Sequence-of-returns stress test
The tidy answer — the two strategies tie at the loan rate — assumes returns arrive as one smooth line. They don't. Start with the steady case, then switch to drawing your own bumpy sequence to see what a real market does to a borrowed position.
The verdict
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Two thresholds split every possible return into three zones. Your assumption is the marker.
01
Return needed just to break even with the cost of borrowing
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Below this, the borrowed money earns less than its interest.
02
End value if you don't borrow and invest the payment instead
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Versus borrow-and-invest.
03
Return at which the two strategies are exactly equal
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Precisely the loan rate. Above it, borrow; below it, don't.
Both lines assume identical monthly cash out of pocket. They cross exactly at the loan rate.
Both strategies model the same out-of-pocket monthly amount and the same annual return compounded monthly. Strategy A invests the borrowed lump sum on day one and repays it through the loan; Strategy B invests that monthly payment as an ordinary annuity. In Draw-your-own mode the return you draw for each year is applied over that year. This is an educational model, not investment advice — it ignores taxes, fees, margin calls, and the fact that real returns aren't constant.