Worked research note
The leverage wrapper game
Three ways to target 2x SPY began from the same exposure idea and finished with different returns and drawdowns.
By ArthaPilot Research
Published 2026-10-11
Research question
Compare a 3x-fund blend, a 2x fund, and uniform financed leverage from 2018 through 2023.
Scope: This is one SPY-family path at one target multiple, not a cross-family or rolling-window study.
The common target concealed three different constructions
The worked case compares three 2x SPY implementations on the same dates and $10,000 principal. One dilutes a 3x daily-reset fund with Treasury bills. One uses a 2x daily-reset fund. The reference applies uniform financed leverage to the base exposure with a constant 40-basis-point spread.
These constructions can agree on target exposure while disagreeing on how exposure resets, how financing enters, and how the path compounds. The unleveraged 1x baseline stays in the result for scale but does not share the target and receives no structure-gap value.
Exhibit 01
Content-pinned result
One target, three realized returns
The recorded CAGRs for the matched 2x candidates over the fixed common window.
How did three recorded constructions for a 2x SPY target compound over the same window?
Construction. Solve each fund blend to reach 2x equity exposure at rebalance. Run every candidate over common dates with the declared 40-basis-point financed spread. Read annualized compound return from each candidate response.
| Category | CAGR |
|---|---|
| 3x fund + T-bills | 15.04% |
| 2x fund blend | 15.78% |
| Uniform financed | 17.94% |
Source and construction: Recorded ArthaPilot Wrapper Comparison fixture; SPY family; 2x target; 2018-01-02 through 2023-12-29; response hash 1e8acc0d493e… .
How this figure was calculated
Inputs
- A $10,000 principal, 2x SPY target, and 2018-01-02 through 2023-12-29 common window.
- The recorded 3x-plus-T-bill blend, 2x fund blend, and uniform financed reference.
Calculation
- Solve each fund blend to reach 2x equity exposure at rebalance.
- Run every candidate over common dates with the declared 40-basis-point financed spread.
- Read annualized compound return from each candidate response.
What this step cannot establish
The shared target does not make the wrappers mechanically identical. The chart describes one window before investor taxes.
Exact values behind the figure
| Series | 2x construction | CAGR (%) |
|---|---|---|
| CAGR | 3x fund + T-bills | 15.04% |
| CAGR | 2x fund blend | 15.78% |
| CAGR | Uniform financed | 17.94% |
The 2.90-percentage-point span between the 3x blend and financed reference is too large to hide behind a common '2x' label in this window.
It is also too aggregated to attribute to one cause. The response observes the joint outcome of the structures; it does not isolate expense ratio, financing, or volatility drag one at a time.
The structure gap names the difference without overexplaining it
ArthaPilot defines the structure gap as candidate CAGR minus the uniform financed candidate's CAGR. On that convention, the recorded 3x blend gap was -2.90 percentage points and the 2x fund gap was -2.16 percentage points.
The field is intentionally descriptive. A negative gap says that the candidate compounded at a lower annualized rate in this sample under the stated model; it does not say why, and it does not promise the same sign in another market path.
Exhibit 02
Content-pinned result
Observed gaps versus uniform financed leverage
The response's annualized return differences, reported in percentage points and kept separate from any cost attribution.
How far did each daily-reset construction finish from the uniform financed reference on an annualized basis?
Construction. Subtract the uniform financed CAGR from each daily-reset candidate CAGR. Keep the result in percentage points and retain the financed candidate at zero as the comparison anchor.
| Category | Gap versus uniform financed |
|---|---|
| 3x fund + T-bills | -2.9% |
| 2x fund blend | -2.16% |
| Uniform financed | 0% |
Source and construction: Same recorded ArthaPilot response; structure gap equals candidate CAGR minus 17.94% financed-reference CAGR.
How this figure was calculated
Inputs
- Candidate and financed-reference CAGRs from the same recorded response.
- The response definition of structure gap as candidate CAGR minus financed-reference CAGR.
Calculation
- Subtract the uniform financed CAGR from each daily-reset candidate CAGR.
- Keep the result in percentage points and retain the financed candidate at zero as the comparison anchor.
What this step cannot establish
Structure gap is an observed path difference. It does not decompose fees, financing, resetting, or rebalance effects.
Exact values behind the figure
| Series | Construction | Structure gap (percentage points) |
|---|---|---|
| Gap versus uniform financed | 3x fund + T-bills | -2.9% |
| Gap versus uniform financed | 2x fund blend | -2.16% |
| Gap versus uniform financed | Uniform financed | 0% |
The financed reference led both daily-reset candidates in CAGR over this period. That finding belongs to the exact SPY window and 40-basis-point spread that produced it.
Changing the underlying, target multiple, financing path, or window could change the magnitude or sign. Those cases are outside this note.
Every 2x path drew down far more than the 1x baseline
Maximum drawdown was 52.77% for the 3x blend, 59.34% for the 2x fund, and 58.80% for uniform financed leverage. The 1x SPY baseline lost 33.71% peak to trough.
The baseline is not an alternative way to achieve 2x exposure. Its purpose is to show the scale of loss amplification. Among the three matched candidates, the lower drawdown of the 3x blend in this episode does not establish a general protection property.
Exhibit 03
Content-pinned result
The drawdown ledger
Peak-to-trough losses for the three 2x constructions and the unleveraged scale reference.
How deep was the maximum drawdown for each recorded construction and the 1x scale reference?
