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.
Published Oct 11, 2026
At a glance
Three ways to target 2x SPY returned 15.04%, 15.78%, and 17.94% annually over 2018–2023: a 3x-fund-and-T-bill blend, a 2x daily-reset fund, and uniform financed leverage.
The common exposure target produced different historical returns and drawdowns. The observed gaps combine the modeled structures; they do not isolate fees or establish which wrapper will lead in another period.
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
One target, three realized returns
The recorded CAGRs for the matched 2x candidates over the fixed common window.
The shared target does not make the wrappers mechanically identical. The chart describes one window before investor taxes.
| Category | CAGR |
|---|---|
| 3x fund + T-bills | 15.04% |
| 2x fund blend | 15.78% |
| Uniform financed | 17.94% |
Source and construction: Archived ArthaPilot Wrapper Comparison calculation; 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.
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
Observed gaps versus uniform financed leverage
The response's annualized return differences, reported in percentage points and kept separate from any cost attribution.
Structure gap is an observed path difference. It does not decompose fees, financing, resetting, or rebalance effects.
| 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.
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
The drawdown ledger
Peak-to-trough losses for the three 2x constructions and the unleveraged scale reference.
The lower drawdown of one candidate in this episode does not establish a general protection property.
| 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 archived result.
- 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.
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 archived request and result.
The note supports no cross-family, cross-window, general-dominance, after-tax, or fee-decomposition claim.
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.
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
- 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.