Updated 2025-01-18 to fix some flaws in the calculations and add new data for 2021–2024. Tables have been updated to include the new results. For more, see 2025 Update: How have things changed? and Appendix A: Changes to calculation methodology.

Under some circumstances, altruists might prefer to leverage their investments. The easiest way to get leverage is to buy leveraged ETFs. But leveraged ETFs charge high fees and incur other hidden costs. These costs vary substantially across different funds and across time, but on average, leveraged ETFs have historically had annual excess costs of about 1.5% per 100% leverage, or around 1% on top of the expense ratio.

Given reasonable expectations for future returns, leveraged ETFs most likely have substantially higher arithmetic mean returns than their un-leveraged benchmarks. They also appear to have higher geometric mean returns than their benchmarks, but only by a small margin. More pessimistic estimates would find that adding leverage decreases geometric return.

Note: Many investors can get leverage more cheaply via other methods, such as margin loans or futures. Even if leveraged ETFs appear better than un-leveraged investments, other forms of leverage might be better still.

Disclaimer: This should not be taken as investment advice.

Contents

Measuring the cost of leveraged ETFs

To calculate costs, I created a list of leveraged ETFs and looked up their historical returns from the start of 2016 to the end of 2020. I paired each leveraged ETF with an equivalent un-leveraged benchmark ETF. I calculated what return you would have earned if you had taken that ETF and applied the appropriate amount of leverage (either 2x or 3x, depending on how much the corresponding leveraged ETF uses), paying only the risk-free rate.1 Then I subtracted the actual return of the leveraged ETF to find the excess cost.

My analysis included these ETFs:

ETF Leverage Index Index ETF
SPXL 3 S&P 500 SPY
UPRO 3 S&P 500 SPY
SSO 2 S&P 500 SPY
UMDD 3 S&P 400 (mid cap) IJH
URTY 3 Russell 2000 (small cap) IWM
EFO 2 EAFE EFA
EURL 3 Europe VGK
EZJ 2 Japan EWJ
EET 2 emerging markets EEM
EDC 3 emerging markets EEM
TQQQ 3 NASDAQ QQQ
TMF 3 long-term US Treasury bonds TLT

The following table shows the total excess cost and after-fee cost for various leveraged ETFs (2016–2024). Excess cost is shown per 100% leverage (so the excess on a 3x ETF is divided by two). After-fee cost tells us the excess cost minus the expense ratio.2 r gives the correlation between the leveraged ETF and the simulated leveraged benchmark ETF.

ETF Excess Cost After Fee r
SPXL 1.14% 0.82% 0.999
UPRO 1.17% 0.85% 0.999
SSO 1.51% 0.80% 0.999
UMDD 0.94% 0.54% 0.991
URTY 1.22% 1.03% 0.999
EFO 2.31% 1.48% 0.947
EURL 1.37% 0.98% 0.995
EZJ 2.32% 2.20% 0.936
EET 1.83% 1.04% 0.987
EDC 1.17% 0.72% 0.998
TQQQ 1.09% 0.97% 0.999
TMF 0.77% 0.48% 0.997
Average 1.40% 0.99%  

The leveraged ETFs generally had an excess cost of 1.43%, or 1.01% in excess of the ETF expense ratios. Almost all fund pairings had high correlations, which tells us that the leveraged ETFs do a good job of tracking their benchmarks (with the possible exceptions of EFO and EZJ).

Excess costs were not stable—they varied substantially from year to year. The next table shows excess cost for each individual year:

ETF 2016 2017 2018 2019 2020
SPXL 1.39 1.63 0.85 1.77 2.74
UPRO 0.99 1.52 0.86 2.22 2.48
SSO 1.44 1.74 1.39 2.57 2.63
UMDD 1.40 1.94 0.56 1.43 0.13
URTY 1.14 1.00 0.46 1.50 3.71
EFO 0.84 2.91 2.05 4.24 1.52
EURL 1.43 2.61 0.72 3.33 1.44
EZJ 2.88 1.63 1.84 3.49 1.78
EET 2.23 1.96 1.37 1.85 1.35
EDC 1.41 1.95 0.49 1.91 1.12
TQQQ 1.05 1.75 0.64 2.30 3.51
TMF 0.71 0.56 0.12 0.94 1.71
Average 1.41 1.77 0.95 2.30 2.01

New data through 2024:

ETF 2021 2022 2023 2024
SPXL 1.94 0.29 1.61 2.13
UPRO 2.06 0.44 1.97 2.14
SSO 2.37 0.86 2.09 2.46
UMDD 1.66 0.37 1.68 1.94
URTY 0.70 0.40 1.71 1.24
EFO 2.71 2.28 3.83 2.28
EURL 2.01 0.32 1.61 1.20
EZJ 2.49 2.08 2.87 2.75
EET 1.08 1.63 3.31 2.10
EDC 1.15 0.44 1.32 1.63
TQQQ 0.66 0.16 0.70 0.99
Average 1.74 0.80 2.12 1.92

For individual years, excess costs ranged from as low as 0.13% to as high as 4.24%.

Some factors that might contribute to this year-to-year variance:

  1. The ETFs’ counterparties charge different rates based on perceived risk.
  2. Market liquidity varies over time.
  3. The ETFs might experience some tracking error.

Excess cost does not include the risk-free rate, so the year-to-year variance has nothing to do with changes in the risk-free rate.

Some people observe that 3x leveraged funds usually provide less than a 3x return due to volatility drag. To be clear, the excess cost I found is not related to volatility drag. Volatility drag equals the difference between the arithmetic mean and geometric mean of an investment. If two investments A and B have the same arithmetic return but B has higher volatility, then B will have lower geometric return.

Specifically, the geometric mean of an investment equals \(\alpha - \sigma^2/2\), where \(\alpha\) is the arithmetic mean and \(\sigma\) is the standard deviation.

The geometric mean of a 3x leveraged ETF is less than 3x the arithmetic mean. For example, if the benchmark has a geometric mean of 5% and an a standard deviation of 16%, then we calculate the geometric mean of the leveraged ETF as:

  1. Arithmetic mean of the benchmark is \(5\% + 16\%^2/2 = 6.28\%\)
  2. Arithmetic mean of the leveraged ETF is \(3 \times 6.28\% = 18.84\%\)
  3. Standard deviation of the leveraged ETF is \(3 \times 16\% = 48\%\)
  4. Geometric mean of the leveraged ETF is \(18.84\% - 48\%^2/2 = 7.32\%\)

In this example, adding 3x leverage only increases the expected geometric return from 5% to 7.32%. If we assume a 3x leveraged ETF has a 2.5% excess cost, that reduces its expected geometric return to 4.82%, which is lower than the return of an un-leveraged ETF.

Are leveraged ETFs worth it?

Mathematically speaking, an agent with a logarithmic utility function wants to maximize geometric mean, while a risk-neutral agent wants to maximize arithmetic mean. A logarithmic utility function is probably still too aggressive for self-interested investors, but it might be appropriate for altruists. Under some circumstances, altruists might even be close to risk-neutral.

For risk-neutral investors, leveraged ETFs pretty clearly have higher expected utility than normal ETFs. (Although they might prefer to get leverage some other way if they can, since leveraged ETFs are one of the most expensive forms of leverage.)

Are leveraged ETFs worth it for investors with logarithmic utility? That is, can we expect leveraged ETFs to have a higher geometric return than ordinary ETFs?

That depends on three things: the expected return of the benchmark, volatility, and excess cost.

Let’s assume an excess cost of 2% and a risk-free rate of 0%. Long-run market volatility generally varies from 15% (for more stable markets like the S&P 500) to 22% (for more volatile markets like US small-caps or emerging markets). Then we can ask, what expected geometric return does an index need to have for a leveraged ETF to be worth it? Let’s assume we can use the optimal amount of leverage, not just 2x or 3x. (We can combine a 3x ETF with an un-leveraged ETF to get an intermediate amount of leverage.)

At a 15% standard deviation, an investment needs an expected (geometric) return higher than 3.125% for leverage to be worth it. At a standard deviation of 22%, the investment must return more than 4.42%.3

If we assume a total cost of 2.5% (e.g., an excess cost of 2% plus a risk-free rate of 0.5%, or an excess cost of 2.5% when the risk-free rate is zero), then an investment with 15% standard deviation must return 3.625%, and one with 22% standard deviation must return 4.92%.

