Leveraged ETFs - New Paper

[Kbg]

https://papers.ssrn.com/sol3/papers.cfm ... id=5119860

I’ve thought the findings of this paper have been evident for quite a while.

Ignoring whether leveraging is or is not “smart”, which there’s not a right or wrong answer to, the paper demonstrates that even daily reset ETFs are an “ok” form of leverage.

Understanding how LETFs compound and what that means for performance is not very well understood.

Investment tip if using LETFs. Have a well constructed rebalancing plan.

[Walkure]

Thanks for posting, will report back when I have had a chance to read it.

[hnd]

basically the decay that takes place as a result of daily rebalancing is not as detrimental as is typically stated? If it were so then we'd see losses be greater than the 3X in downturns? I think it makes sense seeing that downturns of a 3x ETF aren't usually 3X the corresponding indexes downturn.

bottoms since 2011 :
VOO UPRO
-18% -51% - 2011 - less
-13% -39% - 2016 - less was exactly 3X
-19% -50% - 2018 - less
-34% -76% - 2020 - less
-24% -63% - 2022 - less

I didn't look at the at it the other way around.

[FundQuant]

We have a pretty decent long-term track record for leveraged ETFs now. SSO has been around since 2006 and you've mostly gotten screwed from holding it long-term. After fees you earned 1.5X the return of the S&P 500 with 2X the volatility, multiple 50% drawdowns and one 85% drawdown. The decay accounts for about 20% of the discrepancy between it being a true 2X ETF and the reality that it's a 1.5X ETF. The remainder is from the 0.89% fee.

Leverage is a timing game. If you can time it when the market is good it's very good to you. If you time it wrong then it's very bad. These things always lure people in during bull markets if you time it wrong then it's potentially ruinous.

It's not surprising that leveraged ETFs are back in vogue these days after a big bull run. Unfortunately, many people are now finding out that they cut both ways.

[nisiprius]

We have a pretty decent long-term track record for leveraged ETFs now. SSO has been around since 2006 and you've mostly gotten screwed from holding it long-term...

ULPIX is a 2X leveraged, daily-rebalanced S&P 500 mutual fund and it's been around since 1998. It's from the same firm that operates SSO.

If you'd bought ULPIX at inception, the tech crash and the global financial crisis would have put you so far behind the "straight" S&P 500 fund, VFINX, that even after 2010-2025 you would not have caught up. ULPIX went down farther during the downs than it went up during the ups.



And that's not a straw man. Ayers and Nalebuff in their book actually suggested a long-term holding in ULPIX as a sensible investment for young workers.

[spencydub]

We have a pretty decent long-term track record for leveraged ETFs now. SSO has been around since 2006 and you've mostly gotten screwed from holding it long-term...

ULPIX is a 2X leveraged, daily-rebalanced S&P 500 mutual fund and it's been around since 1998. It's from the same firm that operates SSO.

If you'd bought ULPIX at inception, the tech crash and the global financial crisis would have put you so far behind the "straight" S&P 500 fund, VFINX, that even after 2010-2025 you would not have caught up. ULPIX went down farther during the downs than it went up during the ups.



And that's not a straw man. Ayers and Nalebuff in their book actually suggested a long-term holding in ULPIX as a sensible investment for young workers.

I’d argue you should model periodic investments if we’re talking about accumulating young investors. When you model that, ULPIX does outperform, but not by 2x

https://testfol.io/?s=hpk8y26vDZI

[breakfastinbed]

The fact that a 2x or 3x leveraged EFT does not actually produce 2x/3x the returns of the underlying fund does not make it inherently a bad investment.

It is worth noting that these fund may relatively underperform their underlying funds in accumulation, but also may relatively outperform them in drawdowns.

[er999]

If you'd bought ULPIX at inception, the tech crash and the global financial crisis would have put you so far behind the "straight" S&P 500 fund, VFINX, that even after 2010-2025 you would not have caught up. ULPIX went down farther during the downs than it went up during the ups.

