Simulating Returns of Leveraged ETFs

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expecting_unexpected
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Re: Simulating Returns of Leveraged ETFs

Post by expecting_unexpected »

jarjarM wrote: Wed Mar 24, 2021 2:57 am Don’t do 4x (not that there’s one in existence at the moment), a 25% drop will wipe out the LETF. 1987 drop was 22.7%, pretty close to that. Buy and hold 3x LETF is requires understanding the substantial risk that comes with it along with it. You should check out how UPRO performed in the last 18 months vs SPY. It dropped 77% vs 34% for SPY.
After 1987, U.S. regulations implements three levels of a circuit breaker, set to halt trading when the S&P 500 Index drops 7%, 13%, and 20%. Last year's crash proved that circuit breakers worked as expected and UPRO avoided a total wipeout in the event of a 34% drop of SPY. The impact of a 34% drop over several days on leveraged ETFs is drastically different from the same amount of drop in a single day!

IMHO, this is the most under-appreciated property of UPRO and similarly leveraged ETFs -- It's "antifragile", a term coined by Nassim Nicholas Taleb. For small fluctuations in SPY and short time windows, UPRO generally yields ~3X returns. However, over a longer time window, a large drop in SPY generates less than 3X drop in UPRO while a large gain in SPY yields much greater than 3X return in UPRO. If you have a risk parity portfolio and rebalance only on major melt ups/downs rather than regularly (and prematurely), you can better take advantage of the property.
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jarjarM
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Re: Simulating Returns of Leveraged ETFs

Post by jarjarM »

expecting_unexpected wrote: Fri Jul 02, 2021 4:14 pm
jarjarM wrote: Wed Mar 24, 2021 2:57 am Don’t do 4x (not that there’s one in existence at the moment), a 25% drop will wipe out the LETF. 1987 drop was 22.7%, pretty close to that. Buy and hold 3x LETF is requires understanding the substantial risk that comes with it along with it. You should check out how UPRO performed in the last 18 months vs SPY. It dropped 77% vs 34% for SPY.
After 1987, U.S. regulations implements three levels of a circuit breaker, set to halt trading when the S&P 500 Index drops 7%, 13%, and 20%. Last year's crash proved that circuit breakers worked as expected and UPRO avoided a total wipeout in the event of a 34% drop of SPY. The impact of a 34% drop over several days on leveraged ETFs is drastically different from the same amount of drop in a single day!

IMHO, this is the most under-appreciated property of UPRO and similarly leveraged ETFs -- It's "antifragile", a term coined by Nassim Nicholas Taleb. For small fluctuations in SPY and short time windows, UPRO generally yields ~3X returns. However, over a longer time window, a large drop in SPY generates less than 3X drop in UPRO while a large gain in SPY yields much greater than 3X return in UPRO. If you have a risk parity portfolio and rebalance only on major melt ups/downs rather than regularly (and prematurely), you can better take advantage of the property.
Yes, and this being discussed substantially at HFEA thread as well. To be clear, I hold significant amount of LETFs but I'm fully aware of its risk and drawback. There's also quite a bit of discussion and backtesting done to understand benefits of various rebalancing method as well. I prefer a modified version of TAA.

P.S. Interesting profile pic, must have a good story behind it.
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Jughead79
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Re: Simulating Returns of Leveraged ETFs

Post by Jughead79 »

siamond wrote: Sun Jan 24, 2021 1:56 pm
siamond wrote: Fri Jan 15, 2021 5:37 pm I completed my first round of updates for the monthly simulated returns, essentially extending the model to 2020 for all series and updating the comparisons to real-life LETFs. This proved to be quite some work, so many data series to deal with...

I plan to do another round of updates, reworking the bond series for the first few decades, as new historical data emerged which should significantly improve the quality of the data for the time periods where a formal index wasn't available. I should get to it the coming week.

Folks who were waiting impatiently for this update, please contact me via private message. Otherwise, you may want to hold a bit longer until I complete the 2nd round of updates.
Ok, I'm finally done with my updates (I hope!). Same link for those of you who contacted me.

I updated all bonds series with the following improvements (which should moderately affect the first few decades of returns):
- refreshed all yield numbers from FRED
- better modeling technique to simulate biannual distributions
- direct modeling of all relevant indices (i.e. 1-3, 3-7, 7-10 and 20-30) as opposed to more indirect proxies
@Siamond, first I just want to say thanks to you and everyone else in this discussion who's contributed to simulating these ETFs. I've read through the entire thread and very much appreciate everyone's efforts.

I tried to PM you to ask for the simulated monthly returns, but I guess I'm still too new here to be able to PM anyone yet. Could you please PM me? Thanks in advance. Cheers.
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adamhg
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Re: Simulating Returns of Leveraged ETFs

Post by adamhg »

I was able to get a pretty decent result simulating KOLD (and BOIL) with @blackswan 's notebook based off daily ohlc from https://www.investing.com/indices/bbg-natural-gas-tr.

You can pull the last 5000 daily records through their charting api.
Unfortunately, that only takes us back to 2001, so if anybody has access to either Bloomberg Natural Gas Subindex or Bloomberg WTI Crude Oil Subindex full historical data, I'd love to run this farther back.

ETA: Was able to pull the full historical index using my downloader: https://github.com/adamhwang/InvestingQuotes

Here's both BOIL/KOLD and UCO/SCO's index since 11/2/2001 pulled from investing.com:

Here're all four sims results:
ETA: See below for full historical index sim

UCO/SCO are probably not terribly reliable, but BOIL/KOLD seem decent. Here are blackswan's error metrics for the sim above:

Code: Select all

UCO:BCOMCLTR.csv 	params: expense_incr=0.0168
RMSE: 0.1102, MAE: 0.0853, RETRMSE: 0.0153, RETMAE: 0.0084, CAGR: 0.0108, VOL: 0.0759, P99: 0.3096
CUMRET: sim 1.0075 + actual -0.9964 = -0.9927

SCO:BCOMCLTR.csv 	params: expense_incr=-0.0035
RMSE: 0.1332, MAE: 0.0756, RETRMSE: 0.0569, RETMAE: 0.0095, CAGR: -0.0324, VOL: -0.3374, P99: 0.4222
CUMRET: sim -0.9806 + actual -0.9421 = -0.9989

BOIL:BCOMNGTR.csv 	params: expense_incr=0.0014
RMSE: 0.0114, MAE: 0.0086, RETRMSE: 0.0138, RETMAE: 0.0093, CAGR: -0.0005, VOL: 0.0394, P99: 0.0385
CUMRET: sim -0.9998 + actual -0.9981 = -1.0000

KOLD:BCOMNGTR.csv 	params: expense_incr=0.0084
RMSE: 0.0121, MAE: 0.0094, RETRMSE: 0.0138, RETMAE: 0.0094, CAGR: 0.0027, VOL: 0.0386, P99: 0.0366
CUMRET: sim -0.3460 + actual -0.5235 = -0.6884
Last edited by adamhg on Thu Sep 16, 2021 4:36 pm, edited 6 times in total.
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Re: Simulating Returns of Leveraged ETFs

Post by adamhg »

So after trying to get a better fit for UCO/SCO, it becomes obvious that either the ETFs or the index changed during COVID:
Image

Up until then though, it appears to be a fairly consistent simulation. So after re-running only up through 2019, the telltale and error values looks much better:
Image

Code: Select all

UCO:BCOMCLTR.csv 	params: expense_incr=0.0011
RMSE: 0.0111, MAE: 0.0077, RETRMSE: 0.0126, RETMAE: 0.0076, CAGR: -0.0006, VOL: 0.0449, P99: 0.034
CUMRET: sim 1.2208 + actual -0.9792 = -0.9538

SCO:BCOMCLTR.csv 	params: expense_incr=-0.0011
RMSE: 0.0122, MAE: 0.0096, RETRMSE: 0.0119, RETMAE: 0.0075, CAGR: 0.0022, VOL: 0.037, P99: 0.0348
CUMRET: sim -0.9818 + actual -0.7069 = -0.9947

Here's a new sim for both UCO and SCO, only run through 2019


ETA: I found the full history for BCOMCLTR and BCOMNGTR! Here're the sims to the beginnings of each index:
Last edited by adamhg on Thu Sep 16, 2021 4:31 pm, edited 1 time in total.
skierincolorado
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Re: Simulating Returns of Leveraged ETFs

