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TQQQ: Leveraged ETF Decay Costs February 2022 Update

Warwick Langebrink profile picture
Warwick Langebrink


  • As expected, LETF Decay costs have continued to increase.
  • LETF leakage costs still remain very low compared to March 2020 COVID correction.
  • However, unlike March 2020, LETF Decay costs may not be overshadowed by the stratospheric April 2020 and subsequent bounce and bull run.
  • LETF decay costs will bite hard in sideways markets.

Business arrow increase of success graph and growth stock market earnings financial on profit income background with diagram chart investment.

Lemon_tm/iStock via Getty Images

Key points carried forward from January 2022

  • Leveraged ETF decay costs have doubled in the last 3 months and the trend is expected to continue.
  • 2X ProShares Ultra S&P 500 (ARCX:SSO) will leak only 1.5% per year relative to holding

This article was written by

Warwick Langebrink profile picture
Chartered Accountant, CFA, Instrument rated pilot, mountain-biker (stage races), 30 years experience as a "quant" in Investment Banking: Specialized Finance and more recently hedge fund type boutique (Acacia) , fixed Income securities trading, product design, modeling, marketing to corporates, product implementation and execution.  Recently involved, assisted in the establishment of an offshore pension fund / retirement scheme in partnership with a niched international bank, including retirement scheme statutory and regulatory aspects, legal implementation, marketing, investment philosophy and strategy.  Financial areas of interest:  Arbitrage, ETF investing, Long/Short Equity, Bonds.   My area of writing interest is quantitative analysis, finding potential arbitrage opportunities, behavioral finance miss-pricings which are likely to lead to market corrections (sometimes requiring a contrarian investment style), macro economics, "exploring where no man has explored before" in quants, leveraged ETFs.

Analyst’s Disclosure: I/we have a beneficial long position in the shares of QLD, SSO either through stock ownership, options, or other derivatives. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Seeking Alpha's Disclosure: Past performance is no guarantee of future results. No recommendation or advice is being given as to whether any investment is suitable for a particular investor. Any views or opinions expressed above may not reflect those of Seeking Alpha as a whole. Seeking Alpha is not a licensed securities dealer, broker or US investment adviser or investment bank. Our analysts are third party authors that include both professional investors and individual investors who may not be licensed or certified by any institute or regulatory body.

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Comments (28)

I'm trying to understand all of this and need to continue studying it. When day trading, do you think there is an advantage to putting 3x the capital into QQQ or 1x the capital into TQQQ?
Thanks for putting this analysis together. Incredibly useful to find such a thorough, readable article on the decay of leveraged ETF's in relation to the non-leveraged index.
anivale profile picture

Thanks for taking the time to share this piece.

Recently, I learnt about TQQQ and I had been thinking about some of the points that you have highlighted here.

Since TQQQ does daily re-balancing, there is an operating cost associated with it, which is going to erode the long term performance.

You wrote that for the last 10 years:
QQQ has returned 17.178% per year and

TQQQ has returned 39.339% per year.

Agreed that TQQQ rate of return is not 3X of QQQ rate of return, but it's still significant !

Historically, semiconductor industry has been cyclical and I don't think it's going to be different this time either.

Whereas QQQ & TQQQ track the top 100 companies listed on NASDAQ. Hence, in my opinion QQQ / TQQQ are likely to trace a better upward trajectory.

Best wishes,

- A
Warwick Langebrink profile picture
@anivale Yes, Agreed. I am more bullish on TQQQ and QLD and have a higher exposure to TQQQ and QLD than semiconductors. Also TQQQ (3X Nasdaq) and QLD have much lower holding costs (leakage) than 3X and 2X Semiconductor SOXL. So yes I agree. Also markets are depressed at the moment thanks to Putin and my long term investing view is that markets revert onto their upward trajectory in the long run, so now is probably a good time to go long.. Interest rates are also still relatively very low compared to historic levels.
Jamie Ellis profile picture
Keep in mind, that the daily rebalancing is what leads to the decay... and the compounding. If QQQ averaged 17% for the next 5 years, TQQQ could do 30%, 40%, 16%, -10%. We have no idea, because the amount of the decay is a function of 2 things, frequency of directional changes in the index, and the severity of those directional changes. Read Warwicks responses to a few other posts where he explains the difficulty in projecting long-term results.

