Leveraged ETF decay — why 2x does not double your return

The tool models daily returns over a trading year of roughly two hundred and fifty-two sessions, running an unleveraged path and a daily-reset leveraged one side by side from the same random draws. Alongside the simulation it shows the closed-form approximation: the expected leveraged return is the multiple times the drift, minus the multiple times one less than the multiple, halved, times the variance. That second term is the decay, and it depends on volatility squared — which is why it is invisible in a calm market and brutal in a choppy one.

Daily returns are drawn independently, which removes the trending and mean-reverting behaviour real markets show — trends flatter leveraged products and choppiness punishes them, so a single assumption cannot capture both. The model charges no borrowing cost, no management fee and no spread, and real leveraged products carry all three on top of the decay shown here, so this is a floor on the gap rather than an estimate of it. The daily reset itself is assumed perfect. Nothing here is a recommendation to hold these instruments.

Why does the decay happen even when the market goes up?

Because it comes from variance rather than from direction. Compounding a multiplied daily return is not the same operation as multiplying a compounded one, and the gap between them depends on how much the daily returns vary, not on which way they end up pointing. A market that rises steadily produces very little decay; one that rises to the same place in a series of large swings produces a great deal of it.

Is this the same thing as the product's fee?

No, and conflating them understates the cost badly. The decay is structural and would exist in a product that charged nothing at all. On top of it, real leveraged ETFs charge a management fee and pay financing costs on the borrowed exposure, both of which are deducted before you see a return. This page models only the structural part, so treat its output as the best case.

Are these products usable for a long-term holding?

They are built for a daily objective and the arithmetic above is what happens when they are held beyond it. The longer the holding period and the choppier the market, the further the result drifts from the multiple a buyer expected. Whether that is acceptable is a question about your own assumptions, but it should be a decision taken with the decay term in view rather than discovered afterwards.

• Monte Carlo simulation — the range of outcomes, not a single line
• Loss tolerance — what each allocation lost in three real crashes
• TER impact calculator: what an ongoing charge costs over time