Post by skierincolorado »

Volatility decay shouldn't exist long run. If it did, we could arbitrage it by buying 100k of SPY in one account, and shorting 33k of UPRO in another. After 10 years, the 100k of SPY should have gone up more than the 33k of UPRO we shorted. This would have worked very well from 2000-2010 and very poorly 2010-2020. Overall, over a long enough period there shouldn't be much volatility decay - and we are seeing the amount of decay 2000-present start to diminish.
moptop
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Re: Simulating Returns of Leveraged ETFs

Post by moptop »

Okay, I'm struggling here. Does the Simba Spreadsheet have daily data for historically simulated upro? If so how do I find it? I have the spreadsheet downloaded. Thanks for the work guys!
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typical.investor
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Re: Simulating Returns of Leveraged ETFs

Post by typical.investor »

skierincolorado wrote: Thu Sep 16, 2021 2:46 pm Volatility decay shouldn't exist long run. If it did, we could arbitrage it by buying 100k of SPY in one account, and shorting 33k of UPRO in another. After 10 years, the 100k of SPY should have gone up more than the 33k of UPRO we shorted. This would have worked very well from 2000-2010 and very poorly 2010-2020. Overall, over a long enough period there shouldn't be much volatility decay - and we are seeing the amount of decay 2000-present start to diminish.
This is not factually correct. The volatility decay is unknown. It could even be a volatility boost.

It’s not predictable and not short-able. And we can’t assume it’s mean reverting.

Skierincolorado likes repeatedly posting wrong information. I’d ignore it.
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Re: Simulating Returns of Leveraged ETFs

Post by typical.investor »

skierincolorado wrote: Thu Sep 16, 2021 2:46 pm Volatility decay shouldn't exist long run. If it did, we could arbitrage it by buying 100k of SPY in one account, and shorting 33k of UPRO in another. After 10 years, the 100k of SPY should have gone up more than the 33k of UPRO we shorted. This would have worked very well from 2000-2010 and very poorly 2010-2020. Overall, over a long enough period there shouldn't be much volatility decay - and we are seeing the amount of decay 2000-present start to diminish.
This is not factually correct. The volatility decay is unknown. It could even be a volatility boost.

It’s not predictable and not short-able. And we can’t assume it’s mean reverting.

Skierincolorado likes repeatedly posting wrong information. I’d ignore it.

This is theoretically and empirically shown.
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Re: Simulating Returns of Leveraged ETFs

Post by moptop »

typical.investor wrote: Tue Oct 12, 2021 2:01 am
skierincolorado wrote: Thu Sep 16, 2021 2:46 pm Volatility decay shouldn't exist long run. If it did, we could arbitrage it by buying 100k of SPY in one account, and shorting 33k of UPRO in another. After 10 years, the 100k of SPY should have gone up more than the 33k of UPRO we shorted. This would have worked very well from 2000-2010 and very poorly 2010-2020. Overall, over a long enough period there shouldn't be much volatility decay - and we are seeing the amount of decay 2000-present start to diminish.
This is not factually correct. The volatility decay is unknown. It could even be a volatility boost.

It’s not predictable and not short-able. And we can’t assume it’s mean reverting.

Skierincolorado likes repeatedly posting wrong information. I’d ignore it.

This is theoretically and empirically shown.
it actually sounds to me like you are agreeing with him. You are both saying there isn't consistent decay, but just saying it in a different way.
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typical.investor
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Re: Simulating Returns of Leveraged ETFs

Post by typical.investor »

moptop wrote: Tue Oct 12, 2021 8:34 am
typical.investor wrote: Tue Oct 12, 2021 2:01 am
skierincolorado wrote: Thu Sep 16, 2021 2:46 pm Volatility decay shouldn't exist long run. If it did, we could arbitrage it by buying 100k of SPY in one account, and shorting 33k of UPRO in another. After 10 years, the 100k of SPY should have gone up more than the 33k of UPRO we shorted. This would have worked very well from 2000-2010 and very poorly 2010-2020. Overall, over a long enough period there shouldn't be much volatility decay - and we are seeing the amount of decay 2000-present start to diminish.
This is not factually correct. The volatility decay is unknown. It could even be a volatility boost.

It’s not predictable and not short-able. And we can’t assume it’s mean reverting.

Skierincolorado likes repeatedly posting wrong information. I’d ignore it.

This is theoretically and empirically shown.
it actually sounds to me like you are agreeing with him. You are both saying there isn't consistent decay, but just saying it in a different way.
Well that doesn't mean that volatility can't have a significant effect on the returns of an ETF with a daily leverage reset- only that the effect in your holding period will be unknown.

To say there can't be an effect because someone would short it if there were isn't correct.
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Re: Simulating Returns of Leveraged ETFs

Post by skierincolorado »

moptop wrote: Tue Oct 12, 2021 8:34 am
typical.investor wrote: Tue Oct 12, 2021 2:01 am
skierincolorado wrote: Thu Sep 16, 2021 2:46 pm Volatility decay shouldn't exist long run. If it did, we could arbitrage it by buying 100k of SPY in one account, and shorting 33k of UPRO in another. After 10 years, the 100k of SPY should have gone up more than the 33k of UPRO we shorted. This would have worked very well from 2000-2010 and very poorly 2010-2020. Overall, over a long enough period there shouldn't be much volatility decay - and we are seeing the amount of decay 2000-present start to diminish.
This is not factually correct. The volatility decay is unknown. It could even be a volatility boost.

It’s not predictable and not short-able. And we can’t assume it’s mean reverting.

Skierincolorado likes repeatedly posting wrong information. I’d ignore it.

This is theoretically and empirically shown.
it actually sounds to me like you are agreeing with him. You are both saying there isn't consistent decay, but just saying it in a different way.
Exactly.
skierincolorado
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Re: Simulating Returns of Leveraged ETFs

Post by skierincolorado »

typical.investor wrote: Tue Oct 12, 2021 10:17 am
moptop wrote: Tue Oct 12, 2021 8:34 am
typical.investor wrote: Tue Oct 12, 2021 2:01 am
skierincolorado wrote: Thu Sep 16, 2021 2:46 pm Volatility decay shouldn't exist long run. If it did, we could arbitrage it by buying 100k of SPY in one account, and shorting 33k of UPRO in another. After 10 years, the 100k of SPY should have gone up more than the 33k of UPRO we shorted. This would have worked very well from 2000-2010 and very poorly 2010-2020. Overall, over a long enough period there shouldn't be much volatility decay - and we are seeing the amount of decay 2000-present start to diminish.
This is not factually correct. The volatility decay is unknown. It could even be a volatility boost.

It’s not predictable and not short-able. And we can’t assume it’s mean reverting.

Skierincolorado likes repeatedly posting wrong information. I’d ignore it.

This is theoretically and empirically shown.
it actually sounds to me like you are agreeing with him. You are both saying there isn't consistent decay, but just saying it in a different way.
Well that doesn't mean that volatility can't have a significant effect on the returns of an ETF with a daily leverage reset- only that the effect in your holding period will be unknown.

To say there can't be an effect because someone would short it if there were isn't correct.
I didn’t say there is no effect. But if there were a large highly significant effect, then yes, it would be very easy to make a risk free profit by shorting UPRO and buying SPY.

When I say "volatility decay is not real" I mean that the idea that LETFs are doomed to dramatically underperform their gearing ratio over long time horizons is false. They might overperform even over a long period of 20+ years. They will likely be reasonably close (say +/-50%) of their gearing ratio over a 20+ year period. And this is supported by both real and simulated LETF returns of 20+ years.
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Re: Simulating Returns of Leveraged ETFs

Post by seajay »

skierincolorado wrote: Tue Oct 12, 2021 11:28 amWhen I say "volatility decay is not real" I mean that the idea that LETFs are doomed to dramatically underperform their gearing ratio over long time horizons is false. They might overperform even over a long period of 20+ years. They will likely be reasonably close (say +/-50%) of their gearing ratio over a 20+ year period. And this is supported by both real and simulated LETF returns of 20+ years.
Consider a very simplistic LETF that rebalances yearly instead of daily and is closed to sales/purchases. For each $1 of shares bought the fund borrows another $1 and buys $2 of stock exposure. To borrow the fund could issue bonds, so if a investor with $100 invested half in the 2x, half in buying the bonds ignoring costs they'd have 100% 1x stock exposure.