I personally would not be using leveraged ETF's as the increased volatility that I think we have thru the FED normalization process will yield volatility that will increase the decay too much. But who knows... Ive been wrong before.
@Warwick Langebrink

So, I went here:


and looked at the table comparing UPRO vs the SP500.

I arbitrarily selected the 5-year total return data which showed:

UPRO is about 290%
SP500 is about 107%

With that data, let us assume that 5 years ago, I invested:

1k in UPRO and 1k in SP500

Question: Is the following math correct?

UPRO: $1,000 * 290% = $2,900, so do: $1,000 (principle) + $2,900 (return) = $3,900 is total $ amount you have 5 years later.

SP500: $1,000 * 107% = $1,070, so do: 1,000 (principle) + $1,070 (return) = $2,070 is total $ amount you have 5 years later.
Warwick Langebrink profile picture
@cat2005 Yes, Confirmed: your math and factors above are correct.
UPRO: $1,000 grows to $3,900 5 years later.
SP500: $1,000 grows to $2,070 5 years later.

These factors however need further manipulation: UPRO 5 year growth rate of 290% isn't directly comparable to the SP 5yr growth rate of 107% without some compounding adjustments. This is the same as saying that a $1000 5 year 20% roll-up loan will roll up to $2488 (whereas a $1000 5 year 10% roll-up loan will only grow to $1610). The $1488 interest roll-up on the 20% loan isn't directly comparable to twice the $610 interest roll-up on the 10% loan without some mathematical adjustment i.e. reducing both to a v short term compounding rate.

This compounding conversion is one of the critical steps in calculating LETF decay or leakage or beta slippage for periods longer than 1 day without which results for comparison periods longer than one day will always be materially misstated. Comparison between various LETFs is also not possible without adjusting for compounding. The Proshares Prospectus states on page 364 that the use of the simple formula of Drift = (LETF Return Factor [3.90 per yr example] - (IndexReturn Factor [2.07 per yr example] x LETF Multiplier {2X])) does not work for periods longer than 1 day. I agree with this Proshares statement. drive.google.com/...

To solve the relationship between SP and UPRO: You need to calculate the daily (or continuously) compounded rate for both either by using polynomial math or by using my model here: docs.google.com/...

The tricky math makes the analysis of LETFs and their costs difficult and can mask the cost of investing into LETFs for unknowing/unaware investors.
@Warwick Langebrink

Thank you for taking the time to reply. I appreciate it.
@Warwick Langebrink

This was a well-written article but it went over my head.

I looked on Google to answer my question but couldn't, so I will simply ask you my question:

In words that a 10-year old child would understand, what exactly is "decay", as used in your article?

Thank you.
Jamie Ellis profile picture
decay is a generic term in the investment industry... essentially its the slow loss of value to factors other than simple price movement.
In the case of leveraged ETF's, (LETF), the decay comes from what is more commonly referred to as "tracking error", or "beta slippage." Google "leveraged ETF tracking error", or "leveraged ETFbeta slippage" and you will get the explanation.

In a nutshell, it occurs because LETF's apply their leverage DAILY, rather than leverage across a period of time. Simplke example, if the NASDAQ went up 1% today, and down 1% tomorrow a triple leveraged fund would go up 3% and then down 3%. In the index If we started with $100, on day 1 we'd have $100 x 1.01 = $101 as expected. But when we lose 1% the next day, we are losing 1% of $101, not 1% of $100. So now we have $101x .99= $99.99. Now look at the 3x leverage fund. If we started with $100, on day 1 we'd have $100 x 1.03 = $103 as expected. But when we lose 3% the next day, we are losing 3% of $103, not 3% of $100. so now .97x $103= $99.91. 8 cents less than the underlying index. Thats what causes the decay. The higher the leverage, the higher the market volatility, and the more frequent the directional changes, the higher the decay will be.
@Jamie Ellis

This is a very helpful explanation.

I appreciate it.

