A 2x fund whose index drops 10 percent and then rises 10 percent ends the two days down 4 percent while the index is down 1 percent — four times the index move, not twice it. The SEC's bulletin on these funds works that example out in dollars, and the condition that produces it is the daily reset: the multiple is promised for one trading day, not for the holding period.

The reset is the whole mechanism

Most leveraged and inverse funds reset every day, which means each morning the fund starts again from the previous close and applies its multiple to that day's index return. The SEC's bulletin, updated 29 August 2023, states that performance over weeks, months or years can differ significantly from the stated multiple and that the effect grows in volatile markets.

Daily compounding is ordinary arithmetic applied to a moving base. After a losing day the fund multiplies the next day's gain by a smaller number of dollars. The index does the same thing, but at 1x the two effects nearly cancel; at 2x or 3x they do not.

Worked example: $1,000 over two days

The two-day path here is the SEC bulletin's own hypothetical, run at both multiples.

Day 1: an index starts at $1,000 and falls 100 points to $900, a 10 percent loss. A 2x fund starting at $1,000 falls 20 percent to $800. A 3x fund falls 30 percent to $700.

Day 2: the index rises 10 percent, from $900 to $990. The 2x fund rises 20 percent, from $800 to $960. The 3x fund rises 30 percent, from $700 to $910.

Over the two days the index is down 1 percent, from $1,000 to $990. The 2x fund is down 4 percent, and the 3x fund is down 9 percent. Both funds hit their daily target on both days. The two-day results are four times and nine times the index's two-day loss, because 2 and 3 were applied to each day, not to the pair.

Four months, not two days

The bulletin also carries measured outcomes rather than arithmetic. Over one four-month stretch an index gained 2 percent while a 2x fund on it fell 6 percent and a 2x inverse fund fell 25 percent. Over the same period a 3x fund on a different index fell 53 percent while that index gained about 8 percent, and the 3x inverse fund on it fell 90 percent. A positive index and a fund down 53 percent is the same mechanism as the $1,000 example, run for 80-odd sessions instead of two.

What a named fund states

ProShares UltraPro QQQ (TQQQ) seeks daily results, before fees and expenses, that correspond to three times the daily performance of the Nasdaq-100 Index. The fund page dates its inception to 9 February 2010 and puts the gross expense ratio at 0.97 percent and the net expense ratio at 0.82 percent, the difference being a contractual fee waiver running through 30 September 2026. The same page states the objective in its own words: for any holding period other than a day, the return can be higher or lower than the daily target, smaller index moves and higher index volatility push the result below the target, and larger index moves with lower volatility push it above.

Both expense figures are annual, charged against the fund's assets rather than billed to the account, so they sit underneath every one of the daily results above.

That last sentence is the path condition stated by the issuer. The direction of the index over a month does not settle the fund's result for the month; the sequence of daily returns does, and the expense ratio runs alongside it. The related mechanics of borrowing to get a similar effect are in the guide on how leverage changes the size of a move, and the difference between a swinging path and a direction is the subject of the guide on a rising market that is still volatile.

The question the chart cannot answer

A price chart shows where the fund ended. It does not show how many up-and-down pairs produced that ending, and the pairs are what the reset converts into a gap. Two months with the same start and end point, one calm and one choppy, hand a 3x fund two different results. That is why the SEC's bulletin puts the figure of interest in the objective rather than in past performance, and why the bulletin's own four-month cases show an index and its geared funds moving in opposite directions.

The figure to read first on any such fund is its objective period. A prospectus states it in one line, and the guide on reading an ETF objective covers where that line sits.

Source references

Primary sources used for this guide. Follow the links for the original scope, definitions and conditions.