But what if stocks crashed 66%. Well the $100 of stock exposure would have declined to $33 and the fund owes $50 to its bond-holders, negative equity of -$17. By rebalancing daily instead of yearly that risk is mitigated as it scales into compounded percentages, excepting if stocks dropped 50% or more in a single day, but the market has brakes to halt trading well before that.

Measured on a half in 2x, half in bonds, rebalanced frequently, compared to 100% in the 1x and the two might be expected to track relatively closely. However looking at 50/50 2x/bonds rebalanced monthly compared to rebalanced yearly and yearly rebalanced tracked more closely. It would seem that trend following, deferring rebalancing served to add-value.

Deferring rebalancing when stocks are trending sees attenuated declines. If at day 1 you're holding $50/$50 stock/bonds and that transitions to being $40/$50 then selling some of bonds to add to stocks increases stock exposure, so if the trend continues you lose relatively more compared to not having rebalanced. Similarly if $50/$50 sees that transition to $60/$40 and the upward trend continues, then having sold some stock to buy more bonds to reset back to 50/50 % weightings sees less gains than not having rebalanced.

In the real world leveraged funds in effect borrow to scale up exposure. Lenders will want a premium for lending. Generally that premium might be relatively little, perhaps 1.5% above T-Bills/LIBOR/whatever average. BBB type rating costs perhaps, and as such half in 2x, half in bonds as a 100% 1x alternative is inclined to see some lag. That lag however might be similar whether interest rates are at near 0% recent type levels or whether they're at 15% 1980's type levels. Taxes however could play a significant role. 15% interest rates, 16.5% cost to borrow, with half of your money in bonds earning 15% interest but paying 3% in (20% tax), and the difference had widened to 4.5% (2.25% relative lag of 50/50 2x/bonds compared to 100% 1x).

Low rates and upward trends have been great for LETF's and the likes of HFEA. Under different circumstances ???
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Re: Simulating Returns of Leveraged ETFs

Post by skierincolorado »

seajay wrote: Thu Oct 14, 2021 6:02 am
skierincolorado wrote: Tue Oct 12, 2021 11:28 amWhen I say "volatility decay is not real" I mean that the idea that LETFs are doomed to dramatically underperform their gearing ratio over long time horizons is false. They might overperform even over a long period of 20+ years. They will likely be reasonably close (say +/-50%) of their gearing ratio over a 20+ year period. And this is supported by both real and simulated LETF returns of 20+ years.
Consider a very simplistic LETF that rebalances yearly instead of daily and is closed to sales/purchases. For each $1 of shares bought the fund borrows another $1 and buys $2 of stock exposure. To borrow the fund could issue bonds, so if a investor with $100 invested half in the 2x, half in buying the bonds ignoring costs they'd have 100% 1x stock exposure.

But what if stocks crashed 66%. Well the $100 of stock exposure would have declined to $33 and the fund owes $50 to its bond-holders, negative equity of -$17. By rebalancing daily instead of yearly that risk is mitigated as it scales into compounded percentages, excepting if stocks dropped 50% or more in a single day, but the market has brakes to halt trading well before that.

Measured on a half in 2x, half in bonds, rebalanced frequently, compared to 100% in the 1x and the two might be expected to track relatively closely. However looking at 50/50 2x/bonds rebalanced monthly compared to rebalanced yearly and yearly rebalanced tracked more closely. It would seem that trend following, deferring rebalancing served to add-value.

Deferring rebalancing when stocks are trending sees attenuated declines. If at day 1 you're holding $50/$50 stock/bonds and that transitions to being $40/$50 then selling some of bonds to add to stocks increases stock exposure, so if the trend continues you lose relatively more compared to not having rebalanced. Similarly if $50/$50 sees that transition to $60/$40 and the upward trend continues, then having sold some stock to buy more bonds to reset back to 50/50 % weightings sees less gains than not having rebalanced.

In the real world leveraged funds in effect borrow to scale up exposure. Lenders will want a premium for lending. Generally that premium might be relatively little, perhaps 1.5% above T-Bills/LIBOR/whatever average. BBB type rating costs perhaps, and as such half in 2x, half in bonds as a 100% 1x alternative is inclined to see some lag. That lag however might be similar whether interest rates are at near 0% recent type levels or whether they're at 15% 1980's type levels. Taxes however could play a significant role. 15% interest rates, 16.5% cost to borrow, with half of your money in bonds earning 15% interest but paying 3% in (20% tax), and the difference had widened to 4.5% (2.25% relative lag of 50/50 2x/bonds compared to 100% 1x).

Low rates and upward trends have been great for LETF's and the likes of HFEA. Under different circumstances ???
The premium isn't 1.5%. LETFs borrow very close to LIBOR. If LIBOR is high though that can be a drag. Both theoretically and empirically, LETFs return reasonably close (+/-50%) to their gearing ratio over long periods (pre-fees and pre-financing costs).
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Re: Simulating Returns of Leveraged ETFs

Post by cuckoohash »

expecting_unexpected wrote: Fri Jul 02, 2021 4:14 pm
jarjarM wrote: Wed Mar 24, 2021 2:57 am Don’t do 4x (not that there’s one in existence at the moment), a 25% drop will wipe out the LETF. 1987 drop was 22.7%, pretty close to that. Buy and hold 3x LETF is requires understanding the substantial risk that comes with it along with it. You should check out how UPRO performed in the last 18 months vs SPY. It dropped 77% vs 34% for SPY.
After 1987, U.S. regulations implements three levels of a circuit breaker, set to halt trading when the S&P 500 Index drops 7%, 13%, and 20%. Last year's crash proved that circuit breakers worked as expected and UPRO avoided a total wipeout in the event of a 34% drop of SPY. The impact of a 34% drop over several days on leveraged ETFs is drastically different from the same amount of drop in a single day!

IMHO, this is the most under-appreciated property of UPRO and similarly leveraged ETFs -- It's "antifragile", a term coined by Nassim Nicholas Taleb. For small fluctuations in SPY and short time windows, UPRO generally yields ~3X returns. However, over a longer time window, a large drop in SPY generates less than 3X drop in UPRO while a large gain in SPY yields much greater than 3X return in UPRO. If you have a risk parity portfolio and rebalance only on major melt ups/downs rather than regularly (and prematurely), you can better take advantage of the property.
Circuit breaker halts the market by the end of the trading day, but it does not prevent it from opening at a lower price the next day. I think you can’t do anything to liquidate your position until the market reopens the next day in the event of circuit breaking, can you? Would that be a risk?
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Re: Simulating Returns of Leveraged ETFs

Post by bgf »

I thought "volatility decay" was just a poetic phrase for 'we calculate compounding returns by using the geometric mean.'

Is there anything in "volatility decay" that is not otherwise fully explained by how geometric means react to outlier data points?
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siamond
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Re: Simulating Returns of Leveraged ETFs

Post by siamond »

bgf wrote: Sun Dec 26, 2021 7:20 pm I thought "volatility decay" was just a poetic phrase for 'we calculate compounding returns by using the geometric mean.'

Is there anything in "volatility decay" that is not otherwise fully explained by how geometric means react to outlier data points?
You're correct. It's just that when volatility is multiplied by 2x or 3x, the consequences on the geometric mean (vs. the more intuitive arithmetic mean) can be rather jarring.
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Re: Simulating Returns of Leveraged ETFs

Post by expecting_unexpected »

cuckoohash wrote: Sun Dec 26, 2021 6:30 pm
expecting_unexpected wrote: Fri Jul 02, 2021 4:14 pm
jarjarM wrote: Wed Mar 24, 2021 2:57 am Don’t do 4x (not that there’s one in existence at the moment), a 25% drop will wipe out the LETF. 1987 drop was 22.7%, pretty close to that. Buy and hold 3x LETF is requires understanding the substantial risk that comes with it along with it. You should check out how UPRO performed in the last 18 months vs SPY. It dropped 77% vs 34% for SPY.
After 1987, U.S. regulations implements three levels of a circuit breaker, set to halt trading when the S&P 500 Index drops 7%, 13%, and 20%. Last year's crash proved that circuit breakers worked as expected and UPRO avoided a total wipeout in the event of a 34% drop of SPY. The impact of a 34% drop over several days on leveraged ETFs is drastically different from the same amount of drop in a single day!