Thank you.
Warwick Langebrink profile picture
@Jamie Ellis Evening Jamie, You need to use proper polynomial math to get back to exactly 100 for both the index and the LETF. I'm afraid that your 8 cents cited above arises as a result of applying the incorrect math and should net be labelled as "decay" Quoting from your example (but applying the correct compounding math:) if the NASDAQ went up 1% today, and down 1% tomorrow a triple leveraged fund would go up BY A FACTOR OF 1.01^3 and then down AGAIN BY THE SAME FACTOR. In the index If we started with $100, on day 1 we'd have $100 x 1.01 = $101 as expected. But when we lose 1% the next day, we are losing 1% of $101, not 1% of $100. So now we have $101 DIVIDED BY 1.01 = exactly $100.00. Now look at the 3x leverage fund. If we started with $100, on day 1 we'd have $100 x 1.030301 = $103.03. But when we lose the next day, we are losing 3.0301% of $103, not 3% of $100. so now $103.03 DIVIDED BY 1.0301 = exactly $100.00. Both indexes will (applying the correct math) revert back to exactly 100. The 8 cents per your example arises from applying the incorrect growth and loss factors. The 8 cents is not decay. There are no windfall gains, free lunches in the finaincial markets. Likewise the corrolory holds: there is no mathematical anomalies or trickery that is the cause of decay. Consider the following further examples to illustrate:

The following example has been cited on Seeking Alpha to illustrate the wrong way to think about “volatility decay"
"A fund holds $200 of stock and $100 of margin loan. During Day 1, the value of the underlying stock falls by 5%, so at the end of the day the fund has $190 of stock and $100 of debt, netting to $90 of equity. The fund must rebalance its assets to maintain its leverage ratio. So, it pays down $10 of its excess debt by selling $10 of stock, and now its balance sheet includes $180 of stock, and $90 of debt, netting to $90 of equity. During Day 2, the stock rises by 5.263%, which nearly exactly cancels out its previous day loss of 5%. The fund's $180 of stock is now worth $189.47. To maintain the leverage ratio, the amount of debt in the fund is raised from $90 to $94.74. The fund has $189.47 in stock and $94.74 in debt, netting to $94.73 in equity. What was the net result? An investor who owned $100 of stock would still have $100 of stock at the end of Day 2, but an investor who owned $100 of equity in the 2x levered fund would only own $94.73 in equity. Sounds like a terrible deal - over 2 days, the leveraged investor lost 5.27% of their equity!"

My response to the above apparent disparity between TQQQ and QQQ is as follows:
@Stephen: In further support of your findings the corollary of the 5% example must also hold true: Assume that there is an equal probability that the market will rise or fall: Assuming that the market rises, then the corollary 5% "Volatility Drag" example applies as follows: (the maths below does not give an accurate long-term projection for leveraged ETFs btw. - more on that below):

A fund buys $200 of stock at 9.30am on Day 3 and holds $100 of margin loan. During Day 3, the value of the underlying stock rises by 5.263%, so at the end of the day the fund has $210.52 of stock and $100 of debt, netting to $110.52 of equity. The fund must rebalance its assets to maintain its leverage ratio. So, it raises $10.52 of extra debt, and buys further equity and now its balance sheet includes $221.05 of stock, and $110.53 of debt, netting to $110.52 of equity. During Day 4, the stock falls by 5%, which exactly cancels out its previous day’s gain of 5.263%. The fund's $221.05 of stock is now worth $210.00. To maintain the leverage ratio, the amount of debt in the fund is reduced from $110.52 to $105.00. So, it pays down $5.52 of its excess debt by selling $5.52 of stock, and now its balance sheet includes $210.00 of stock, and $105.00 of debt, netting to $105.00 of equity. What was the net result? An investor who owned $100 of stock would still have $100 of stock at the end of Day 2, but an investor who owned $100 of equity in the 2x levered fund would now own $105.00 in equity. Sounds like an amazing deal - over 2 days, the leveraged investor is up 5% of their equity! [if you correct the flawed maths logic this $5 “windfall gain” on days 3 and 4 matches and offsets the $5.27 “unlucky” losses on Days 1 and 2. So the net effect of the "Volatility Drag" per the example above (ie arising out of some mischievous mathematical anomaly) should offset and cancel each other over time.

Leveraged ETFs make use of option strategies and Total Return Equity Swaps to fine tune their hedging and prevent calamitous losses, and in so doing pay away "Volitility Spreads" but Volatility spreads (on options) are not what is being described in the (mathematically flawed) example above.

