invest. The firm invests the money in company ABC. 3 months later, the investment has returned 10% and the manager decides to liquidate the investment, for a capital gain of $2 million. Assume a short-term marginal tax rate of 40% for the sake of simplicity. At this point, the investor has the opportunity to withdraw their investment (minus the firm's take) or to leave it with the firm. The investor chooses to stay with the firm.

My understanding is that capital gains tax must be paid any time an investment is sold for a profit. So my question is, when exactly must this tax be paid? Can this tax be deferred until the investor withdraws their money from the fund? The way I see it, there are three possibilities for when the tax must be paid: When the investment is sold, at the end of the tax year, or when the investor withdraws their money from the fund. If the pattern I described above is repeated many times, there starts to appear a divergence in the rate of return if the tax is paid immediately (or set aside in an account for payment later), versus if it is deferred until the investor withdraws their money from the fund. The latter scenario allows the portion of the return which would have been paid in taxes to generate additional return for the investor.

The question is: When the fund manager is about to reinvest the capital in company XYZ, will the second investment be for $22M with 0.8M in tax deferred, or for a straight $21.2M.

To illustrate the difference between the two scenarios, and why I'm asking this question, these are the results if the pattern is repeated for a period of two years:

Tax paid immediately: $20M * (1.06 ^ [4*2]) = $31.87M - $20M = $11.87M ROI.

Tax deferred: $20M * (1.1 ^ [4*2]) = $42.87M - $20M = $22.87M * 0.6 = $13.72M ROI.

These results do not factor in the firm's 20% share of profits, for simplicity.

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