However, most people don’t do a single lump sum. If you ran it buying every 2 weeks or every month for the past 30 years (inception date 1997) you’d probably have a different result. Whether anyone could do it in the real world after 2000 and 2008 major losses is questionable, though.

[typical.investor]

ULPIX is a 2X leveraged, daily-rebalanced S&P 500 mutual fund and it's been around since 1998. It's from the same firm that operates SSO.

If you'd bought ULPIX at inception, the tech crash and the global financial crisis would have put you so far behind the "straight" S&P 500 fund, VFINX, that even after 2010-2025 you would not have caught up. ULPIX went down farther during the downs than it went up during the ups.



And that's not a straw man. Ayers and Nalebuff in their book actually suggested a long-term holding in ULPIX as a sensible investment for young workers.

I’d argue you should model periodic investments if we’re talking about accumulating young investors. When you model that, ULPIX does outperform, but not by 2x

https://testfol.io/?s=hpk8y26vDZI

It's a good point, and a 12.48% MWRR (money weighted return rate) for ULPIX is better than 10.02% for VFINX. But ULPIX has a max drawdown at -89.67%. It's pretty extreme. VFINX is much less alarming at -55.26% which would still unnerve many.

Holding 70% ULPIX and 30% bonds does outperform VFINX (10.84% vs 10.02) with a hefty drawdown of -67.19% which is still less than the -89.67% of ULPIX alone but more than -55.26% for VFINX.

And even more interesting, holding 25% ULPIX 75% VFINX has better returns than 70% ULPIX and 30% bonds or 100% VFINX (10.90% vs 10.84% vs 10.02%) and a lower max drawdown than holding bonds but higher than VFINX alone (-64.14% vs -67.19% vs. 55.26%).

https://testfol.io/?s=iXIw7pOksDK

That was then though, and I don't know about tomorrow.

[Kbg]

It’s an interesting study to compare 100% of an index fund with a 2x ETF and 50% of a vanilla bond fund and do the same with 3x ETF and 67% of a vanilla bond fund. (Or dial it down to whatever your allocation to stocks is divided by the leverage factor and allocate the remainder to the bond fund.) Typically the 3x version outperforms the other two with a modest decrease in the Sharpe ratio.

Comparisons of a 100% allocation to an unleveraged fund with a 100% allocation to a leveraged one I think is silly (and financially suicidal).

[Valuethinker]

Am I right that in these products you are accepting counterparty risk on the derivatives.

i.e. the bank that issues the ETF? Who will "lay off" that risk to other financial institutions?

So somewhere out there in financial markets, you have accepted the systemic risk of a failure of one of the counterparties.

There's somebody on the other side of this thing. What entity is that somebody?

[seajay]

basically the decay that takes place as a result of daily rebalancing is not as detrimental as is typically stated? If it were so then we'd see losses be greater than the 3X in downturns? I think it makes sense seeing that downturns of a 3x ETF aren't usually 3X the corresponding indexes downturn.

bottoms since 2011 :
VOO UPRO
-18% -51% - 2011 - less
-13% -39% - 2016 - less was exactly 3X
-19% -50% - 2018 - less
-34% -76% - 2020 - less
-24% -63% - 2022 - less

I didn't look at the at it the other way around.

So if you held a third of the amount in the 3x, two thirds in cash (T-Bills), in each case you'd have lost less. Daily rebalancing reduced exposure.
If in the opposite case you might expect the third in 3x to rise more. Daily rebalancing adds more exposure.
Negating that and the higher volatility lowers compounding.
Broadly and 100% SPY or 33.3/67.3 SPXL (3x)/cash https://www.portfoliovisualizer.com/bac ... AHIXQFHOiv yielded similar rewards/motions

For some, holding just a third in a brokerage (3x), two thirds in Treasury's might have appeal over 100% in a brokerage (1x). There's also less need to hold cash (reserves) when you might 'borrow' from yourself instead (at T-Bill interest rate).

[seajay]

Am I right that in these products you are accepting counterparty risk on the derivatives.

i.e. the bank that issues the ETF? Who will "lay off" that risk to other financial institutions?

So somewhere out there in financial markets, you have accepted the systemic risk of a failure of one of the counterparties.