We know that the effects of compounding increase exponentially with time and also increase exponentially as returns increase. Using a “Polynomial Method” to include compounding concepts in our modelling work very well when applied to pricing long term leveraged ETF movements:

Returning to the two WindfallGain vs Unlucky Funds example above, the correct maths (I believe) should be described as follows: A 2X leveraged ETF investor holds $100 of stock (roughly comprising $200 of synthetic and actual equity positions) and roughly $100 of synthetic and actual debt (including Swaps). During Day 1, the value of the underlying stock falls by 5%. The value of the 2X leveraged ETF is calculated using the compounding method as follows: $100* ((1-5%)^2) = $90.25. [In Excel type: “=100*((1-5%)^2)”]

During Day 2, the stock rises by the reciprocal of 5%, which exactly cancels out its previous day loss of 5%. The value of the 2X leveraged ETF is calculated using the compounding method as follows: $90.25* ((1-5%)^-2) = $100.00. [In Excel type: “=90.25*((1-5%)^2)”]

And a 3X ETF would be calculated as follows: Day 1 (5% index drop) $100* ((1-5%)^3) = $85.73. Day 2 (reciprocal $5 index increase): $85.73* ((1-5%)^-3) = $100. [In Excel type: “=100*((1-5%)^3)” and “=85.73*((1-5%)^-3)” into cells A1 and A2.

Compounding can be explained in polynomial expressions as follows:
"(1+0.01) is 1.01 or 1 plus 1%. If you make 1% per period -- let's say per week -- then you multiply your account times 1.01 each period. If you start out with 1000, then after a week it's 1000 * 1.01= 1010. After 2 weeks you multiply by 1.01 again, so after 2 weeks it's 1000 * 1.01 * 1.01 = 1020.1. After three weeks it's 1000 * 1.01 * 1.01 * 1.01. Multiplying the $1000 account by 1.01 3 times is represented as $1000 * 1.01^3. After N periods, you raise the periodic growth to the Nth power. So if you made 1% per week, after a year your $1000 account would grow to $1000 * 1.01^52. Which is actually 67.7% growth, not 52%, because the earnings compound.

Jamie Ellis profile picture
I believe the increased "decay" as you call it, will be here for awhile. Personally, I dont think decay is an accurate term as that word is usually associated with options. Many use the term "beta slippage", but I personally think the more accurate terminology would be "volatility erosion". LETF's "decay" for several reasons as you have pointed out in excellent detail.... but the primary reason is that they are leveraged to an index on a DAILY basis. Daily rebalancing of the X amount leverage is what causes the greatest amount of the "decay". The higher the volatility of the underlying index, the higher the decay will be. its that simple.

Options can be used to take advantage, but as the author states...timing would be needed. I dont fight the decay, i think its too hard. I capture it. In the chart that Warwick gives the visual example, rather than buy TQQQ, I would short the inverse SQQQ. I get the direction of the market, and I capture the "decay". Warwick explains that some of these LETF's have expected decay of 41%. So i would capture the index plus the 41% (not quite that simple but you get the idea)

Keep in mind shorting a leveraged fund is fraught with danger. This is were you can use that 41% of excess gain from the "decay" to hedge yourself. I urge you to not try this unless you are a sophisticated investor and very knowledge about the risks of LETF's and shorting.

Good article and math details...
good luck with your trading to all.
Convoluted profile picture

So, the inverse LEFTs ‘leak more oil?’

I recall an academic paper a few years ago that thought the differential roughly equaled the cost inherent in shorting shares.

I never thought about again-until I read your article. Do you agree with that, or is the disparate leakage attributable to something else?

Great article BTW.
Warwick Langebrink profile picture
@Convoluted Thank you for your feedback. I guess the crux of my article is that positive and inverse LETF costs do not always move in lockstep with the costs of shorting stocks and also do not fluctuate in tandem with the costs of hedging using options. Leveraged ETF costs fluctuate wildly in multiples from time to time and also vary significantly between different LETFs: Refer Figure 1 and 4 above. And these fluctuations do not always track fluctuations in volatility. (where VIX volatility is a proxy for option prices). If possible, investors should consider the alternative costs before making material, (long term) hedging decisions. In November 2021, LETFs were relatively inexpensive compared to alternative hedging alternatives. LETF leakage costs have become much more expensive in current market conditions (March2020 COVID scenario). Unfortunately LETF leakage costs are difficult to quantify and are hidden by highly variable LETF returns and by compounding effects. Incidentally, the head of Blackstone (which owns Proshares TQQQ) made USD1.1 billion last year which is 500 times more than the CEO of Goldman Sachs. Schwarzman received $1.1bn in income at Blackstone in 2021 | Financial Times
Convoluted profile picture
@Warwick Langebrink

Thanks-I use an assortment of LETFs. I have an unquantified theory that selling option premium on the LETF will mitigate the impact of path dependency.

