--- title: "Leveraged ETF Decay Simulator" description: "Leveraged ETF decay simulator: model cumulative return vs the underlying index across volatility scenarios and see how daily reset compounding causes decay." canonical: https://www.getswoopr.com/etf-investing/leveraged-etf-decay-simulator/ source: "Swoopr Investment: https://www.getswoopr.com" --- ## Direct Answer > Leveraged ETF decay is the gap between a leveraged fund's actual multi-day return and the simple multiple of its underlying index's return, caused by daily rebalancing compounding gains and losses over time. Decay accelerates in choppy, volatile markets even when the index ends flat, which is why leveraged ETFs are built for short-term trades, not buy-and-hold positions. Enter a return path and leverage factor below to simulate how much decay erodes the fund's value over your chosen holding period. # Leveraged ETF Decay Simulator Set a leverage factor, daily volatility, and annual drift. The simulator runs a day-by-day compounding model showing the leveraged ETF's actual cumulative return alongside the index return and the "naive multiple", what the leveraged ETF would return if daily reset didn't create compounding effects. The gap between the naive multiple and the actual ETF return is volatility decay. ![Close-up shot of multiple US twenty dollar bills spread out, symbolizing wealth and finance.](https://www.getswoopr.com/images/hero/etf-investing-leveraged-etf-decay-simulator.webp) *Photo by [John Guccione www.advergroup.com](https://www.pexels.com/@john-guccione-www-advergroup-com-1874301/) via [Pexels](https://www.pexels.com/photo/bundle-of-money-on-a-table-15633962/)* ## Simulation Parameters Leverage factor 2x (e.g. SSO, SPUU) 3x (e.g. SPXL, TQQQ) -1x inverse -2x inverse -3x inverse Daily volatility (%) Annual drift (%) index expected return Simulation days 63 days (1 quarter) 126 days (6 months) 252 days (1 year) 504 days (2 years) 1,260 days (5 years) ETF expense ratio (%/yr) Run Simulation New random path Simulation Methodology Returns are simulated using normally distributed daily returns (Box-Muller transform) with the specified daily volatility and daily drift derived from the annual drift input (daily drift = annual drift / 252). The index grows by each simulated daily return; the leveraged ETF grows by L × that daily return minus the daily expense ratio (expense ratio / 252). The "naive multiple" is L × the index's cumulative return applied to a $1 starting value. The gap between naive and actual ETF is the accumulated volatility decay. Each run uses a new random seed. Results are illustrative, real volatility is not normally distributed and real-world paths vary significantly. ## What You're Seeing ### Three Lines on the Chart - **Index (green):** The underlying index cumulative return. Starts at $1.00 (or 100%). Each day it compounds by one simulated daily return drawn from a normal distribution with the specified mean and volatility. - **Leveraged ETF (yellow/acid):** The actual leveraged ETF, compounding at L× each daily index return minus the daily expense ratio. This is how the fund actually behaves. - **Naive multiple (dashed blue):** What the fund would return if it simply delivered L× the index's cumulative return, the return a naive investor might expect. This is a hypothetical line, not how any real product works. ### The Decay Gap The gap between the naive multiple and the actual ETF is the accumulated volatility decay. In smooth uptrends the lines stay close or the ETF may even beat the naive multiple. In choppy, volatile markets the gap widens rapidly. The metrics panel shows the total decay amount in percentage points and as an estimated annualized drag. ### What to Try - Set drift to 0% (flat market), watch decay accumulate regardless of trend direction - Raise daily vol to 2-3% (high-vol underlying), see how decay accelerates with the square of volatility - Switch to 3x leverage, decay increases dramatically relative to 2x - Switch to 1,260 days (5 years) to see long-run divergence with moderate volatility - Set a strong drift (e.g. 30%) with low vol (e.g. 0.7%), observe when the ETF can beat the naive multiple in a smooth bull market ## Methodology The simulator uses a **daily-reset compounding model**, the same real-world mechanism leveraged and inverse ETFs use. Each simulated day, the index moves by a randomly drawn daily return `r`. The index path compounds by `1 + r`; the leveraged ETF path compounds by `1 + L×r − daily expense ratio`, where L is your chosen leverage (positive or negative). A separate "naive multiple" path, `1 + L×(index cumulative return − 1)`, represents what a naive investor might expect L times the index return to look like if daily resetting didn't matter. Volatility decay is the gap between the actual ETF return and this naive multiple. ![3D illustration of stacked dollar bills and coins, symbolizing