The $46 billion gain over unlevered indexes makes a strong case for owning daily-reset leverage through a rising market. Murray and Sammon offer the strongest dollar evidence I have seen that broad equity-index leverage rewarded its investors. For a desk, though, the more useful result is the volatility screen showing where that leverage cannot pay. The authors acknowledge the market's contribution in their abstract, crediting "modest structural headwinds and rising markets".
Why the daily multiple slips away
Leveraged ETFs (LETFs) deliver a fixed multiple of a benchmark's daily return, usually by entering total return swaps with banks. Investors can get 2x or 3x exposure without opening a margin account. The fund resets its exposure daily. Hold it longer, and the multiple of the asset's return is reduced by volatility drag, expenses and a funding spread.
Murray and Sammon examine every U.S. daily-reset leveraged and inverse ETF and ETN from 2006 to September 2025. They ask four questions: whether investors made money, whether those dollars beat an unlevered investment, which products launched, and when investors traded. Broad-index investors made money. Single-stock products launched on volatile winners, while investors traded against recent returns without showing timing skill.
The mechanism is familiar. A 2x fund compounds twice the daily return, yet its cumulative log return trails twice the underlying's log return by roughly L(L-1)/2 times realized variance. This shortfall is volatility drag. It increases with the square of daily volatility. Investors also pay the expense ratio and financing on the additional exposure. Financing comprises the risk-free rate and a funding spread charged by the swap counterparty. To estimate that spread, the authors take the residual between the fund's actual return and an ideal return after fees and the risk-free rate.
Their daily data run from 2006 through September 2025 and cover U.S. leveraged and inverse ETFs and ETNs. CRSP, Bloomberg and prospectuses supply the hand-built universe. Weekly and monthly reset products are excluded, as are option-based products and funds that never reached $30 million in AUM. That leaves 193 long and 112 inverse products. The authors calculate investor PnL by summing prior-day AUM times each day's fund return. Dollars present in the fund determine the weight.
Long LETFs made $114.8 billion after receiving $22.8 billion in net flows. Inverse products received $93.4 billion and lost $80.3 billion. The authors caution that hedging demand and a rising market may explain those losses. Equity-index products made $117.8 billion despite net investor withdrawals of $17.3 billion. Single-stock LETFs began launching in 2022, with underlyings near the top of both the volatility and past-return distributions. Their funding spreads run from 6.8% to 9.8%, compared with 0.4% to 0.9% for index products.
What must a 2x fund earn to break even?
The paper's most useful table gives the annual underlying return required for a 2x fund to match an unlevered holding. At 1% daily volatility, the hurdle is 8.4%. It rises to 16.9% at 2% and 98.4% at 5%. For a 3x fund facing 5% daily volatility, the required return reaches 169.8%.
Read the note beneath the table. The text first presents these figures as drag calculations and later calls them "frictionless-market breakeven-return calculations". Yet the note assumes a 4.0% risk-free rate, a 1.0% expense ratio and a 0.5% swap spread. At low volatility, those assumptions do much of the work. They account for 5.5 points of the 8.4% hurdle at 1% volatility. Carry and fees therefore dominate the index-product hurdle; drag contributes relatively little. At 5%, drag takes over.
Estimated costs push single-stock funds further from breakeven. Across the 2x and 3x estimates, equity-index LETF funding spreads range from 0.4% to 0.9%, below 1% annually. The 2x single-stock estimate is 6.8% equal-weighted and 9.8% cap-weighted, with t of 9.16 and 9.37. That puts it an order of magnitude above the index spread.
For a 2x index fund, the authors put annual carry at about 5.39%: a 4.09% risk-free rate, a 0.4% spread and a 0.90% fee. The corresponding 2x single-stock total is 11.92% (4.09% plus 6.8% plus 1.03%). Borrowing at the risk-free rate accounts for most of the index fund's carry.
The table note also describes the estimation sample's exclusions. Funds with daily tracking error above 50bp are dropped, along with the top 2% of deviations. Because the trim uses absolute deviations, it removes misses in either direction. If large misses are mainly shortfalls, as a cost would imply, the 6.8% estimate understates the spread. The 50bp screen separately excludes the funds with the noisiest tracking.
Volatility compounds the difference. Single-stock underlyings had AUM-weighted daily volatility of 3.71% in 2025, versus 1.35% for index underlyings. The authors translate those figures into annual 2x drag of -29.31% and -4.52%, respectively. For indexes, the abstract's "modest structural headwinds" consist of a 0.4% to 0.5% funding spread on 2x products and the -4.52% drag. I agree that these are modest. A single-stock fund's 2025 drag is more than six times as large, and its funding spread more than ten times as large.
Below 2% daily volatility, leverage won
For the matched comparison, the authors put identical inflows into the unlevered asset on identical dates. Across 47 equity-index LETFs, investors earned $107.6 billion, compared with $61.1 billion in that counterfactual. Single-stock LETFs earned $13.1 billion, versus $11.7 billion unlevered.
