Leveraged ETF Analysis

When to use this tool#

Use this tool to see how leverage changed an asset's historical growth. You can also compare a modeled daily-reset path with an actual fund.

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.

Page walkthrough#

1. Enter a Base ticker. The model uses this return series for the theoretical and simulated outputs.
2. Set the dates. The Full history preset covers the available range of the base ticker and the return basis.
3. Change the fee, financing, spread, and Kelly tokens to change the synthetic assumptions. Minimum leverage holds the lower bound, which allows negative leverage.
4. Valid edits update results after a short pause. Select Run below the configuration to calculate immediately.
5. In Empirical comparison, select, change, or clear a Comparison fund. After a run on the page, the section loads the first mapped fund. A reopened or shared analysis loads no fund until you select one.
6. Read the statistics table, then the modeled and observed paths in the sections.

Key inputs#

• 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 for borrowed notional. The default Composite model uses broker-call money before 1928, then Fed Funds, then SOFR. Alternatives are SOFR only, Fed Funds only, 3-month T-bill, Flat override, and Constant spread over RF. SOFR-only analyses require a start date in or after April 2018. Use Composite for older history.
• Spread model: how the tool applies the swap/margin spread. Flat bps uses a constant user value in basis points, hundredths of a percent (default 40 bps, or 0.40% per year). Rate-dependent scales the spread with the financing rate using a calibrated slope. 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.

How to read the top metrics#

k* is the leverage multiple that maximized modeled compound growth over the selected history and costs. Above it, volatility drag outweighed added return. The Kelly fraction scales this historical estimate. A value of 0.5 uses half of k*. Future returns can differ.

Read the Kelly-adjusted or growth-maximizing leverage alongside the Kelly fraction used for the calculation.

• Ann. Return: annualized return of the base ticker over the selected period.
• Ann. Volatility: annualized volatility of the base ticker over the selected period.
• Kelly-adjusted leverage: the historical leverage estimate after applying the selected Kelly fraction and synthetic costs.
• Uncapped leverage: the full-Kelly optimum before the tool applies the selected Kelly fraction.
• Kelly k* boundary alert: appears when the historical estimate reaches the visible leverage floor or ceiling.
• Period: total span of history used in the run.

Result sections#

• Annualized return vs leverage: plots the modeled return curve across leverage multiples and marks 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 no-reset levered buy-and-hold reference. This shows 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.
• Slippage comparison: runs on its own Run. It lets you declare a real fund, underlying, leverage, fee, underlying expense backout, spread, and swap exposure. It returns the synthetic equation, real-vs-synthetic path, telltale ratio, and daily-return regression.
• 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.

Empirical comparison#

Compare the base asset and modeled paths with an actual fund when one has overlapping history.

• Base: the unlevered base ticker path.
• Synthetic daily-reset: a simple replay of the base series at the selected leverage, using the tool's default comparison baseline. This remains on the chart even when you select a fund overlay.
• 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 LETFs on the same base ticker. The page selects the first match when available, and clearing the selector returns to the default synthetic comparison baseline.

Slippage comparison#

Slippage comparison is for daily-reset LETFs. It compares an observed path with a synthetic expectation. The fund does not need an entry in ArthaPilot's LETF registry. Enter the fund ticker, underlying ticker, and daily leverage directly to test a newer product.

• Real vs synthetic: plots the observed fund against the modeled path under the selected fee, financing, spread, and swap-exposure assumptions.
• Telltale ratio: shows observed fund value divided by synthetic value. A persistent slope away from 100% indicates systematic tracking drift under the selected assumptions.
• Regression: fits fund daily returns against the underlying daily returns. The slope estimates realized leverage. The intercept estimates persistent daily drag.
• Swap exposure: controls spread-bearing notional. Financing still uses the collateral-netted L - 1 multiplier, while the spread applies to the declared swap notional.

Financing attribution#

The chart splits modeled drag into expense ratio, financing, spread, and a volatility-drag residual. Annualized cards and cumulative percent-of-NAV series show each part. Together they reconstruct the gap between the arithmetic leverage reference and the daily-reset path.

• 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 drag: residual gap between the arithmetic stretched-base reference and the daily-reset path. Daily rebalancing causes it, and it rises with L² × σ².

Cost decomposition metrics#

When comparison data exists, the tool splits fund underperformance into operating friction and the effect of daily resetting. It measures both against frictionless daily-reset and buy-and-hold references. Before fund selection, placeholders show the chart and metric layout.

• Annualized 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 rebalancing 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.
• Average Fed funds rate / excess over Fed funds rate: the average rate is the average effective federal funds rate over the decomposition window. The excess compares the implied carry rate with this average. The Fed funds rate is an overnight rate that represents risk-free financing.
• Friction share / rebal. Share: percentage of total underperformance attributed to operating friction versus daily reset.

Growth rate theory#

Leverage scales both expected return and volatility. A common approximation for compound growth is:

g ≈ μ·L − ½·σ²·L²

Where μ is the 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 net-realistic charts include fund fee, financing, and spread assumptions.

Interpretation notes#

• 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 modeled leverage estimate.
• The synthetic views are model outputs, not promises about how a listed fund will behave.
• A missing real-fund overlay means there is no known mapped fund for that base ticker, or there is not enough overlapping data.