Leveraged ETF Analysis

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 Rate / Spread Cost: cost assumptions used by the net-realistic curve. Financing is entered as an annual percent, spread is entered in annual basis points, and both default to 0 so the first run stays fee-only.
• 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.
• 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 is filtered from /api/ticker/letf-options to show only known leveraged funds on the same base ticker. The page seeds the first sorted match when available, and clearing the selector returns to the default synthetic comparison baseline.

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.