Setup: Stock XYZ trades at $100. You put $1,000 into the stock itself and $1,000 into a 2x daily leveraged fund tracking it. Twelve sessions of realistic chop for a volatile name — moves in the 3–8% range — ending with the stock back at exactly $100. Session 12’s +6.73% is whatever move it takes to land it precisely back at the start, because that’s the scenario you asked for: same point reached, what’s the damage.

The 2x fund does exactly what it promises every single day: double the daily percentage move. No tracking error, no fees, no funny business. Watch what happens anyway.

Final score: the stock holder has $1,000.00 — literally the same shares at the same price, zero gain, zero loss. The 2x holder has $965.64. Down $34.36, a −3.4% loss, on an underlying that went nowhere. Nobody stole it, no fee took it, and every single day the fund delivered exactly 2x. The money evaporated purely from the path.

Where it went: the fund rebalances at every close to keep exposure at twice its NAV. After day 1’s −5%, the fund is at $900 and must hold $1,800 of exposure — but it entered the day holding $2,000 worth, now worth $1,900, so it sells $100 of stock at the low. Day 2 the stock rips +4% and the fund has to buy back in at the higher price to re-lever. Sell low, buy high, twelve times in a row. Each individual rebalance costs pennies; compounded across a choppy path it’s your $34.36.

You can see the asymmetry building inside the table. Day 7, the stock’s worst point: it’s down 9.6% from the start, but the 2x is down 20.1% — a bit more than double, because the losses compound against you. Then the recovery leg: the stock needs +10.7% from its low to get home and gets it. The 2x needs +25% from its low to get home, gets +20.9%, and falls short. A leveraged fund digs its hole at 2x speed but has to climb out at compound-interest prices.

Now the part that makes this predictable instead of mystical. The realized daily volatility of that 12-day path is about 5.4%. The drag formula from before — L(L−1)/2 × σ² — says a 2x fund (coefficient = 1) bleeds roughly σ² per day: 0.054² ≈ 0.29% daily, times 12 sessions ≈ 3.5% predicted decay. Actual result: 3.44%. The formula nailed a random chop path to within a rounding error. That’s the point — this isn’t bad luck, it’s arithmetic. Hand me any stock’s volatility and I can tell you the approximate toll before the path even happens.

Scale it: this stock was running ~5.4% daily moves, which annualizes to ~85% vol — IREN-flavored territory, not crazy for the stuff you watch. At that vol, the 12-session toll of 3.4% compounds to roughly 50%+ per year of pure path decay if the name keeps chopping around the same levels. The underlying can finish the year exactly flat and the 2x wrapper is down by half, having honored its prospectus to the letter.

Two honest caveats. First, real funds are slightly worse than this table: add roughly a 1% annual expense ratio plus financing on the borrowed dollar-for-dollar sleeve at short-rates-plus-spread — call it another ~$3 over these 12 sessions, so closer to $963 in practice. Second, and this cuts the other way: the decay is a bet on path, not a guaranteed tax. If those same 12 sessions had been a clean trend — stock grinding from $100 to $114 with small pullbacks — the daily reset compounds for you and the 2x beats double the stock’s return. The wrapper punishes round trips and rewards escapes. Twelve sessions that end where they started is the exact scenario it’s built to lose, and most sideways markets are just that scenario on repeat.