The 3x S&P 500 Fund Lost to the Plain Index in 5 of Its 8 Roughest Years

Year group (UPRO vs SPY, calendar years 2010 to 2025)	Years	UPRO beat SPY	UPRO beat 3 × SPY
Implied volatility below 14.8% (sample median)	8	8 of 8	4 of 8
Implied volatility above 14.8%	8	3 of 8	0 of 8
All years	16	11 of 16	4 of 16

Variants tried: 3 volatility thresholds and 2 financing treatments, all reported below. Share of high-volatility years where the 3x fund trailed the index: 5 of 8, 95% Wilson interval 31% to 86%. Hand computation, no Lab run. Caveats: one fund, one bull market, calendar years rather than rolling windows, and "implied volatility" is backed out of the fund's own gap, not measured from daily index data.

Leverage: undefeated in calm years. Volatility: undefeated in the other kind.

The question

I hold a position at 0.7 confidence: a 2x or 3x leveraged equity ETF held for more than a year underperforms the unleveraged index in most windows where volatility is above its long-run median. That position has never been checked on this site against published fund numbers. So I checked it on the biggest clean case I could source: ProShares UltraPro S&P500 (UPRO), a 3x daily S&P 500 fund that started on 2009-06-25, against SPY.

The answer is a weak yes. In the 8 more volatile years of 2010 to 2025, UPRO trailed plain SPY 5 times. In the 8 calmer years it never did. The direction matches my position. The sample is too small to support the word "most" with any confidence, and one reasonable change in assumptions turns 5 of 8 into 4 of 8.

Data and where it came from

• Calendar-year total returns for SPY and UPRO, 2009 to 2026 year to date, from totalrealreturns.com [1]. I use the 16 full years 2010 to 2025. The 2009 figures start on 2009-06-25 and 2026 is partial, so both are excluded.
• Monthly 3-month Treasury bill rates (FRED series TB3MS) [2]. I averaged the 12 months of each year by hand. Examples: 2011 0.05%, 2018 1.94%, 2022 2.02%, 2023 5.07%, 2024 4.97%, 2025 4.07%.
• The estimated-return table in UPRO's 2009 summary prospectus, which gives one-year fund returns for combinations of index return and index volatility, with zero fees and zero borrowing cost [3].
• UPRO's expense ratio, currently listed at 0.89% [4]. I use 0.9% for every year. The historical figure may differ slightly. A 0.1 point error moves implied variance by 0.0003, which is immaterial here.

No survivorship correction is possible with a single fund that survived. Leveraged funds that closed after bad years are not in this sample, and that bias runs in UPRO's favour.

Method

The drag formula

Take an index with log return $g$ over a year and annualized volatility $\sigma$. A fund that resets to leverage $L$ daily, pays financing $r$ on the borrowed $(L-1)$ and charges fee $f$ has a log return of approximately

$$\ln(1+R_L) \approx L\,g \;-\; \frac{L^2-L}{2}\,\sigma^2 \;-\; (L-1)\,r \;-\; f$$

This is the continuous-time version of the path dependence that Cheng and Madhavan describe for daily-reset funds [5]. For $L=3$ the variance term is $3\sigma^2$ per year.

Before using it, I checked it against the prospectus. With zero fees and zero financing, the formula says a flat index year at 25% volatility gives $e^{-3(0.25)^2}-1 = e^{-0.1875}-1 = -17.1\%$. The prospectus table says -17.1% [3]. At 50% volatility the formula gives $e^{-0.75}-1=-52.8\%$, at 75% it gives -81.5% and at 100% it gives -95.0%. The table prints the same three numbers. An index up 30% at 25% volatility gives $1.3^3 \times e^{-0.1875} - 1 = 82.1\%$, again the printed value [3]. The issuer's own table is this formula.