IMHO, this is the most under-appreciated property of UPRO and similarly leveraged ETFs -- It's "antifragile", a term coined by Nassim Nicholas Taleb. For small fluctuations in SPY and short time windows, UPRO generally yields ~3X returns. However, over a longer time window, a large drop in SPY generates less than 3X drop in UPRO while a large gain in SPY yields much greater than 3X return in UPRO. If you have a risk parity portfolio and rebalance only on major melt ups/downs rather than regularly (and prematurely), you can better take advantage of the property.
Circuit breaker halts the market by the end of the trading day, but it does not prevent it from opening at a lower price the next day. I think you can’t do anything to liquidate your position until the market reopens the next day in the event of circuit breaking, can you? Would that be a risk?
Why do you want to liquidate your position in the event of major market crash? It's the exact time to increase your equity exposure.

For example, suppose that your portfolio have 50% in UPRO and 50% TMF. There is a major crash, e.g. 5 consecutive 20% daily drops (much severe than coronavirus crash). Your equity exposure (UPRO) will lose ~99%* of its value (but not completely wipe out), but your bond (TMF) should spike, say 2X. If you stick to your 50~50% split, you will move half of your TMF to UPRO. Even if it takes 10 or 20 years (comparable to great depression) for the market (UPRO) to recover, it's a lifetime opportunity (100X).

* 1 - (1-.2x3)^5 = ~99%
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Re: Simulating Returns of Leveraged ETFs

Post by cuckoohash »

expecting_unexpected wrote: Thu Jan 06, 2022 1:39 am
cuckoohash wrote: Sun Dec 26, 2021 6:30 pm
expecting_unexpected wrote: Fri Jul 02, 2021 4:14 pm
jarjarM wrote: Wed Mar 24, 2021 2:57 am Don’t do 4x (not that there’s one in existence at the moment), a 25% drop will wipe out the LETF. 1987 drop was 22.7%, pretty close to that. Buy and hold 3x LETF is requires understanding the substantial risk that comes with it along with it. You should check out how UPRO performed in the last 18 months vs SPY. It dropped 77% vs 34% for SPY.
After 1987, U.S. regulations implements three levels of a circuit breaker, set to halt trading when the S&P 500 Index drops 7%, 13%, and 20%. Last year's crash proved that circuit breakers worked as expected and UPRO avoided a total wipeout in the event of a 34% drop of SPY. The impact of a 34% drop over several days on leveraged ETFs is drastically different from the same amount of drop in a single day!

IMHO, this is the most under-appreciated property of UPRO and similarly leveraged ETFs -- It's "antifragile", a term coined by Nassim Nicholas Taleb. For small fluctuations in SPY and short time windows, UPRO generally yields ~3X returns. However, over a longer time window, a large drop in SPY generates less than 3X drop in UPRO while a large gain in SPY yields much greater than 3X return in UPRO. If you have a risk parity portfolio and rebalance only on major melt ups/downs rather than regularly (and prematurely), you can better take advantage of the property.
Circuit breaker halts the market by the end of the trading day, but it does not prevent it from opening at a lower price the next day. I think you can’t do anything to liquidate your position until the market reopens the next day in the event of circuit breaking, can you? Would that be a risk?
Why do you want to liquidate your position in the event of major market crash? It's the exact time to increase your equity exposure.

For example, suppose that your portfolio have 50% in UPRO and 50% TMF. There is a major crash, e.g. 5 consecutive 20% daily drops (much severe than coronavirus crash). Your equity exposure (UPRO) will lose ~99%* of its value (but not completely wipe out), but your bond (TMF) should spike, say 2X. If you stick to your 50~50% split, you will move half of your TMF to UPRO. Even if it takes 10 or 20 years (comparable to great depression) for the market (UPRO) to recover, it's a lifetime opportunity (100X).

* 1 - (1-.2x3)^5 = ~99%
I get your point. Yes, it makes sense to maintain a constant balanced portfolio.

But I was meant to discuss a hypothetical scenario where circuit breaker might not be able to prevent 3x ETF from being wiped out. Let’s say the market drops 20% on the first day and the second day opens with another 20% drop (this is an extreme case but let’s assume it happens), would the 3x ETF fund manager still be able to maintain the constant daily leverage ratio by liquidating or hedging some of its positions during this period? If not, the 36% drop would wipe out the fund.
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Re: Simulating Returns of Leveraged ETFs

Post by typical.investor »

cuckoohash wrote: Thu Jan 06, 2022 2:37 am
expecting_unexpected wrote: Thu Jan 06, 2022 1:39 am
cuckoohash wrote: Sun Dec 26, 2021 6:30 pm
expecting_unexpected wrote: Fri Jul 02, 2021 4:14 pm
jarjarM wrote: Wed Mar 24, 2021 2:57 am Don’t do 4x (not that there’s one in existence at the moment), a 25% drop will wipe out the LETF. 1987 drop was 22.7%, pretty close to that. Buy and hold 3x LETF is requires understanding the substantial risk that comes with it along with it. You should check out how UPRO performed in the last 18 months vs SPY. It dropped 77% vs 34% for SPY.
After 1987, U.S. regulations implements three levels of a circuit breaker, set to halt trading when the S&P 500 Index drops 7%, 13%, and 20%. Last year's crash proved that circuit breakers worked as expected and UPRO avoided a total wipeout in the event of a 34% drop of SPY. The impact of a 34% drop over several days on leveraged ETFs is drastically different from the same amount of drop in a single day!

IMHO, this is the most under-appreciated property of UPRO and similarly leveraged ETFs -- It's "antifragile", a term coined by Nassim Nicholas Taleb. For small fluctuations in SPY and short time windows, UPRO generally yields ~3X returns. However, over a longer time window, a large drop in SPY generates less than 3X drop in UPRO while a large gain in SPY yields much greater than 3X return in UPRO. If you have a risk parity portfolio and rebalance only on major melt ups/downs rather than regularly (and prematurely), you can better take advantage of the property.
Circuit breaker halts the market by the end of the trading day, but it does not prevent it from opening at a lower price the next day. I think you can’t do anything to liquidate your position until the market reopens the next day in the event of circuit breaking, can you? Would that be a risk?
Why do you want to liquidate your position in the event of major market crash? It's the exact time to increase your equity exposure.

For example, suppose that your portfolio have 50% in UPRO and 50% TMF. There is a major crash, e.g. 5 consecutive 20% daily drops (much severe than coronavirus crash). Your equity exposure (UPRO) will lose ~99%* of its value (but not completely wipe out), but your bond (TMF) should spike, say 2X. If you stick to your 50~50% split, you will move half of your TMF to UPRO. Even if it takes 10 or 20 years (comparable to great depression) for the market (UPRO) to recover, it's a lifetime opportunity (100X).

* 1 - (1-.2x3)^5 = ~99%
I get your point. Yes, it makes sense to maintain a constant balanced portfolio.

But I was meant to discuss a hypothetical scenario where circuit breaker might not be able to prevent 3x ETF from being wiped out. Let’s say the market drops 20% on the first day and the second day opens with another 20% drop (this is an extreme case but let’s assume it happens), would the 3x ETF fund manager still be able to maintain the constant daily leverage ratio by liquidating or hedging some of its positions during this period? If not, the 36% drop would wipe out the fund.
Hi! I am a bit worried by the implications of your question. To me it suggests you believe that *IF* the fund doesn't get wiped out, that it *WILL* recover assuming equities overall recover.

That is not true though given what we know about the leverage reset and how volatility can combine with the leverage reset to potentially generate returns that are even in the opposite direction of the market.

I use 3X funds myself and am not a scare mongrel, but I am concerned.

Here is what I plan if the 3X fund gets wiped out or get nearly wiped out under high volatility [makes no difference - both cases will have returns far below the 3X the index (after costs)]. Another scenario is that the fund is closed. To me, you are remiss if you have not planned for all.

The simple solution (in concept but more difficult in practice) is to maintain exposure. As such, I have a futures account open and know how to use it to maintain leverage if the fund is closed.

The solution to a negative volatility effect [and again I don't mean to be a scaremonger, we haven't seen this in the life of the 3X funds but the possibility is real] which seems more likely in a wipeout or near wipeout is to re-leverage. Say I have $100k in VTI and 10K in UPRO for a total exposure of $130k, and say the market drops by 50%. Effectively I will then have only $50k. I want, though, to have $65k in exposure so that if the market then recovers back to even, I will too.