There's somebody on the other side of this thing. What entity is that somebody?

Yes but that can be reduced exposure to such risk. 67/33 SPY/T-Bills and considering T-Bills as 100% safe, that leaves 67% in a brokerage/custodian (SPY). Compared to 17/33/50 TQQQ (3x QQQ)/T-Bills/Gold and that's just 17% having counter party risk (assuming in-hand physical gold to be safe).

https://www.portfoliovisualizer.com/bac ... uplflbcV2b

Compensated risk in that links case, 6.9% real versus 11.4% real (whilst sitting on 50% gold and 33% in T-Bills with low/no counter-party risk).

For the leverage a fund might simply borrow at daily rates in order to scale up the amount of stock they buy/hold that day. Or they could hold Futures/Options. More often however I believe they arrange/hold total return swaps.

[nisiprius]

...If you'd bought ULPIX at inception, the tech crash and the global financial crisis would have put you so far behind the "straight" S&P 500 fund, VFINX, that even after 2010-2025 you would not have caught up. ULPIX went down farther during the downs than it went up during the ups....

And that's not a straw man. Ayers and Nalebuff in their book actually suggested a long-term holding in ULPIX as a sensible investment for young workers.

I’d argue you should model periodic investments if we’re talking about accumulating young investors. When you model that, ULPIX does outperform, but not by 2x...

It speaks to the paper's statement that "We find that LETFs’ multi-day returns closely align with those of non-reset portfolios across most indices and holding periods (up to one year)." Maybe up to one year. The abstract says "While substantial deviations can occur under high volatility and long holding periods..." which was what I illustrated. It says "... they are positively skewed and generally favorable," which was not the case.

[ScubaHogg]

And that's not a straw man. Ayers and Nalebuff in their book actually suggested a long-term holding in ULPIX as a sensible investment for young workers.

IIRC Ayers and Nalebuff’s book came out in 2010. Since then ULPIX has slaughtered VFINX for a buy and hold investor

https://testfol.io/?s=7hpXJWpjcEJ

Same thing for an accumulator

https://testfol.io/?s=73gFwHVbPfR

Seems like it was very good, possibly life changing, advice

Even for an accumulator, starting in 1998 with a 10x lump sum, followed by annual cash flows, ULPIX has a much higher MWRR…which is kinda the whole point of Ayers and Nalebuff

https://testfol.io/?s=73gFwHVbPfR

[seajay]

I’d argue you should model periodic investments if we’re talking about accumulating young investors. When you model that, ULPIX does outperform, but not by 2x...

It speaks to the paper's statement that "We find that LETFs’ multi-day returns closely align with those of non-reset portfolios across most indices and holding periods (up to one year)." Maybe up to one year. The abstract says "While substantial deviations can occur under high volatility and long holding periods..." which was what I illustrated. It says "... they are positively skewed and generally favorable," which was not the case.

Appropriate rebalancing intervals reduces with degree of leverage. For 2x once/year rebalancing will tend to suffice, for 3x you'd want to rebalance every 6 months, for Zvi Bodie's 10x (via Options) ... monthly. Outside of that and the drifts are more inclined to become "significant".

[seajay]

The drifts however can be beneficial, "similar" shorter term outcomes drifting enough to be "different" over the mid term.

Consider that 25/75 3x stock/gold can approximate 1x. So instead of 67/33 SPY/cash holding 17/50/33 3x/gold/cash

With SPY (SPXL 3x)
https://www.portfoliovisualizer.com/bac ... FxO8vyuZgS

With QQQ (TQQQ 3x)
https://www.portfoliovisualizer.com/bac ... Fgcxea6J5R

rebalanced once/year ... and generally similar outcomes. A coin flip as to which of the two might be better/worse.

Extended back (using synthetic data) 30 year MaxWR outcomes since 1933 (when 'fiat' started to be introduced via the compulsory purchase of gold, to which a investor might have held silver ... up to 1976 when holding gold again became permitted)



and each had their good/bad times, where if we focus upon the bad cases it was better to have diversified across both (33/9/25/33 SPY/3x/gold/cash) rather than one of the individuals alone.