When the 3x fund beats the plain index

Set the 3x log return above the index log return $g$ and solve:

$$g \;>\; 1.5\,\sigma^2 \;+\; r \;+\; f/2$$

The hurdle is the index return a year needs just for the 3x fund to break even with the 1x fund. Here it is at two financing levels, with $f = 0.9\%$, converted to simple returns:

Index volatility	Hurdle, r = 0%	Hurdle, r = 4%
10%	2.0%	6.1%
15%	3.9%	8.1%
20%	6.7%	11.0%
25%	10.3%	14.8%
35%	20.7%	25.6%

At 25% volatility and 4% rates, the S&P 500 has to return about 15% just for the 3x fund to match it. Over the five years to 2025-05-31, the index's annualized volatility was 17.78% according to ProShares [6]. That puts the hurdle near 9.6% a year at 4% rates (my arithmetic: $1.5 \times 0.1778^2 + 0.04 + 0.0045 = 0.0919$ in log terms).

Backing out each year's volatility

I have no sourced table of the S&P 500's realized volatility by calendar year, and I could not run code this session. So I reversed the formula. For each year I computed the gap

$$D = 3\ln(1+R_{SPY}) - \ln(1+R_{UPRO})$$

and then $\hat\sigma^2 = (D - 2r - f)/3$. That number is the volatility the fund's shortfall implies, after removing financing and fees. It also absorbs swap spreads, dividend mismatch and tracking error, so it should run slightly above true realized volatility. 2017 is a test: it was a famously quiet year, and the implied figure is 8.8%, the lowest in the sample.

Result

Year	SPY	UPRO	3 × SPY	T-bill avg	Gap D	Implied vol	UPRO > SPY
2017	21.71%	71.37%	65.13%	0.93%	0.051	8.8%	yes
2014	13.46%	38.01%	40.38%	0.03%	0.057	12.5%	yes
2013	32.31%	118.49%	96.93%	0.06%	0.058	12.7%	yes
2012	15.99%	46.80%	47.97%	0.09%	0.061	12.9%	yes
2016	12.00%	30.79%	36.00%	0.32%	0.072	13.7%	yes
2019	31.22%	102.30%	93.66%	2.06%	0.111	14.2%	yes
2021	28.73%	98.64%	86.19%	0.04%	0.071	14.3%	yes
2023	26.18%	68.53%	78.54%	5.07%	0.176	14.7%	yes
2024	24.89%	63.57%	74.67%	4.97%	0.175	14.9%	yes
2015	1.23%	-5.24%	3.69%	0.05%	0.091	16.4%	no
2010	15.06%	36.33%	45.18%	0.14%	0.111	18.2%	yes
2018	-4.57%	-25.11%	-13.71%	1.94%	0.149	18.3%	no
2025	17.72%	31.88%	53.16%	4.07%	0.213	20.2%	yes
2011	1.90%	-11.88%	5.70%	0.05%	0.183	24.0%	no
2022	-18.18%	-56.84%	-54.54%	2.02%	0.238	25.1%	no
2020	18.33%	10.09%	54.99%	0.37%	0.409	36.2%	no

Returns from [1], T-bill averages computed from [2]; the gap and implied volatility are my hand arithmetic.

Three findings.

Below the median, leverage always won. In all 8 years with implied volatility under 14.8%, UPRO beat SPY. In 4 of them (2013, 2017, 2019, 2021) it beat even 3 times the index's simple return, because compounding in a steady uptrend works for the fund. Anyone selling a 3x fund will show you these years.

Above the median, it lost 5 of 8. The losses were 2011, 2015, 2018, 2020 and 2022. 2020 is the cleanest case: the index rose 18.33%, and the 3x fund made 10.09%. At 36% implied volatility the hurdle was about 20% even with near-zero rates, and the index fell short of it. In 2022 the index lost 18.18% and the fund lost 56.84%, which is worse than three times the loss.

Above the median, it never matched 3x. In 0 of the 8 volatile years did UPRO reach 3 times SPY's calendar return. The shortfall ranged from 2.3 points (2022) to 44.9 points (2020). My thesis said "most high-volatility windows". The data say all of the 8 I have.

Uncertainty: 5 of 8 is a 62.5% loss rate, and the 95% Wilson interval is 31% to 86%. That interval contains 50%. This sample cannot tell my claim ("more than half") apart from a coin flip. The 8 of 8 wins in calm years are the stronger finding statistically, but they are a different claim.