HedgeFundies Excellent Adventure uses leveraged treasuries to provide funds for re-leveraging your equity exposure. I think it will work. If though, we see rates rise for a while in a stagflation type environment, that won't help. Bonds won't provide a means to re-establish your leverage.

My fallback strategy to re-leverage then is to sell VTI and buy UPRO (or futures if UPRO has closed) to bring me back to the desired exposure. In my example above, where I have 50K in VTI and UPRO was wiped out, I would sell around $8k or so of VTI and buy UPRO so my exposure would still be near $65k.

I don't ever expect that to happen, but if it does I will do that.

Of course, this limits how much leverage you can employ (could't be 100% in a 3X equity fund), but give the risks of volatility loss that a 3X fund faces in a sideways market, you (or at least someone with my risk tolerance) shouldn't be doing that anyway.
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Re: Simulating Returns of Leveraged ETFs

Post by expecting_unexpected »

cuckoohash wrote: Thu Jan 06, 2022 2:37 am
expecting_unexpected wrote: Thu Jan 06, 2022 1:39 am
cuckoohash wrote: Sun Dec 26, 2021 6:30 pm
expecting_unexpected wrote: Fri Jul 02, 2021 4:14 pm
jarjarM wrote: Wed Mar 24, 2021 2:57 am Don’t do 4x (not that there’s one in existence at the moment), a 25% drop will wipe out the LETF. 1987 drop was 22.7%, pretty close to that. Buy and hold 3x LETF is requires understanding the substantial risk that comes with it along with it. You should check out how UPRO performed in the last 18 months vs SPY. It dropped 77% vs 34% for SPY.
After 1987, U.S. regulations implements three levels of a circuit breaker, set to halt trading when the S&P 500 Index drops 7%, 13%, and 20%. Last year's crash proved that circuit breakers worked as expected and UPRO avoided a total wipeout in the event of a 34% drop of SPY. The impact of a 34% drop over several days on leveraged ETFs is drastically different from the same amount of drop in a single day!

IMHO, this is the most under-appreciated property of UPRO and similarly leveraged ETFs -- It's "antifragile", a term coined by Nassim Nicholas Taleb. For small fluctuations in SPY and short time windows, UPRO generally yields ~3X returns. However, over a longer time window, a large drop in SPY generates less than 3X drop in UPRO while a large gain in SPY yields much greater than 3X return in UPRO. If you have a risk parity portfolio and rebalance only on major melt ups/downs rather than regularly (and prematurely), you can better take advantage of the property.
Circuit breaker halts the market by the end of the trading day, but it does not prevent it from opening at a lower price the next day. I think you can’t do anything to liquidate your position until the market reopens the next day in the event of circuit breaking, can you? Would that be a risk?
Why do you want to liquidate your position in the event of major market crash? It's the exact time to increase your equity exposure.

For example, suppose that your portfolio have 50% in UPRO and 50% TMF. There is a major crash, e.g. 5 consecutive 20% daily drops (much severe than coronavirus crash). Your equity exposure (UPRO) will lose ~99%* of its value (but not completely wipe out), but your bond (TMF) should spike, say 2X. If you stick to your 50~50% split, you will move half of your TMF to UPRO. Even if it takes 10 or 20 years (comparable to great depression) for the market (UPRO) to recover, it's a lifetime opportunity (100X).

* 1 - (1-.2x3)^5 = ~99%
I get your point. Yes, it makes sense to maintain a constant balanced portfolio.

But I was meant to discuss a hypothetical scenario where circuit breaker might not be able to prevent 3x ETF from being wiped out. Let’s say the market drops 20% on the first day and the second day opens with another 20% drop (this is an extreme case but let’s assume it happens), would the 3x ETF fund manager still be able to maintain the constant daily leverage ratio by liquidating or hedging some of its positions during this period? If not, the 36% drop would wipe out the fund.

I see what you mean now. Yes, there is a risk associated with all leveraged ETF/ETNs on how the providers implement the leverage. In the event of extreme stress, the exact actions that providers take could be a make-or-break factor. One famous example is XIV and SVXY, one was wiped out and the other survived.

Another implementation risk could be counter-party risk. When leveraged ETF started more than a decade ago, the net asset of these leveraged ETFs, e.g. FAS/UPRO/TQQQ, is less than or around a couple of billions, and the corresponding short ETFs have similar AUM. After long bull market, TQQQ has ballooned to 12.4B and SQQQ 1.75 B. This skew is probably caused by buy-and-hold participants.

If the trend continues, I could imagine that, one day, the total AUM of leveraged long ETFs would grow so big that it could swing and exacerbate the daily movement of the market. It might impose significant risk to all banks and counterparties providing the leverage. If some leverage providers have a large exposure to the wrong side movement of the market like AIG, and government doesn't step in to bail it out, we could see the collapse of some leveraged ETFs.
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Re: Simulating Returns of Leveraged ETFs

Post by expecting_unexpected »

typical.investor wrote: Thu Jan 06, 2022 1:26 pm Hi! I am a bit worried by the implications of your question. To me it suggests you believe that *IF* the fund doesn't get wiped out, that it *WILL* recover assuming equities overall recover.
Mathematically speaking, if the underlying, e.g. SPY, has an infinite time horizon and positive geometry mean, a constantly leveraged position would eventually outperform the unleveraged underlying infinitely as long as the circuit breaker prevents complete ruins of the levered position.

Of course, this must not happen in reality. Something will always break due to the cost of leverage and other implementation factors. Therefore, in practice, you have to make a personal decision 1) how faithfully the providers can implement the leveraged as advertised; 2) whether the market will recover during your lifetime; and 3) whether you have enough financial cushion to wait for the recovery.
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Re: Simulating Returns of Leveraged ETFs

Post by expecting_unexpected »

typical.investor wrote: Thu Jan 06, 2022 1:26 pm Of course, this limits how much leverage you can employ (could't be 100% in a 3X equity fund), but give the risks of volatility loss that a 3X fund faces in a sideways market, you (or at least someone with my risk tolerance) shouldn't be doing that anyway.
I actually think daily reset and volatility decay are second order consideration for leveraged portfolio. The paramount consideration if you apply leverage should be whether and how you survive once-in-a-decade or once-in-a-lifetime market crashes. If you do, the leverage will take care of the rest. If you don't, you're doomed.

One thing to keep in mind is, in the event of extreme stress, the margin requirement and leverage cost will increase dramatically and liquidity will vanish overnight, as demonstrated during 2008/9 financial crisis.
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Re: Simulating Returns of Leveraged ETFs

Post by typical.investor »

expecting_unexpected wrote: Thu Jan 06, 2022 2:22 pm
typical.investor wrote: Thu Jan 06, 2022 1:26 pm Hi! I am a bit worried by the implications of your question. To me it suggests you believe that *IF* the fund doesn't get wiped out, that it *WILL* recover assuming equities overall recover.
Mathematically speaking, if the underlying, e.g. SPY, has an infinite time horizon and positive geometry mean, a constantly leveraged position would eventually outperform the unleveraged underlying infinitely as long as the circuit breaker prevents complete ruins of the levered position.
Which is exactly what I said.
expecting_unexpected wrote: Thu Jan 06, 2022 2:22 pm Of course, this must not happen in reality. Something will always break due to the cost of leverage and other implementation factors. Therefore, in practice, you have to make a personal decision 1) how faithfully the providers can implement the leveraged as advertised; 2) whether the market will recover during your lifetime; and 3) whether you have enough financial cushion to wait for the recovery.
In practice, I believe there is also 4) whether a 3X leveraged fund and it's daily reset would negatively affect you in a sideways market.
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Re: Simulating Returns of Leveraged ETFs

Post by expecting_unexpected »

typical.investor wrote: Thu Jan 06, 2022 3:02 pm In practice, I believe there is also 4) whether a 3X leveraged fund and it's daily reset would negatively affect you in a sideways market.
yeah, "japanification" is also in the back of my mind :-)
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Re: Simulating Returns of Leveraged ETFs

Post by typical.investor »

expecting_unexpected wrote: Thu Jan 06, 2022 2:58 pm
typical.investor wrote: Thu Jan 06, 2022 1:26 pm Of course, this limits how much leverage you can employ (could't be 100% in a 3X equity fund), but give the risks of volatility loss that a 3X fund faces in a sideways market, you (or at least someone with my risk tolerance) shouldn't be doing that anyway.
I actually think daily reset and volatility loss are second order consideration for leveraged portfolio. The paramount consideration if you apply leverage should be whether and how you survive once-in-a-decade or once-in-a-lifetime market crashes. If you do, the leverage will take care of the rest. If you don't, you're doomed.