[Investing Lawyer]

Thank you for sharing. Here's my summary in case its helpful for others.

This paper compares a leveraged ETF which is rebalanced daily using swaps versus borrowing a fixed amount of margin to get equivalent exposure. It's comparing leverage to leverage and not a leveraged ETF to an unlevered benchmark as other papers have done, which is a good comparison to think through. The paper finds that leveraged ETFs will match close enough with the fixed borrowing amount leverage style. It also uses empirics of observed autocorrelation to show that leveraged ETFs can outperform the fixed period margin result.

A couple disclosures are in order. First, this paper was funded by Proshares. Second, it doesn't use the geometric brownian construction for returns as other papers have done. It uses a discrete time period return formula, and attempts to "correct" other papers' formulas for leveraged ETF returns.

There is one part of this paper that strikes me as manifestly odd, and in my opinion, incorrect:

Furthermore, Equation (6), the expected return of an LETF, does not depend on volatility
(σ) (contrast with points #2 above).

I've held leveraged ETFs for years and use futures as well. The expected return of any leveraged investment does depend on volatility. The Proshares prospectus for their LETFs confirms this in their charts breaking down returns at different volatility levels. Ed Thorpe's equations conclude the same. I am unable to explain why the paper comes to a different conclusion, and I lack the chops and interest to challenge his proofs.

However, nothing in this paper will change my behavior: I use LETFs for my 401k and futures for my taxable.

[nisiprius]

...First, this paper was funded by Proshares...

Missed that. Thanks for noticing.

[jdibber]

Thought the conclusion was quite bold, then saw this, first footnote page 1

"We thank Mark Flannery, Stephen Horan, Xuewei Yang, and Xiaoyan Zhang for their valuable comments. The author acknowledges funding for this project from ProShares Advisors, LLC."

I'm a leverage fan, would have preferred an independent analysis.

[edit, beat me to it, nisiprius]

[Nathan Drake]

Thank you for sharing. Here's my summary in case its helpful for others.

This paper compares a leveraged ETF which is rebalanced daily using swaps versus borrowing a fixed amount of margin to get equivalent exposure. It's comparing leverage to leverage and not a leveraged ETF to an unlevered benchmark as other papers have done, which is a good comparison to think through. The paper finds that leveraged ETFs will match close enough with the fixed borrowing amount leverage style. It also uses empirics of observed autocorrelation to show that leveraged ETFs can outperform the fixed period margin result.

A couple disclosures are in order. First, this paper was funded by Proshares. Second, it doesn't use the geometric brownian construction for returns as other papers have done. It uses a discrete time period return formula, and attempts to "correct" other papers' formulas for leveraged ETF returns.

There is one part of this paper that strikes me as manifestly odd, and in my opinion, incorrect:

Furthermore, Equation (6), the expected return of an LETF, does not depend on volatility
(σ) (contrast with points #2 above).

I've held leveraged ETFs for years and use futures as well. The expected return of any leveraged investment does depend on volatility. The Proshares prospectus for their LETFs confirms this in their charts breaking down returns at different volatility levels. Ed Thorpe's equations conclude the same. I am unable to explain why the paper comes to a different conclusion, and I lack the chops and interest to challenge his proofs.

However, nothing in this paper will change my behavior: I use LETFs for my 401k and futures for my taxable.

Which LETFs do you use?

[Investing Lawyer]

....

Which LETFs do you use?

Currently, mostly just TQQQ and a tiny bit of remaining TMF. In the past, I've held all of the main 3x and 2x one: UPRO, SSO, QLD.

My theoretical framework for daily rebalanced leveraged ETFs, using a brownian motion framework, is that they work best when the drift component is large in relation to volatility. So equity index LETFS will be the best real world application of the whole daily rebalanced idea.

[jdibber]

Which LETFs do you use?

Same here, TQQQ and UPRO. As bitcoin has slowly crept to correlating w/ stock market, I've been dabbling with BITX. NTSX is a nice buy and hold if you're trying to squeak extra room in your AA.