My mission is to pick up some of that cash flow you referenced. I spend a lot of time trying to game all the new instruments the mad scientists of Wall Street come up with. I find that to be more interesting than traditional analysis.
Warwick Langebrink profile picture
@Convoluted I like the idea of "selling option premium", particularly in depressed, low price, high volatility environment: The idea of writing long dated at-the-money or near-the-money puts (without betting the farm) (and provided you are well collateralized against margin calls increasing in multiples), and can ride the position until maturity - even in the event that Putin presses the Nuke button (God forbid)). This places you in the space until recently out of reach of retail investors - previously only dominated by the big banks and institutions. Goldman Sachs looks to increase , optimize their "Value At Risk". That is how they make money. ref "Goldman Sachs: The culture of success": Amazon. I like yr strategy (provided u can accurately objectively measure your worst case scenario March2020-black-swan-event margining scenarios and set cash aside to ride out that storm
There is a free site called splithistory.com. This site shows that if you had invested $10,000 10 years ago in the QQQ versus TQQQ You would have have $53,000 versus $333,000 respectively. The key to these index letf is it the ones that split regularly give you significantly higher number of shares. I realized this was a bull market but the numbers don't lie.
Warwick Langebrink profile picture
@Kww1 Hi Kww1: The share splits in themselves do not (should not) give rise to additional value for investors because a 2:1 share split is accompanied by a halving of the share price ; so the total market capitalization (investor wealth) in theory remains constant immediately prior to and immediately after the split. Have a look at Amazons recent 20:1 share split announcement "Each shareholder at the close of business on May 27, 2022 will have 19 additional shares for every one share held as of such date reflected in their accounts on or about June 3, 2022" The market Capitalization (value) of the underlying Amazon business and its future cash generating ability does not change. The only thing that changes is the number of share in issue, and in theory this value should be exactly split 20 ways for each old share. Market Cap shouldn't change.

Having said that, the news publicity , hype surrounding the share split, and the increase of Amazons tradability (not all retail investors can afford paying $3000 per share), and possible positive market signals arising from directors buying back Amazon Stock (seen as a positive signal that directors consider the share price undervalued), and confirmation that the company has the surplus cash sloshing around to buy back its own shares: all these factors can have a small positive impact on share price.

But there is not obvious/guaranteed positive arbitrage opportunity arising from a share split, (no free lunch in the financial markets) and sometimes a share split has the opposite effect to that intended: a negative impact on adjusted share price and shareholder wealth.

So adjusting for share splits, (and I am not saying that you are making this incorrect inference) it would be incorrect to say, by your numbers that TQQQ's 33.3 times return over 10 years is well above the 3X QQQ return. QQQ grew 5.3 times over 10 years. It would incorrectlyb appear (on the face of it using simple math) that TQQQ well outperformed its objectives and achieved a 6.3X return (well above its 3X return) relative to QQQ over the 10 year term [33.3/5.3=6.3X]. Please refer my section on compounding and excel compounding model above: TQQQ's returns were actually in truth well below 3X. By your numbers when daily compounding is calculated: Insert into EXCEL/GOOGLE: QQQ : "=((1+5.3)^(1/10/365)-1)*365" = 18.4%nacd QQQ return over 10 years. And for TQQQ: "=((1+33.3)^(1/10/365)-1)*365" = 35.4% annualized compounded daily "nacd" TQQQ return over 10 years (35.4% is actually less than 2X QQQ return of 18.4% when compounding effects are eliminated) comparing apples with apples. i.e. well below ProShares TQQQ objectives of a 3X return.

This example explains why a lot of the analysis and pricing of LETF decay for period longer than 1 day (without eliminating the effects of compounding) is incorrect by light years, and a lot of analysts get this wrong..3)
Wez profile picture
"Investors should migrate from 3x to 2x LETFS, avoid LETFs on less liquid indices other than on the S&P500 and Nasdaq100, and avoid short LETFs in current market conditions."

The solution is to buy puts on the 3x bullish LETFS.
Warwick Langebrink profile picture
@Wez Hi Wez. Yes, buying puts would reduce market exposure. The main thrust of the article was to reduce leakage costs while maintaining market exposure. 2X. LETFs leak a lt less in decay cost terms (when grossed up for the same market exposure) than 3X : Particularly in these market conditions: decay costs become v expensive on 3X, Short and less main-stream LETFs.
Wez profile picture
@Warwick Langebrink

Gotcha. My suggestion was to take advantage of both market selloff and decay.
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