One thing you keep in mind is the margin requirement and leverage cost will increase dramatically and liquidity will vanish in the event of extreme stress, as demonstrated during 2008/9 financial crisis.
Yes, increased margin requirements is an additional concern I didn't mention.

As for volatility loss being a secondary consideration, perhaps but proper risk management requires you to address it.

If the index (e.g. SPY) returns 5% per year indefinitely, and the index volatility is 25%, you will go broke as the 3X leveraged fund will be returning -4% yearly instead of the 15% that you might expect. (see page 43 https://www.proshares.com/globalassets/ ... mation.pdf)
expecting_unexpected wrote: Thu Jan 06, 2022 1:39 am Why do you want to liquidate your position in the event of major market crash? It's the exact time to increase your equity exposure.

For example, suppose that your portfolio have 50% in UPRO and 50% TMF. There is a major crash, e.g. 5 consecutive 20% daily drops (much severe than coronavirus crash). Your equity exposure (UPRO) will lose ~99%* of its value (but not completely wipe out), but your bond (TMF) should spike, say 2X. If you stick to your 50~50% split, you will move half of your TMF to UPRO. Even if it takes 10 or 20 years (comparable to great depression) for the market (UPRO) to recover, it's a lifetime opportunity (100X).
I agree you need to increase exposure in a 3X fund after a crash. I did so in March 2020. However, one can not assume that TMF will always spike when UPRO crashes. Triple leverages long term treasuries will suffer tremendously with rate hikes. It's always been assumed that stagflation was off the table and that higher rates would coincide with a booming economy. What we are seeing now is that an inflationary globalization rollback might be in the cards and COVID certainly is raising costs and harming productivity.

So as usual, an investor should be prepared for the effects of sideways movement without the benefit or treasury values rising to save the portfolio; or that investor may panic and abandon the strategy as the most inopportune time.

Saying not to worry about the real potential of a volatility effect (especially given high valuations) and assuming that treasuries will stabilizing things isn't good planning I think.
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Re: Simulating Returns of Leveraged ETFs

Post by typical.investor »

expecting_unexpected wrote: Thu Jan 06, 2022 3:11 pm
typical.investor wrote: Thu Jan 06, 2022 3:02 pm In practice, I believe there is also 4) whether a 3X leveraged fund and it's daily reset would negatively affect you in a sideways market.
yeah, "japanification" is also in the back of my mind :-)
Sure, but I think triple leveraged Japanese equities with triple leveraged long US treasuries would have been fine because of the absence of inflation and ability to rebalance back in from appreciating bonds.

Sideways volatility induced loss in both equities and treasuries is really the achilles heel in HFEA, and the only way around it is to be able to contribute more until at least one of those things recover. Not saying I expect this to happen, but just we should be aware of the possibility so as to mentally prepare.
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Re: Simulating Returns of Leveraged ETFs

Post by expecting_unexpected »

typical.investor wrote: Thu Jan 06, 2022 3:21 pm As for volatility loss being a secondary consideration, perhaps but proper risk management requires you to address it.

If the index (e.g. SPY) returns 5% per year indefinitely, and the index volatility is 25%, you will go broke as the 3X leveraged fund will be returning -4% yearly instead of the 15% that you might expect. (see page 43 https://www.proshares.com/globalassets/ ... mation.pdf)
I think I understand your point on volatility loss, but focusing on volatility number alone might miss some life-and-death moments.

If the index, e.g. SPY, experiences extreme volatility, it's usually triggered by some kind of major market dislocations. The YTD returns might be 5%, or an arbitrary positive, flat, or negative number, and these are accidental artifacts largely determined by when the year starts and ends and how the event unfolds. Your predominant concern during that period will be how to survive and react to the major event causing the spike of volatility. Your optionality and reaction in a very short period will determine whether you are seriously wounded or thrive on such rare events.

* An interesting case is 2010 flash crash, the fluctuation of normalized returns is far more violent than 1987 crash, dot.com bubble burst, 2008/9 crisis, or 2020 covid crash, but it won't show up on any simulation using daily stats.

BTW. The "japanification" I'm worried about to is a prolonged sideway movement of the market, like Nikkei index in the past 30 years. In order for 3X leveraged portfolio work in the long run, the determining factor is the geometry mean of market return during your lifetime.
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Re: Simulating Returns of Leveraged ETFs

Post by knowledge.needer »

Hi, loving the thread. I have been trying to find simulated leveraged ETFs for etfs other than UPRO or s&p500 based LEFTs. Specifically im interested in simulated returns for TQQQ? thanks in advance.
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Re: Simulating Returns of Leveraged ETFs

Post by adamhg »

knowledge.needer wrote: Wed Jan 12, 2022 8:53 pm Hi, loving the thread. I have been trying to find simulated leveraged ETFs for etfs other than UPRO or s&p500 based LEFTs. Specifically im interested in simulated returns for TQQQ? thanks in advance.
blackswan wrote: Mon Jan 25, 2021 2:36 am OK, I've updated my simulations, too.

https://nbviewer.jupyter.org/urls/gitla ... ETFs.ipynb

NOW with over 50 leveraged ETFs! New and improved more accurate data!**
**(Probably. I hope. :wink: )

CSV:
https://gitlab.com/doctorj/quantitative ... line=false
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Re: Simulating Returns of Leveraged ETFs

Post by Phyneas »

expecting_unexpected wrote: Fri Jul 02, 2021 4:14 pm
jarjarM wrote: Wed Mar 24, 2021 2:57 am Don’t do 4x (not that there’s one in existence at the moment), a 25% drop will wipe out the LETF. 1987 drop was 22.7%, pretty close to that. Buy and hold 3x LETF is requires understanding the substantial risk that comes with it along with it. You should check out how UPRO performed in the last 18 months vs SPY. It dropped 77% vs 34% for SPY.
After 1987, U.S. regulations implements three levels of a circuit breaker, set to halt trading when the S&P 500 Index drops 7%, 13%, and 20%. Last year's crash proved that circuit breakers worked as expected and UPRO avoided a total wipeout in the event of a 34% drop of SPY. The impact of a 34% drop over several days on leveraged ETFs is drastically different from the same amount of drop in a single day!

IMHO, this is the most under-appreciated property of UPRO and similarly leveraged ETFs -- It's "antifragile", a term coined by Nassim Nicholas Taleb. For small fluctuations in SPY and short time windows, UPRO generally yields ~3X returns. However, over a longer time window, a large drop in SPY generates less than 3X drop in UPRO while a large gain in SPY yields much greater than 3X return in UPRO. If you have a risk parity portfolio and rebalance only on major melt ups/downs rather than regularly (and prematurely), you can better take advantage of the property.
I hope this doesn't derail the thread, but something I've wondered about with leveraged ETFs, specifically 3x ones, is if there is an over-night gap-down risk. I don't understand the circuit breaker rules very well, but don't they only apply during trading hours? If there is a flash-crash over-night, or whatever event precipitates it, and the markets gap-down between close and open, isn't there still a risk of a 3x equity LETF, maybe even a 2x equity LETF, going to 0 by sunrise?
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Re: Simulating Returns of Leveraged ETFs

Post by siamond »

knowledge.needer wrote: Wed Jan 12, 2022 8:53 pm Hi, loving the thread. I have been trying to find simulated leveraged ETFs for etfs other than UPRO or s&p500 based LETFs. Specifically I'm interested in simulated returns for TQQQ? thanks in advance.
Trouble is we can easily find the price series ("NASDAQ Composite PR USD") starting from Feb 1971, but what we really need is the total return series ("NASDAQ Composite TR USD") and I can't find credible numbers for this one before 1995... And without such total return (dividends included) numbers of the core index, we can't assemble a proper simulation. Sorry! :(
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Re: Simulating Returns of Leveraged ETFs

Post by Gecko10x »

siamond wrote: Wed Feb 17, 2021 12:28 pm After some meandering, I finally came back to updating our backtesting spreadsheet (aka Simba), customized with LETF annual returns. This includes my latest research about historical numbers, so the data is a tad different from what I shared a couple of years ago, although the big picture shouldn't have changed much.

