Twice the daily return is a specific target
An ETF is a fund whose shares trade on an exchange. Your share gives you a stake in the investments and contracts inside it. A leveraged ETF aims to magnify a specified investment's movements. The daily +2x fund here targets twice its index's percentage gain or loss over one specified day, in the same direction.
The word daily matters. It describes which return gets doubled. The fund defines the start and end of that day; our example uses one trading close to the next. Buying at 11 a.m. does not start a separate 24-hour target for you. Some products use a different target period, so read the prospectus, the document describing the fund's investments and risks, for the actual interval.
Assume the fund meets its daily +2x target exactly. There are no fees, financing costs, taxes, tracking differences, distributions or currency effects. Financing costs are the costs of funding the investment scale. Distributions are cash paid out to investors. Setting these aside lets us see what the daily calculation does on its own.
For the fund, we follow net asset value, or NAV: the value based on what it owns minus what it owes. Assume its traded market price equals NAV. The index and NAV each start at 100 as comparison scales, not actual share prices or dollar amounts. The large daily changes are invented to make the arithmetic visible; they are not forecasts.
Up 25%, then down 20%: the index gets back to 100
Start the index at 100. A 25% gain adds 25, taking it to 125. The next day's 20% loss applies to 125, removing 25 and returning it to 100. Doubling each day's percentage for the ETF means a 50% gain followed by a 40% loss. Now follow its value separately.
Scroll wide tables sideways. Keyboard: focus the table, then use the arrow keys.
| Point in time | Index daily return | Index value | ETF daily return | ETF NAV |
|---|---|---|---|---|
| Start | — | 100 | — | 100 |
| End of day 1 | +25% | 125 | +50% | 150 |
| End of day 2 | −20% | 100 | −40% | 90 |
| Total over both days | 0% | −10% | ||
The ETF's first day adds 50: 100 × 50%. It finishes at 150. On day two, losing 40% of 150 removes 60. It ends at 90, a 10% loss from its original 100. Subtracting 40 from the original 100 would use the wrong starting amount for the second day.
In one line, the index is 100 × 1.25 × 0.80 = 100. The ETF is 100 × 1.50 × 0.60 = 90. Doubling the two daily percentages has not doubled the combined return.
Both daily targets were met: +50% against +25%, then −40% against −20%. The two-day loss does not by itself show a missed target or a hidden charge. A fund designed to double each day has done exactly that.
If the index had stayed at 100 throughout both days, the ETF would also have stayed at 100 under these cost-free assumptions. Starting and ending at the same level after a rise and fall is a different path from never moving.
A daily reset does not erase yesterday's loss
After each day, the fund adjusts its investment scale to the value it now has. That scale is its exposure: how much a market movement affects the fund. This daily reset prepares it to target twice the next day's return. It does not put back money that was lost. After our two-day example, the next calculation starts from 90.
To get from 90 back to 100, the fund needs 10 ÷ 90, or approximately 11.11%. A 10% gain would add only 9 and leave it at 99. The loss percentage used the original 100; the recovery percentage uses the smaller 90.
This tells us the gain needed in the fund, rather than the index's required gain over some unspecified future period. To calculate that, we would need the future daily index changes. Its final level alone would leave out what happened along the way, just as the first table's equal starting and ending index values leave out its rise to 125.
Compounding does not always reduce the return
Change the example to two consecutive gains of 10%. Keep the same idealised assumptions. Each day the ETF now gains 20%. Applying each new percentage to a value already changed by earlier gains or losses is called compounding.
| Point in time | Index value | ETF NAV |
|---|---|---|
| Start | 100 | 100 |
| End of day 1 | 110 | 120 |
| End of day 2 | 121 | 144 |
| Total return | +21% | +44% |
The index gains 21%, while the ETF gains 44%. Twice 21% is 42%, so the ETF's return is 2 percentage points higher than twice the index's two-day return. The second 20% gain applies to 120 and adds 24, rather than the 20 added on day one.
Suppose instead that the index stayed flat on day one and rose 21% on day two. It would still finish at 121, but the ETF would stay at 100 and then gain 42%, ending at 142. The index's total return is identical; the individual daily returns are different.
This is why “a leveraged ETF always loses value with time” is too broad. Our two examples use the same daily multiplier and produce different relationships to the index's overall return. The rising example does not predict a profitable holding period. The ETF's return depends on the individual daily moves, not just the index's final level.
What changes when you buy an actual fund?
Real funds have operating expenses. They may use derivatives, contracts whose values depend on another asset or index, to create the magnified investment effect. Funding those arrangements can cost money, and the fund may not achieve its daily target exactly. Those effects come in addition to applying each day's return to the previous day's value.
The price you actually pay or receive can differ from NAV too. Your trade time, the gap between the prices offered by buyers and sellers—the bid–ask spread—and any currency conversion affect your own result.
An inverse fund targets the other direction. A daily −1x objective aims for the opposite of each day's index return. It does not promise the opposite of the index's combined return over your whole holding period. That needs a separate daily calculation as well.
In the prospectus, find the full benchmark name, target multiple and direction, measurement period and costs. Then match those terms to your own dates and prices. Holding for one day still carries a risk of loss. A “2x” label alone does not tell you what you will earn.
About the examples
The tables and additional examples are fictional. Starting values of 100 are comparison scales, not prices. The model delivers an exact daily +2x NAV return, equates market price with NAV and excludes fees, financing costs, tax, distributions and currency effects. The price paths are not forecasts. Editorial policy.