Leveraged ETF Analysis

• Synthetic leverage from any base ticker at any multiplier
• Empirical comparison with observed LETF data when available
• Cost decomposition: expense ratio, borrow spread, and rebalancing drag
• Growth-rate decomposition showing expected vs realized returns
• Volatility drag and compounding decay across holding periods

Use this tool when you want to understand how leverage changes long-run compounding for a base asset such as SPY, QQQ, or SPY.SIM. It is useful for questions like whether 2x or 3x leverage was historically favorable and how that compares with actual fund behavior.

The default run uses raw-price history, a 0.95% annual fee, no extra financing or spread drag, and a 0.5 Kelly fraction. Switch to total_return when you want dividend-reinvested history instead.

1. A top configuration panel with Base Ticker and a date range picker.
2. An Advanced Settings accordion for fee, min leverage, price mode, financing, spread cost, and Kelly fraction.
3. Results in a fixed order: summary metrics, theoretical charts, empirical comparison with a fund selector, rolling leverage, and a cost decomposition section that populates when comparison data is available.

1. Enter a Base Ticker. This is the return series used for the theoretical and simulated outputs.
2. Set the Date range. Use Maximize Dates to fill the full available range for the base ticker and selected Price Mode.
3. Open Advanced Settings if you want to change synthetic assumptions or allow negative leverage.
4. Run the analysis to populate the results.
5. In Empirical Comparison, optionally select a Comparison Fund. When the base ticker has known leveraged funds, the page seeds the first available match so the comparison-specific sections populate immediately. You can swap or clear that selection at any time.
6. Review the results from top to bottom. The page starts with summary metrics and moves toward more detailed empirical and decomposition views.

• Base Ticker: the asset whose return history drives the model.
• Synthetic Fund Fee: annual fee drag applied to the synthetic model. The default is 0.95%.
• Min Leverage: lower bound for the theoretical leverage grid.
• Price Mode: selects raw-price or total-return history. This can materially change both returns and the recommended leverage. The default is raw.
• Financing Model: selects the rate series used for borrowed notional. The default is Composite, which stitches broker-call money (pre-1928) → Fed Funds → SOFR. Alternatives are SOFR only, Fed Funds only, 3-month T-bill, a flat override, or a constant spread over the composite risk-free rate.
• Spread Model: how the swap/margin spread is applied. Flat bps uses a constant user value (default 40 bps), Rate-dependent scales the spread with the financing rate using a calibrated slope, and Fund calibrated uses the selected comparison fund's own calibrated spread base.
• Rate Floor: optional floor in percent applied to the financing-rate series. Use 0 to stress ZIRP/NIRP environments without negative carry.
• Flat Override / Constant Spread: shown only when the financing model requires a user-supplied rate. In Flat override mode this is the annual percent used for every day; in Constant spread over RF it is the percent added on top of the composite risk-free rate.
• Kelly Fraction: scales the model away from full Kelly sizing. Enter a value from 0 to 1. The default is 0.5.

The summary row shows five cards. The third card changes label based on the selected Kelly fraction, so you will see either Recommended k* or Optimal k*, not both at the same time.

• Ann. Return: annualized return of the base ticker over the selected period.
• Ann. Volatility: annualized volatility of the base ticker over the selected period.
• Recommended k* (Kelly-adjusted): the leverage recommendation after applying the selected Kelly fraction and synthetic cost assumptions.
• Uncapped k*: the full-Kelly optimum before the selected Kelly fraction is applied.
• k* boundary alert: appears when the selected date range and assumptions push the recommendation into the visible leverage floor or ceiling.
• Period: total span of history used in the run.

• Annualized Return vs Leverage: plots the modeled return curve across leverage multiples and marks the recommended k*.
• Volatility Drag Decomposition: separates the return-lift and volatility-drag terms behind compound growth.
• Growth Rate Contour Map: shows expected growth across return and volatility regimes.
• Simulated Historical Growth: replays the base series at evenly spaced leverage multiples between the selected minimum leverage and the inferred display maximum. These are synthetic paths.
• Path-Dependent Diagnostics: compares the realized daily-reset path with a true no-reset levered buy-and-hold reference so you can see when the realized sequence helped or hurt daily reset.
• Empirical Comparison: compares the base series, a synthetic daily-reset path, a levered buy-and-hold reference, and an optional selected live fund overlay.
• Rolling Optimal Leverage: trailing 5-year estimate of the recommended leverage through time. If the selected run is too short, the section stays visible with an explanatory placeholder instead of a blank chart.
• Cost Decomposition: always visible so you can see the expected chart and metrics, and populated when a mapped comparison fund has enough overlapping history.

The empirical comparison section helps separate the base asset's historical return profile from the observed behavior of actual products.

• Base: the unlevered base ticker path.
• Synthetic daily-reset: a simple leveraged replay of the base series using the tool's default comparison baseline. This remains on the chart even when a fund overlay is selected.
• Levered stretched-base reference: a simple linear stretch of the base cumulative path. It is not the financing-aware levered buy-and-hold series used in the decomposition section.
• Actual fund overlay: shown when the backend can map the selected comparison fund to overlapping live history for the chosen base series and date range.
• Comparison Fund selector: the dropdown shows only known leveraged funds on the same base ticker. The page selects the first match when available, and clearing the selector returns to the default synthetic comparison baseline.

The attribution section decomposes the total modeled drag of the primary leverage path into four stacked components: expense ratio, financing, spread, and volatility-decay residual. Each component is shown as an annualized metric card and as a cumulative percent-of-NAV series in the stacked-area chart. The four components together reconstruct the gap between the arithmetic leverage reference and the daily-reset path, making it easier to tell whether a given LETF's underperformance is dominated by costs or by path dependence.

• Expense ratio: constant annual fee drag from the synthetic fund fee input.
• Financing: (L − 1) × rate applied daily. Negative for inverse LETFs because short positions earn carry on cash collateral.
• Spread: the swap/margin spread applied to the financed notional. Driven by the selected spread model.
• Volatility decay: residual gap between the arithmetic stretched-base reference and the daily-reset path. A structural property of daily rebalancing; rises with L² × σ².

When comparison data is available, the tool runs a Bessembinder-style decomposition against frictionless daily-reset and levered buy-and-hold references. Before a fund is selected, the section stays visible with placeholder dashes so you can see the chart and metric layout in advance.

• Ann. Friction Drag: annualized gap between the actual fund and the frictionless daily-reset reference.
• Monthly Friction: average monthly drag from fees, spreads, and financing costs.
• Monthly Rebal. Effect: average monthly gap between levered buy-and-hold and the frictionless daily-reset reference. Positive values mean buy-and-hold outperformed daily reset over that window.
• Implied Carry Rate: annualized carry rate implied by the observed friction.
• Avg FFR / Excess over FFR: compare the implied carry rate with the average risk-free rate over the decomposition window.
• Friction Share / Rebal. Share: percentage of total underperformance attributed to operating friction versus daily reset.

The core intuition is that leverage scales both expected return and volatility. A common approximation for compound growth is:

g ≈ μ·L − ½·σ²·L²

Where μ is expected return, σ is volatility, and L is leverage. As leverage rises, the return term grows linearly while volatility drag grows roughly with the square of leverage. The live charts then layer on fund fee, financing, and spread assumptions in the net-realistic view.

• A high historical k* does not mean the same leverage will be optimal going forward. It only summarizes the selected sample and assumptions.
• Price Mode and date range can materially change the recommendation.
• The synthetic views are model outputs, not promises about how a listed fund will behave.
• A missing real-fund overlay usually means there is no known mapped fund for that base ticker, or there is not enough overlapping data.