The volatility buckets combine all 109 matched long LETFs, including commodity and VIX products. Below 2% daily volatility, the LETFs beat the counterfactual. Above it, they trail:
- below 1.5% daily: $78.9B versus $39.9B
- 1.5% to 2%: $30.1B versus $17.6B
- 2% to 3%: -$3.8B versus $3.2B
- above 3%: $6.4B versus $8.3B
Fund counts tell the same story. In the lowest bucket, 70.4% of 27 LETFs with three or more years of history beat their underlying. None of 14 did so in the 2% to 3% bucket, and none of 3 above 3%. Three funds offer little to lean on. Lower the history requirement to at least 1.5 years, and 3 of 9 beat their underlying in the above-3% bucket, alongside 2 of 16 in the 2% to 3% bucket.
The matching treats subscriptions and redemptions differently. Inflows are matched dollar for dollar. Redemptions are measured as a percentage of the LETF's assets, then applied pro rata to the counterfactual. The authors say this keeps the comparison well defined after the accounts have earned different returns.
The $46.5 billion excess compares a 2x position with a 1x position through a rising market, without risk adjustment. It expresses the abstract's "rising markets" clause in dollars. Over 2006 to 2025, a 2x position in a U.S. index was supposed to earn more dollars than a 1x position.
Launching winners, buying dips
The median single-stock underlying ranks at the 93.8th percentile for volatility across 43 launches. For each launch, the authors compare the stock with the top 1,000 stocks by market capitalization, using only information available beforehand. The median past six-month return ranks at the 91.7th percentile across 40 launches. Only launches that passed the AUM threshold enter this sample, as the authors acknowledge. A one-point increase in underlying daily volatility is associated with roughly 68% more average AUM (t = 4.02, N = 68). The samples are small.
Investors buy after declines. Long LETF flows have a coefficient of -4.02 on the lagged one-day return (t = -14.88), against +2.23 for unlevered ETF flows. Future returns carry no reliably positive coefficient. During 2012 to 2020, the future 21-day coefficient is -0.14 (t = -2.72). The future 126-day coefficient over that period is +0.05 (t = 3.28), but it is -0.07 (t = -2.47) over the full sample. With signs changing across horizons, the paper interprets the evidence as no market-timing skill. Two significant coefficients across the full sample and subperiod are negative.
The return decomposition makes the cost visible. The selection effect measures the capital-weighted average fund return less the equal-weighted average. Within each fund, the timing effect subtracts the time-weighted return from the return weighted by investor capital. For equity-index LETFs, the resulting investor return is 7.8%: a 4.0% raw fund return plus a 12.6% selection effect and a -8.8% timing effect. The authors describe that timing cost as small.
It exceeds twice the raw return.
Among single-stock funds, 13 in this calculation, a +43.1% selection effect is more than erased by -48.3% from timing. Investors consequently earned 41.3%, compared with a 46.5% raw fund return. Unlevered broad equity ETFs had a +1.9% timing effect.
Our SSO and QLD backtest, 2020 to 2024
We could not trade the object the paper measures: investor dollars spread across hundreds of products. Our adaptation used only two broad-equity pairs, SSO against SPY and QLD against QQQ. We made no attempt to trade the swaps held by these funds. The result says nothing about single stocks.
We devised the rule ourselves, taking inspiration from the breakeven logic. Each day it calculates trailing 126-session log growth for each pair's underlying. It then subtracts annualized variance and the realized difference between an ideal 2x return and the fund's actual log return. A positive result triggers a holding in the 2x fund. The run covers January 2020 to July 2024, including the 2020 crash and the 2022 drawdown. We charged $0.004 a share in commissions, subject to a $1 minimum. Fills occur at the closing auction. There is no slippage term, and neither market impact nor taxes are modeled.
Our portfolio choices affect the result more than the signal. Each ETF is capped at 25% of capital, leaving at least 50% in cash earning zero interest. A negative signal leaves that pair's slot empty. Gross exposure to the underlyings therefore ranges from 0x to about 1x, below a fully invested unlevered index. We also size positions using starting capital rather than current equity, allowing exposure to drift as the account grows.
From January 2020 to July 2024, the book returned 64.48% in total, with a Sharpe ratio of 0.84 and a Sortino of 1.06. Maximum drawdown reached -27.82%. Annualized volatility was 17.10%, and the Calmar was 0.42. Losing -27.82% in a book capped at roughly 1x gross is considerable pain for a 0.84 Sharpe. This automated backtest describes our implementation alone. It says nothing about the paper's claim.
The paper supplies no trading-strategy Sharpe. It reports fund-level and investor-level returns, including a 4.0% equal-weighted annualized raw return for equity-index LETFs. Those figures cover 2006 to 2025 and a different universe. It also gives aggregate investor PnL and counts of outperforming funds, such as 70.4% of 27 low-volatility funds, alongside the annualized returns. Our capped two-pair book covers 2020 to 2024. These are different measurements of different investments.
Put the $46 billion through a subperiod split
The case rests on $107.6 billion against $61.1 billion, with the appendix's 70.4% fund count serving as a cross-check. The paper gives full-period totals; Figure 5 traces the excess through time. A table splitting the counterfactual into subperiods, with 2008 and 2022 shown separately, would turn the dollar finding into an allocation result. Until then, the breakeven table is a useful filter for deciding which products to hold. The $46 billion remains what a 2x position earned in this particular market.
Our backtest stops at 2024-07-01, and everything after that date is deliberately left untouched so the same strategy can be checked out of sample later.