What returns can we expect from various market indexes? We can’t know with high confidence, but we can try to estimate it. The following table gives return estimates for various equity regions according to Research Affiliates (RA) and AQR, and standard deviation estimates from Research Affiliates.4

Index Return (RA) Return (AQR) Stdev (RA)
US large 2.0% 5.9% 15.4%
US small 4.3% N/A 20.7%
EAFE 6.3% 6.5% 17.3%
Europe 6.4% 6.3% 19.2%
Japan 5.8% 6.3% 17.6%
emerging 7.6% 7.0% 21.7%

The next table gives the expected (geometric) return of an optimally-leveraged portfolio5 minus the expected return of the index, constructed using a leveraged ETF with a 1.5% cost.6

Index Improvement (RA) Improvement (AQR)
US large 0.1% 2.2%
US small 0.1% 1.5%
EAFE 1.8% 2.1%
Europe 1.3% 1.2%
Japan 1.2% 1.7%
emerging 1.5% 1.1%

Applying leverage at least marginally increases expected geometric return in every sample case. However, leverage provides only a modest improvement, with the best case being 2.2 percentage points, and the projected improvements in some cases being as low as 0.1 percentage points.

Vanguard’s return expectations produce similar numbers (not shown).

Of course, these results heavily depend on what inputs we use for expected return, volatility, and costs, and the true numbers might differ significantly. If costs turn out to be closer to 3%, or if true (ex-ante) expected returns are one percentage point lower, that would eliminate the benefit of using leverage.

Or suppose you are trying to decide between two ways of investing:

  1. Buy leveraged ETFs in a donor-advised fund (DAF).
  2. Buy un-leveraged ETFs in a taxable account, and use margin to get leverage.

Say your DAF has to pay a 0.3% fund fee plus a 1% fee for an investment manager, and margin costs 0.5% over the risk-free rate. That means the DAF has to pay an extra 2.3% cost above what the taxable account pays (DAF fees plus leveraged ETF cost minus margin cost), whereas the taxable account must pay taxes. 2.3% is a lot. It’s not obvious whether it outweighs the tax benefits of a DAF, but I personally would lean toward keeping my money in a taxable account.

2025 Update: How have things changed?

I ran the numbers again to cover the four years since this post was first published. In short:

  • My previous methodology had some flaws, and overestimated the true average cost by about 0.5 percentage points. (See Appendix A for a full explanation.)
  • Since 2021, excess costs have continued to vary a lot from year to year.
  • Excess costs were just as high after 2020 as they were before 2020.

2016–2020 had an average annual cost of 1.77% (taking the arithmetic mean across all ETF-year pairs) and 2021–2024 had an average of 1.74%. The difference was highly insignificant (p = 0.87).

Source code

Source code for the 2025 revision of this article is available on GitHub.

Appendix A: Changes to calculation methodology

In the 2025 update to this post, I made several changes to my original methodology that changed the numbers.

  1. Based on the script I originally used, the average excess cost of ETFs (2016–2020) was 2.09%.
  2. I discovered that I had been calculating the risk-free rate incorrectly. I converted annualized T-bill yields into daily interest by raising to the power of 1/365. That’s not correct because there are not 365 trading days per year—there are approximately 252. Raising to the power of 1/252 instead reduced the average excess cost to 1.64%.
  3. I completely re-wrote the calculations because I lost my original script (I later re-discovered it). The new script uses a more rigorous method for calculating the cost of leverage. Instead of assuming the interest paid is uniform across 252 trading days, it pays interest on every calendar day, using the last known rate on days when the market is closed. The new script also correctly handles days where the stock market is open but the Treasury is not (which happens occasionally). The new script produces an excess cost of 1.61%.

There is one additional issue that has no simple resolution: there are multiple ways to define “average excess cost”, and it’s not clear which one is best.

We can calculate excess cost in at least three ways:

  1. Take the total return of the simulated leveraged ETF; annualize it by raising to the power of the number of years in the sample; do the same for the actual leveraged ETF. Let the excess cost be the difference between those two numbers. (This is the method my original script used.)
  2. For each individual year, calculate the difference in annual return between the simulated and actual ETFs. Let the excess cost be the simple average of each year’s costs. (That’s the method I used above when I wrote that 2016–2020 had an average annual cost of 1.69%.)
  3. Let the excess cost be the number such that, if you took the simulated ETF and deducted that number from the return every year, the resulting total return (across the full sample) would equal the total return of the actual ETF.

The third method seems most reasonable to me, so it’s what I used in my new script. I like the third method because if an ETF charged a management fee, the third method is how you would calculate the impact of the fee.

While the first method found an average cost of 1.65%, the third method found a cost of 1.35%.