Download the custom spreadsheet here (Excel file): https://drive.google.com/file/d/1H5DvKA ... sp=sharing

More information about the Simba backtesting spreadsheet: https://www.bogleheads.org/wiki/Simba%2 ... preadsheet
Awesome! Super helpful!
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Re: Simulating Returns of Leveraged ETFs

Post by brendon4565 »

siamond wrote: Sat Mar 09, 2019 1:11 pm
HEDGEFUNDIE wrote: Sat Mar 09, 2019 12:39 pmStay tuned everybody, it's gonna be a wild ride :D
Yeah, 'wild ride' is the exact right way to put it... You'll see... :mrgreen:

PS. I'm fine with you sharing the monthly leveraged numbers that you input to Portfolio Visualizer. Just not the underlying data that led to those numbers. I'll do something similar with a Simba derivative.
Hi Siamond, could you share the monthly simulated numbers of UPRO and TMF going back to 1956? It would be of great help for some backtests that I am trying to do.
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Re: Simulating Returns of Leveraged ETFs

Post by drumboy256 »

I'll let you know in about 20 years as I'm running TNA, TQQQ, UPRO and TMF in 25% chunks; makes me wonder if all of the ETFs will still be around in 20 years....!? :sharebeer
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Re: Simulating Returns of Leveraged ETFs

Post by DarkMatter731 »

drumboy256 wrote: Tue Mar 29, 2022 12:06 am I'll let you know in about 20 years as I'm running TNA, TQQQ, UPRO and TMF in 25% chunks; makes me wonder if all of the ETFs will still be around in 20 years....!? :sharebeer
I mean ETFs being around shouldn't really be a problem in the slightest - they probably will be and you can simply use futures if they're not for all 4 of the ETFs you've listed.

That's not even a concern.
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Re: Simulating Returns of Leveraged ETFs

Post by Jil »

Phyneas wrote: Thu Jan 13, 2022 7:52 am
expecting_unexpected wrote: Fri Jul 02, 2021 4:14 pm
jarjarM wrote: Wed Mar 24, 2021 2:57 am Don’t do 4x (not that there’s one in existence at the moment), a 25% drop will wipe out the LETF. 1987 drop was 22.7%, pretty close to that. Buy and hold 3x LETF is requires understanding the substantial risk that comes with it along with it. You should check out how UPRO performed in the last 18 months vs SPY. It dropped 77% vs 34% for SPY.
After 1987, U.S. regulations implements three levels of a circuit breaker, set to halt trading when the S&P 500 Index drops 7%, 13%, and 20%. Last year's crash proved that circuit breakers worked as expected and UPRO avoided a total wipeout in the event of a 34% drop of SPY. The impact of a 34% drop over several days on leveraged ETFs is drastically different from the same amount of drop in a single day!

IMHO, this is the most under-appreciated property of UPRO and similarly leveraged ETFs -- It's "antifragile", a term coined by Nassim Nicholas Taleb. For small fluctuations in SPY and short time windows, UPRO generally yields ~3X returns. However, over a longer time window, a large drop in SPY generates less than 3X drop in UPRO while a large gain in SPY yields much greater than 3X return in UPRO. If you have a risk parity portfolio and rebalance only on major melt ups/downs rather than regularly (and prematurely), you can better take advantage of the property.
I hope this doesn't derail the thread, but something I've wondered about with leveraged ETFs, specifically 3x ones, is if there is an over-night gap-down risk. I don't understand the circuit breaker rules very well, but don't they only apply during trading hours? If there is a flash-crash over-night, or whatever event precipitates it, and the markets gap-down between close and open, isn't there still a risk of a 3x equity LETF, maybe even a 2x equity LETF, going to 0 by sunrise?
I don't understand the circuit breaker rules very well, but don't they only apply during trading hours? => The max drawdown of SPX is 20% in a day, and UPRO is 60% in a day as the last circuit breaker (20%) halts trading for the whole day.
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hiddenpower
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Re: Simulating Returns of Leveraged ETFs

Post by hiddenpower »

blackswan wrote: Mon Jan 25, 2021 2:36 am OK, I've updated my simulations, too.

https://nbviewer.jupyter.org/urls/gitla ... ETFs.ipynb

NOW with over 50 leveraged ETFs! New and improved more accurate data!**
**(Probably. I hope. :wink: )

CSV:
https://gitlab.com/doctorj/quantitative ... line=false

The main update is empirical selection of a curve-fitting model, i.e., which variables do we "fudge." TL;DR: a simple additive constant is best, and throwing out bad data is even better.

Taking Uncorrelated and siamond's suggestions, I assembled about 50 leveraged ETFs and mutual funds, fit models to the last half, and measured their accuracy on the first half. I also threw out any "rough start" data at the start of each ETF's history, determined by manually eyeballing the fit. (Wouldn't you know, this usually boils down to throwing out ProShares data before 2009 and Direxion data before 2013.)

So: model selection. I took the basic equation:

Code: Select all

lev = factor * ret - exp - (factor - 1) * borrow
And added fudge factors: scaling the leverage factor, applied to returns only (A); adding to the leverage factor that multiples borrow rates (B); scaling the borrow rate (C); and an overall additive constant (D).

Code: Select all

lev = factor * A * ret - exp - (factor + B - 1) * borrow * C + D
I then took all 16 possible subsets of fudge factors A B C D and found the best fit with that subset on the most recent half of the data, for each of the ~50 leveraged funds independently. That is, for each combination of fitting each parameter or leaving it at the default (1 for scales, 0 for increments), I found the best fit on the last half of the fund, then measured the error on the first half. I used median relative RMSE (of the telltale) as the main figure of merit; this essentially weights each fund equally. Fitting only D (an overall additive constant) gives the best out-of-sample RMSE of .0124 and the smallest IQR spread, followed closely by the combo of A and D (factor scale and additive constant) at .0129. D is typically in the range .001 to .01 (annualized).

I also tried adding a factor for T-bill rates, but it didn't really help.

One nice additional property of only using a single additive constant is that it makes it easy to spot bad data from a telltale.

The single additive constant is also very near the best when including bad data (RMSE within .004), so it's fairly robust. Incidentally most leveraged funds had large misses during the coronavirus crash in March 2020, which also tweaks the fit. I did not exclude it for the overall final fit because it didn't make a huge difference. In the "future work" department, filtering individual large outlier days (large deviations from "the formula") and/or bootstrapping could provide an even more robust fit.

However, the results are already not terrible. Using the single-constant model and fitting all the data (except bad initial data), all simulated funds are virtually always within 30% of actual over the life of the fund. Most funds are within 6%. The median (absolute) CAGR difference is .003 and the largest is .014.

Image

So, just to be explicit, the final model / formula is:

Code: Select all

lev = factor * ret - exp - (factor - 1) * borrow + D
where D is the only curve-fit parameter.

I included leveraged mutual funds in model selection because they have a good long history. They seem to be playing the same basic game under the hood as ETFs, but if there are reasons why they would not use the same leverage formula, let me know. Incidentally, I had to throw out many mutual funds because Yahoo just has complete garbage prices for them. Their charts are correct, but the historical data download is completely different.

Let me know what you think!
This is straight up epic. Has anyone had success importing multiple series into portfoliovisualizer? i've been able to do it when I strip down the csv to a single series (then set to daily index values), but I get errors with the bulk import.
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hiddenpower
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Re: Simulating Returns of Leveraged ETFs

Post by hiddenpower »

Additionally, does anyone have a SIM dating back to the 70s or 80s? I'd love to experiment with these LETFs during a period of high inflation
kicker9977
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Re: Simulating Returns of Leveraged ETFs

Post by kicker9977 »

Siamond,

Thank you so much for your hard work on this! I just came across the thread and was riveted reading all of it. Would you be so kind as to share the historic models that you put together? Thanks in advance!
Hydromod
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Re: Simulating Returns of Leveraged ETFs

Post by Hydromod »

kicker9977 wrote: Tue Nov 08, 2022 12:26 pm Siamond,

Thank you so much for your hard work on this! I just came across the thread and was riveted reading all of it. Would you be so kind as to share the historic models that you put together? Thanks in advance!
Siamond has said that you'd get faster responses nowadays if you PM him.
johnsmithsf
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Re: Simulating Returns of Leveraged ETFs

Post by johnsmithsf »

seajay wrote: Thu Oct 14, 2021 6:02 am
Measured on a half in 2x, half in bonds, rebalanced frequently, compared to 100% in the 1x and the two might be expected to track relatively closely. However looking at 50/50 2x/bonds rebalanced monthly compared to rebalanced yearly and yearly rebalanced tracked more closely. It would seem that trend following, deferring rebalancing served to add-value.
You didn't do it right, that's why your monthly balanced leveraged portfolio of 50% 2x S&P500 + 50% Bonds is underperforming S&P500.