finance and wealth.](https://www.getswoopr.com/images/accent/etf-investing-leveraged-etf-decay-simulator-accent-1.webp) *Photo by [crazy motions](https://www.pexels.com/@crazy-motions-80195021/) via [Pexels](https://www.pexels.com/photo/3d-render-of-paper-bills-and-coins-12198529/)* Daily inputs are derived from your annualized entries: daily volatility = your entered daily volatility percentage directly; daily drift = annual drift ÷ 252; daily expense ratio = annual expense ratio ÷ 252 (252 trading days per year). Each day's random return is drawn from a normal distribution via a Box-Muller transform, driven by a deterministic seeded generator so results can be reproduced (e.g., by the WebMCP tool or unit tests) or, for the on-page "Run Simulation" button, by fresh randomness each run. The simulator also reports a theoretical annualized decay estimate, `L×(L−1)×σ²×252/2`, where σ is daily volatility, a closed-form approximation of the same effect shown by the simulated paths. ### Assumptions and limitations - **Daily returns are simulated as independent and normally distributed** with constant volatility. Real markets exhibit fat tails, volatility clustering, and autocorrelation that this model does not capture, actual decay can differ from the simulated path. - **Only the stated expense ratio is modeled as drag.** Real leveraged ETFs can incur additional costs from swap financing, borrowing, and rebalancing transaction costs that aren't represented here. - Leverage magnitude is restricted to 1×, 10× and the simulation horizon to 1-5,000 trading days; inputs outside those ranges are rejected. - This is an illustrative simulation of a statistical mechanism, not a forecast of any specific fund's future returns. ## Frequently Asked Questions ### What is volatility decay in a leveraged ETF? Volatility decay is the gap between what a leveraged ETF actually returns, compounding L times each daily index return minus its daily expense, and the naive multiple an investor might expect, L times the index's cumulative return. The gap grows with the square of the underlying's volatility, widens quickly in choppy markets, and can even run in the fund's favor in a smooth trend. ### Why does a 3x ETF decay more than a 2x ETF? Because the daily reset compounds the leverage factor into every daily move, the drag from volatility rises faster than the leverage itself: at the same underlying volatility, moving from 2x to 3x triples the theoretical decay, since the drag scales with L times (L minus 1), which is 2 for 2x and 6 for 3x. The simulator shows this directly when you switch the leverage input and hold volatility and drift fixed. ### How does the simulator turn annual inputs into daily ones? Daily drift is the annual drift divided by 252 trading days, the daily expense ratio is the annual expense ratio divided by 252, and daily volatility is the figure you enter directly. Each simulated day draws one return from a normal distribution with that mean and volatility, compounds the index by it, and compounds the ETF by the leverage multiple of it minus the daily expense. ## References - [SEC: Updated Investor Bulletin: Leveraged and Inverse ETFs](https://www.investor.gov/introduction-investing/general-resources/news-alerts/alerts-bulletins/investor-alerts/sec) - [FINRA: The Lowdown on Leveraged and Inverse Exchange-Traded Products](https://www.finra.org/investors/insights/lowdown-leveraged-and-inverse-exchange-traded-products) ## Related Reading - [ETF Investing & Fund Analysis](https://www.getswoopr.com/etf-investing/) the section this guide belongs to - [Bond ETF Mechanics](https://www.getswoopr.com/etf-investing/bond-etf-mechanics/) a companion guide in this cluster - [ETF Concentration Risk: How to Measure It](https://www.getswoopr.com/etf-investing/etf-concentration-risk/) a companion guide in this cluster - [ETF Cost Comparison Tool](https://www.getswoopr.com/etf-investing/etf-cost-comparison-tool/) a companion guide in this cluster - [ETF Due Diligence Framework](https://www.getswoopr.com/etf-investing/etf-due-diligence-framework/) a companion guide in this cluster - [ETF Overlap Analyzer: Weighted Overlap Across Two to Five Funds](https://www.getswoopr.com/etf-investing/etf-overlap-analyzer/) a companion guide in this cluster - [Expense Ratios and Total Cost of ETF Ownership](https://www.getswoopr.com/etf-investing/expense-ratios-and-total-cost-of-etf-ownership/) a companion guide in this cluster - [Factor and Smart-Beta ETFs](https://www.getswoopr.com/etf-investing/factor-and-smart-beta-etfs/) a companion guide in this cluster - [How ETFs Work: Creation, Redemption, and Arbitrage](https://www.getswoopr.com/etf-investing/how-etfs-work-creation-redemption-and-arbitrage/) a companion guide in this cluster - [How to Read an ETF Holdings File](https://www.getswoopr.com/etf-investing/how-to-read-an-etf-holdings-file/) a companion guide in this cluster