The table above reported an average of 1.43% not 1.35%, because (1) the 2025 version includes a longer date range and (2) it includes two new leveraged ETFs.

For the 2025 edition, I added these leveraged ETFs and their corresponding index ETFs:

Leveraged ETF Leverage Index Index ETF
SSO 2 S&P 500 SPY
TQQQ 3 NASDAQ QQQ

Updated again 2025-01-22. I realized there was a data entry error where for 2016–2017 I incorrectly used the 4-month Treasury yield as the risk-free rate rather than the 3-month Treasury yield. This only slightly changed the results.

Appendix B: Original tables, for posterity

These are the tables I originally included in the post in 2021.

ETF Excess Cost After Fee r
SPXL 2.23% 1.72% 0.995
UPRO 2.12% 1.64% 0.995
UMDD 1.31% 0.84% 0.995
URTY 2.08% 1.61% 0.993
EFO 2.47% 1.14% 0.978
EURL 1.97% 1.44% 0.984
EZJ 2.79% 1.84% 0.981
EET 2.18% 1.25% 0.994
EDC 1.67% 1.20% 0.994
ETF 2016 2017 2018 2019 2020 Min Max
SPXL 1.39 2.02 1.22 3.25 3.01 1.22 3.25
EET 2.73 2.63 1.55 2.71 1.58 1.55 2.73
UPRO 1.03 1.90 1.27 3.51 2.76 1.03 3.51
UMDD 1.58 0.85 1.04 2.03 0.06 0.06 2.03
URTY 1.05 1.59 0.87 2.48 3.88 0.87 3.88
EURL 1.51 3.08 1.15 4.21 1.34 1.15 4.21
EZJ 2.05 2.07 2.11 4.71 1.87 1.87 4.71
EDC 1.45 2.55 0.73 2.89 1.30 0.73 2.89
EFO 0.83 2.73 2.51 4.02 1.32 0.83 4.02
Min 0.83 0.85 0.73 2.03 0.06 0.06 2.03
Average 1.51 2.16 1.38 3.31 1.90 1.03 3.47
Max 2.73 3.08 2.51 4.71 3.88 1.87 4.71
Index Improvement (RA) Improvement (AQR)
US large <0% 1.6%
US small 0.0% N/A
EAFE 1.3% 1.5%
Europe 0.9% 0.8%
Japan 0.8% 1.2%
emerging 1.1% 0.7%

Notes

  1. I used the 3-month T-bill yield as the risk-free rate. ↩

  2. I looked at the ETFs’ current expense ratios (as of 2025-01-18) and assumed that they stayed the same over the whole sample period, which might not be true.

    I did not use the actual expense ratios for EFA and EEM. Instead I used the expense ratios for VEA and VWO respectively. EFA/VEA and EEM/VWO cover the same markets but use different benchmarks so they are not perfectly correlated. Realistically, if you wanted to invest in EAFA or emerging markets, you’d buy VEA or VWO respectively, not EFA/EEM. But I used EFA/EEM as the benchmarks for EFO/EET/EDC because they’re more strongly correlated, which means the estimated excess costs have less variance. ↩

  3. In general, a leveraged ETF has the same geometric return \(\mu\) as the index when \(\mu = \sigma^2 / 2 + R + c\) for standard deviation \(\sigma\), risk-free rate \(R\), and excess cost \(c\).

    Another way to put it: when \(\mu = \sigma^2 / 2 + R + c\), optimal leverage is exactly 1x. For any higher value of \(\mu\), adding leverage increases geometric return. ↩

  4. Research Affiliates estimates are as of 2021-01-31; AQR estimates are as of January 2021.

    I did not update these numbers for the 2025 revision because the exact numbers don’t matter too much, they’re more meant as an illustration of how different return assumptions affect the viability of leveraged ETFs. ↩

  5. If geometric mean maximizing leverage is less than 3x (which it usually is), then we can construct an optimally-leveraged portfolio by holding both a 3x leveraged ETF and an un-leveraged ETF and rebalancing their weights daily. ↩

  6. Improvements can be calculated using the following Python code:

    def return_improvement(mu, sigma, cost):
    leverage = (mu + sigma**2/2 - cost) / (sigma**2)
    return (
        leverage * (mu + sigma**2/2) - (leverage * sigma)**2/2
        - (leverage - 1) * cost
        - mu
    )

    ↩