You have to use ETFs like SSO (2X S&P500), UPRO/ SPXL (3x S&P500), as they are more efficient and less costly than mutual funds for this leveraged strategy.

A monthly balancing portfolio of 50% 2x S&P500 + 50% Total Bond Index , or 34% 3x S&P500 + 66% Total Bond Index, will slightly OUTPERFORM 100% S&P500 VFINX but at the same time cannot lose more than 50% or 33% of value respectively even if S&P500 drops 99% due a sudden catastrophe.

https://www.portfoliovisualizer.com/bac ... tion4_3=34
Kbg
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Re: Simulating Returns of Leveraged ETFs

Post by Kbg »

The Nasdaq 100 is similar and your last para is why I do leveraged ETFs (at least 50% is left) and if you have the gumption at some point to refill the leverage tank it is very likely you will be smiling after 2-3 years due to the out performance of leveraged ETFs in low volatility bull markets.

However, I think a safe assumption is the results will be close and will be path dependent over longer term holds.
chris319
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Re: Simulating Returns of Leveraged ETFs

Post by chris319 »

I have updated my LETF simulator which I created last year. The simulator was created in collaboration with others on this forum. It applies a daily leverage multiplier and various "friction" costs such as expense ratio, etc.

Here are the results updated through 11/8/2022:

NDX (NASDAQ 100) from 10/1/1985 (9354 trading days)

1X: CAGR = 13.2%

2X CAGR = 17.4%

3X CAGR = 14.9%

That is not a typo: the 2X fund actually did better than the 3X fund during the period under test.
Financial decisions based on emotion often turn out to be bad decisions.
Hydromod
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Re: Simulating Returns of Leveraged ETFs

Post by Hydromod »

johnsmithsf wrote: Tue Nov 08, 2022 6:08 pm
seajay wrote: Thu Oct 14, 2021 6:02 am
Measured on a half in 2x, half in bonds, rebalanced frequently, compared to 100% in the 1x and the two might be expected to track relatively closely. However looking at 50/50 2x/bonds rebalanced monthly compared to rebalanced yearly and yearly rebalanced tracked more closely. It would seem that trend following, deferring rebalancing served to add-value.
You didn't do it right, that's why your monthly balanced leveraged portfolio of 50% 2x S&P500 + 50% Bonds is underperforming S&P500.

You have to use ETFs like SSO (2X S&P500), UPRO/ SPXL (3x S&P500), as they are more efficient and less costly than mutual funds for this leveraged strategy.

A monthly balancing portfolio of 50% 2x S&P500 + 50% Total Bond Index , or 34% 3x S&P500 + 66% Total Bond Index, will slightly OUTPERFORM 100% S&P500 VFINX but at the same time cannot lose more than 50% or 33% of value respectively even if S&P500 drops 99% due a sudden catastrophe.

https://www.portfoliovisualizer.com/bac ... tion4_3=34
If you break down the estimates into shorter durations, you'll notice that essentially the entire difference in outcome from rebalancing monthly vs. annually over the period from 1998 to 2021 is explained by the difference in performance over the months of November and December, 2008.

That seems like a slender reed to be a basis for any sweeping conclusions on rebalancing strategy merits.
comeinvest
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Re: Simulating Returns of Leveraged ETFs

Post by comeinvest »

Hydromod wrote: Wed Nov 09, 2022 7:15 am
johnsmithsf wrote: Tue Nov 08, 2022 6:08 pm
seajay wrote: Thu Oct 14, 2021 6:02 am
Measured on a half in 2x, half in bonds, rebalanced frequently, compared to 100% in the 1x and the two might be expected to track relatively closely. However looking at 50/50 2x/bonds rebalanced monthly compared to rebalanced yearly and yearly rebalanced tracked more closely. It would seem that trend following, deferring rebalancing served to add-value.
You didn't do it right, that's why your monthly balanced leveraged portfolio of 50% 2x S&P500 + 50% Bonds is underperforming S&P500.

You have to use ETFs like SSO (2X S&P500), UPRO/ SPXL (3x S&P500), as they are more efficient and less costly than mutual funds for this leveraged strategy.

A monthly balancing portfolio of 50% 2x S&P500 + 50% Total Bond Index , or 34% 3x S&P500 + 66% Total Bond Index, will slightly OUTPERFORM 100% S&P500 VFINX but at the same time cannot lose more than 50% or 33% of value respectively even if S&P500 drops 99% due a sudden catastrophe.

https://www.portfoliovisualizer.com/bac ... tion4_3=34
If you break down the estimates into shorter durations, you'll notice that essentially the entire difference in outcome from rebalancing monthly vs. annually over the period from 1998 to 2021 is explained by the difference in performance over the months of November and December, 2008.

That seems like a slender reed to be a basis for any sweeping conclusions on rebalancing strategy merits.
Conversely, wouldn't the Mar 2020 dip then grossly benefit the monthly rebalancing, as yearly rebalancing lost out on this rebalancing opportunity?
Hydromod
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Re: Simulating Returns of Leveraged ETFs

Post by Hydromod »

comeinvest wrote: Wed Nov 09, 2022 5:11 pm Conversely, wouldn't the Mar 2020 dip then grossly benefit the monthly rebalancing, as yearly rebalancing lost out on this rebalancing opportunity?
There was a bit of a difference using the example (ULPIX and VBMFX), but 1/20 through 12/21 had a CAGR of 20.84% (annual) vs. 21.66% (monthly). Pretty much all May through August 2020.

Deviations due to rebalancing strategy are more important with 3x funds than with 2x/1x, I guess.
johnsmithsf
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Re: Simulating Returns of Leveraged ETFs

Post by johnsmithsf »

Hydromod wrote: Wed Nov 09, 2022 7:15 am
johnsmithsf wrote: Tue Nov 08, 2022 6:08 pm
seajay wrote: Thu Oct 14, 2021 6:02 am
Measured on a half in 2x, half in bonds, rebalanced frequently, compared to 100% in the 1x and the two might be expected to track relatively closely. However looking at 50/50 2x/bonds rebalanced monthly compared to rebalanced yearly and yearly rebalanced tracked more closely. It would seem that trend following, deferring rebalancing served to add-value.
You didn't do it right, that's why your monthly balanced leveraged portfolio of 50% 2x S&P500 + 50% Bonds is underperforming S&P500.

You have to use ETFs like SSO (2X S&P500), UPRO/ SPXL (3x S&P500), as they are more efficient and less costly than mutual funds for this leveraged strategy.

A monthly balancing portfolio of 50% 2x S&P500 + 50% Total Bond Index , or 34% 3x S&P500 + 66% Total Bond Index, will slightly OUTPERFORM 100% S&P500 VFINX but at the same time cannot lose more than 50% or 33% of value respectively even if S&P500 drops 99% due a sudden catastrophe.

https://www.portfoliovisualizer.com/bac ... tion4_3=34
If you break down the estimates into shorter durations, you'll notice that essentially the entire difference in outcome from rebalancing monthly vs. annually over the period from 1998 to 2021 is explained by the difference in performance over the months of November and December, 2008.

That seems like a slender reed to be a basis for any sweeping conclusions on rebalancing strategy merits.
ULPIX is just an inferior instrument when compared with SSO

See this plot over last 10 years
https://www.portfoliovisualizer.com/bac ... tion3_2=50
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siamond
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Re: Simulating Returns of Leveraged ETFs

Post by siamond »

I finally took some time to finish a blog article documenting the modeling effort we went through in this precise thread. Hopefully, this should help as a reference for subsequent research. Feedback welcome.

In the past decade, a specialized type of fund gained increased popularity, funds implementing leverage over a given index. A previous blog article explored funds leveraging the S&P 500 index and a follow-up article explored a portfolio-level approach mixing stocks and treasury bonds. Unfortunately, leveraged funds have relatively little history, making it difficult to assess trajectories in various economic situations. This article will focus on simulation techniques used to model what leveraged funds might have returned in the past, from 1955 till recently.

https://www.bogleheads.org/blog/2022/12 ... -modeling/
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