Construction. Read each candidate's peak-to-trough maximum drawdown. Plot all four on one percentage scale without converting the baseline into a 2x candidate.
| Category | Maximum drawdown |
|---|---|
| 3x fund + T-bills | 52.77% |
| 2x fund blend | 59.34% |
| Uniform financed | 58.8% |
| 1x baseline | 33.71% |
Source and construction: Same recorded ArthaPilot response; common dates and $10,000 starting principal; results before investor taxes.
How this figure was calculated
Inputs
- Maximum drawdown from all four candidates in the committed response.
- Common start and end dates with the 1x baseline kept outside the matched-target ranking.
Calculation
- Read each candidate's peak-to-trough maximum drawdown.
- Plot all four on one percentage scale without converting the baseline into a 2x candidate.
What this step cannot establish
The lower drawdown of one candidate in this episode does not establish a general protection property.
Exact values behind the figure
| Series | Construction | Maximum drawdown (%) |
|---|---|---|
| Maximum drawdown | 3x fund + T-bills | 52.77% |
| Maximum drawdown | 2x fund blend | 59.34% |
| Maximum drawdown | Uniform financed | 58.8% |
| Maximum drawdown | 1x baseline | 33.71% |
The report's practical result is not a wrapper ranking. It is that target multiple, compounding path, and drawdown must be reviewed together; the exposure label alone did not describe the investor experience.
This worked note describes SPY over one fixed window. It does not generalize to QQQ, XLK, or rolling five-year windows.
Method and constraints
Method
The displayed 2x SPY wrapper results reconcile to one committed request and response fixture.
Verification: Preserve the fixture path, source commit, and request/response SHA-256 hashes with the note.
Verification: Recompute the two structure gaps directly from the displayed CAGRs, allowing for response rounding.
Verification: Keep the common dates, principal, spread, tax basis, and baseline exposure attached to every comparison.
Assumptions held fixed
- The worked case uses the SPY family, a 2x target, a $10,000 principal, and common dates from 2018-01-02 through 2023-12-29.
- The financed reference uses the model's composite reference rate plus a constant 40-basis-point spread.
- Structure gap is candidate CAGR minus financed-reference CAGR in percentage points; it is not a fee or financing decomposition.
- All recorded results are before investor taxes. The 1x baseline is a scale reference with a different exposure target.
What this study establishes
A leverage multiple is not a return contract. In the recorded 2x SPY case, the 3x-plus-T-bill blend, the 2x daily-reset fund, and the uniform financed reference produced CAGRs of 15.04%, 15.78%, and 17.94%. The shared exposure target did not erase the difference in wrapper mechanics.
The observed gaps of -2.90 and -2.16 percentage points versus uniform financed leverage are path results, not fee decompositions. They combine expenses, financing differences, daily resetting, and portfolio construction over one fixed 2018 to 2023 window. The same discipline applies to the drawdowns: the comparison shows what happened in this case, not which wrapper must dominate in the next one.
Limitations
- This is one SPY-family path at one target multiple, not a cross-family or rolling-window study.
- The financed candidate is idealized and omits margin calls, collateral rules, futures roll, changing spreads, and taxes.
- Modeled `.SIM` histories and daily-reset candidates depend on the platform's documented calibration and cost assumptions.
- The results do not recommend a leverage level or wrapper; leveraged exposures can produce rapid and substantial losses.
Sources and prior research
- Minder Cheng and Ananth Madhavan, The dynamics of leveraged and inverse exchange-traded funds (2009)
Primary research on daily rebalancing and path dependence in leveraged-fund returns over multi-day horizons.
- U.S. Securities and Exchange Commission, Office of Investor Education and Advocacy, Updated investor bulletin: leveraged and inverse ETFs (2023)
Authoritative description of daily objectives, multi-day compounding differences, costs, and risks.
- ArthaPilot, Leverage Wrapper Comparison (2026)
Calculation contract for candidate construction, common-date comparison, the financed reference, and the observed structure-gap field.
Evidence and reproducibility
leverage-wrapper-game-recorded-demo-fixture
A descriptive worked note comparing the recorded 3x blend, 2x fund, uniform financed reference, and 1x baseline for one 2x SPY case from 2018-01-02 through 2023-12-29.
Evidence date: 2026-08-17. Basis and units are stated in each recorded fact.
note=932143da4605de0016bf9d72947856de3919560b811617fd97fd9775bb02685f; request=b75bc320edca30ef870fec29bec227d473d1b5ed80fde479c3c887f2b482fc6c; response=1e8acc0d493ea92b9d0b6b295c1a9a03b1a1f15937f9cb5b225d37e28ea4c4db
Source: web/src/data/research/portfolio/fixtures/wrapper-comparison.record.json. Versions: fixture1=4a7f4f2c08bc894fabebdfe37b720a4eb8bda276.
- A result for QQQ, XLK, another leverage target, or another window
- A claim that one wrapper generally dominates
- A decomposition of the observed structure gap into fees, financing, and compounding
Inspect the same question with your own inputs
The linked tools expose the assumptions, dates, and result tables behind this report.
- Compare leverage wrappers Run the matched-exposure comparison for a selected family, multiple, window, principal, and financing spread.
- Inspect daily-reset behavior Study path dependence, volatility drag, and cost behavior for one leveraged fund.
- Model a financed position Make borrowing assumptions explicit before placing leverage inside a broader scenario.