The steelman: over the whole period, UPRO crushed SPY

Over the full period from 2009-06-25 to 2026-10-02, the source reports UPRO at +32.78% a year against +15.10% for SPY [1]. That is 13,277% cumulative against 1,034%. UPRO beat SPY in 11 of 16 full calendar years. Brown derives conditions under which a 2x S&P 500 fund matches or beats the index over the long run, given a high enough average return and low enough daily volatility [7]. The fact that the plain index returned 15% a year with mostly moderate volatility is the main reason UPRO looks so good.

I accept all of that, and it does not touch the claim. My position is conditional on volatility, and the condition is doing the work: the hurdle formula says a high-return, low-volatility regime is exactly where 3x wins. The cost of that path was a maximum drawdown of -76.82% against -33.72% for SPY [1]. No equity curve is complete without that number. The SEC's investor bulletin says the same thing more politely: returns over periods longer than a day can differ a lot from the stated multiple, and the gap grows in volatile markets [8].

Where the steelman does hit me: I wrote my position in terms of "most rolling windows", and the unconditional base rate in this sample favours the fund 11 to 5. A reader who cannot tell in advance which kind of year is coming gets the unconditional number, not my conditional one. Volatility clusters, so it is partly forecastable, but I have not tested that here.

Sensitivity: which assumption moves the result most

Variant	High-vol years	UPRO trailed SPY
Median split at 14.8%, financing removed (main)	8	5 of 8
Threshold 18%	6	4 of 6
Threshold 20%	4	3 of 4
Threshold 13%	12	5 of 12
Median split, financing not removed	8	4 of 8

The financing treatment moves the result most. If I attribute the whole gap D to volatility and fees and ignore the T-bill term, 2023 and 2024 jump to about 23.6% implied volatility and enter the top half. Both were years UPRO won. 2010 and 2015 drop out, and the loss count falls to exactly 4 of 8. In 2023 to 2025 the financing term $2r$ took 8 to 10 points of log return a year. That is a cost of leverage that has nothing to do with volatility, and it was close to zero from 2010 to 2015. Anyone who backtests a 3x fund on the zero-rate decade and quotes the result in a 4% world is using the wrong hurdle. (Same disease as the paper alpha I wrote about in the anomaly decay review: the cost line is the one nobody tunes.)

The threshold is the second lever. Higher volatility cutoffs make the claim stronger (3 of 4 at 20%). A cutoff below the median makes it false (5 of 12 at 13%). My position names the long-run median. I used the in-sample median instead, because I do not have a sourced long-run series. The prospectus five-year figures, 23.70% to June 2009 [3] and 17.78% to May 2025 [6], suggest the long-run median sits above 14.8%. If so, the high-volatility group would shrink toward the 18% row, where the claim holds better.

Calendar years are a third, untested lever. Twelve-month windows starting in March 2020 or October 2022 would look very different from the calendar years. Rolling 252-day windows give about 4,000 overlapping observations but only about 16 independent ones, so a block bootstrap is needed before any interval can be taken seriously.

Where this leaves my position

The direction holds, and the drag formula reproduces the issuer's own table exactly. The magnitude does not support "most" at the confidence I gave it. I am lowering the position from 0.7 to 0.6 and narrowing it: a 3x S&P 500 fund held for a calendar year trails 3 times the index in essentially every above-median-volatility year, and trails the plain index in roughly half to two thirds of them, depending on how financing is attributed.

What would make me wrong

The implied volatilities are backed out of the same gap that decides who wins, so they are not independent evidence. The test that settles it: compute realized volatility from daily S&P 500 total returns for each rolling 252-day window from 2009-06-25 to 2025-12-31, split at the full-history median of daily-index realized volatility since 1990, and count the windows where UPRO's total return trails SPY's, with a block-bootstrap interval. If the trailing share in the high-volatility half has a lower 95% bound below 50%, the "more than half" claim fails and I drop it to 0.5. If the lower bound is above 50%, the claim stands at 0.7.