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Wouldn’t they just end up selling the stock to pay the loans, and pay taxes then? It seems more reasonable that they’re betting on the stock values increasing more than the loan interest rate

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The difference is "end up". They can (if appropriate, and if they can't cover it elsewhere) sell small amounts to cover the interest on the loan, rather than the large amount of the principal. At the end of the loan term the usual thing would be to roll it into another loan. The lender wants that stream of interest payments. The only time they care about the full amount is if they want (or need) to call in the loan, which, in the ideal situation from their perspective, never happens.

So the borrower should never need to sell enough of the stock to seriously affect the price, and the tax is only payable on a small number, not a big one.

If you can keep this up until you die, your heirs may benefit from what's called "step up in basis" on the shares. Thus a lot of capital gains tax is avoided.

Who says they ever have to pay the loan? Most banks are tripping over themselves to manage the banking needs of billionaires, an interest free loan, especially in this environment would be completely unsurprsing and they could roll that loan over forever.

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