Are 3x leveraged ETFs the long-term winning strategy?

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Hydromod
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by Hydromod »

chris319 wrote: Thu Apr 08, 2021 6:34 pm It was a chore but I managed to get ^GSPC daily data into a spreadsheet going back to December 30, 1927.

I implemented a LETF simulator in the spreadsheet. The leverage sweet spot is 2x. The worst one-day loss was on October 19,1987, losing 40.9%.

3x leverage is great in bullish times but 2x (SSO) is the better all-weather leverage through bull and bear markets.

At 2x leverage, CAGR is "only" 8.3%. $10,000 became $17,003,711.

Past performance is no guarantee of future results.
This is a great example of the sensitivity to starting point. December 30, 1927 is near the top of a big bubble, having just doubled in price over 5 years (and a bit more to climb). You get a horrendous drop soon afterward, which would drop the 3x fund 2.5 orders of magnitude relative to the starting point by 1932 and 3 orders of magnitude by 1942.

It makes a huge difference if one starts before, during, or after a big bubble.

Starting in at the rebound peak in 1937, right before the 3x index would have dropped 30-fold to 1942, and the 3x would still have returned 11.7% to date (2x => 10.7, 2.5x => 11.6%). Rather different return.

I agree, 2x leverage would probably have been more bearable. It appears that the 3x would have been slightly better, but I expect that expenses would have taken care of that.

If I calculate correctly, 1x would have returned 5.96% from 12/30/1927 and 6.65% from 1/1/1937.

I'm not advocating buy-and-hold UPRO or SSO in isolation by any means, I wouldn't dream of it myself, but my point is that it may make sense to draw conclusions based on a starting point roughly similar to current conditions rather than extremes. If you think we are near the top of a bubble, then perhaps a starting point on a bubble makes sense. If not, perhaps start away from a bubble. I'm pretty sure we aren't at the trough right now though!
chris319
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by chris319 »

why not use the peer-reviewed (well, Boglehead-reviewed, at least) siamond model?
Where do I find it?

The math behind these things is not complicated. The point of contention is the periodic interest rate. I assume an expense ratio of 0.95% and add it to the daily interest.
Financial decisions based on emotion often turn out to be bad decisions.
chris319
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by chris319 »

I'm not advocating buy-and-hold UPRO or SSO in isolation by any means, I wouldn't dream of it myself, but my point is that it may make sense to draw conclusions based on a starting point roughly similar to current conditions rather than extremes. If you think we are near the top of a bubble, then perhaps a starting point on a bubble makes sense. If not, perhaps start away from a bubble.
I don't have access to data prior to 1928. Even if I did, I wouldn't cherry-pick the start date based on subjective analysis of market action.

You need nerves of steel to hang on to these LETFs through the dips. On the bright side, you'll never get a margin call if you don't own them on margin.
Financial decisions based on emotion often turn out to be bad decisions.
DMoogle
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by DMoogle »

chris319 wrote: Thu Apr 08, 2021 8:32 pm
why not use the peer-reviewed (well, Boglehead-reviewed, at least) siamond model?
Where do I find it?

The math behind these things is not complicated. The point of contention is the periodic interest rate. I assume an expense ratio of 0.95% and add it to the daily interest.
There's a link to it here: viewtopic.php?f=10&t=272007&start=1050#p4426310

It's been said before, but it's really worth reading the whole Simulating Leveraged ETFs thread.
britcoal
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by britcoal »

Apologies to all - I have not read the entire thread - but I do want to ask a question. I see the dangers of using 3X leveraged ETFs 100% all the time.. but what about using 3X leveraged ETFs whenever one sees a 30%+ drop in the market? Yes, there is still risk, but if things don't return to normal we're all pretty screwed, right? It seems like a good time to take advantage of a discount and multiply that. I suppose there is the danger of a prolonged downturn..
DMoogle
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by DMoogle »

britcoal wrote: Thu Apr 08, 2021 11:25 pm Apologies to all - I have not read the entire thread - but I do want to ask a question. I see the dangers of using 3X leveraged ETFs 100% all the time.. but what about using 3X leveraged ETFs whenever one sees a 30%+ drop in the market? Yes, there is still risk, but if things don't return to normal we're all pretty screwed, right? It seems like a good time to take advantage of a discount and multiply that. I suppose there is the danger of a prolonged downturn..
Two flaws in your thinking: (1) you're basically trying to time the bottom - is 30% the bottom, or will it drop down to 40%? Or more? (2) it sounds like you're assuming that the market will "recover," i.e. reach its previous price point quickly. The 2008/2009 crash did, and so did the pandemic crash last year, but that is not always the case. It's a bit of a cliche at this point, but look at Japan as an example.
jarjarM
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by jarjarM »

britcoal wrote: Thu Apr 08, 2021 11:25 pm Apologies to all - I have not read the entire thread - but I do want to ask a question. I see the dangers of using 3X leveraged ETFs 100% all the time.. but what about using 3X leveraged ETFs whenever one sees a 30%+ drop in the market? Yes, there is still risk, but if things don't return to normal we're all pretty screwed, right? It seems like a good time to take advantage of a discount and multiply that. I suppose there is the danger of a prolonged downturn..
Market dropping another 30% after dropping 30% is possible. That's really just total of 50% drop, which happened twice in the "lost decade" of 2000s. Also, Japan has the biggest financial market by market cap on 1989 at 45% of global market cap (of course that's after a huge run up in the 80s) and it still hasn't return back to that high 30+ years later. Not saying it will happen to US market but just pointing out that a stock market bubble burst may not have as dramatic of an effect on the countries economy.
chris319
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by chris319 »

The S&P 500 index as we know it today came into existence on March 4, 1957. I have created an alternate version which goes back to 3-4-1957. Using data from 1957 forward the sweet spot is 3x.

What is salient from the 7-page thread on simulating LETF's?
Financial decisions based on emotion often turn out to be bad decisions.
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

Hydromod wrote: Thu Apr 08, 2021 11:03 am
I did some fairly exhaustive testing a while back.

It turns out that end of month and end of quarter have historically been especially favorable rebalancing points. These are what PV uses. Using other parts of the quarter gave worse results than monthly.

Daily rebalancing would have been best without trading costs and slippage, but disappoint when these are accounted for.

Whether this behavior persists going forward, who knows.
So if I understand you correctly, you are saying that it makes a difference whether one rebalances at the 31st day of the month of each quarter instead of on the 15th or any other day? How is that possible? Doesn't this create a massive arbitrage opportunity?

Could you show me the data and calculations that show that daily rebalancing would be superior theoretically?
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

MotoTrojan wrote: Thu Apr 08, 2021 11:05 am
I am showing relative performance compared to S&P500. Returns aren't absolute for your strategy, they are relative to the S&P500.

Small-value did well over 14% if you go back to the 1955 window as you have shown, but again, relative returns is all you can expect.
Could you show me the evidence that suggests that small cap value would have done that much better in the past?

I haven't done a ton of research in that area, but Ben Felix recently published a video on multifator investing which showed a table showing that most factor premiums delivered about 2+% more than the opposite factor, meaning that they outperformed even less than that when comparing it to a total stock market index. (https://youtu.be/jKWbW7Wgm0w at 9:12)

Also, I am a bit skeptical that historical backtesting is as useful in that particular case, as much more people are looking for value (and other factors) today then they were before Warren Buffet got famous.
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

MotoTrojan wrote: Thu Apr 08, 2021 11:10 am
If it only works in one market, that suggests it is not a well founded strategy but is just overfitting. I am not talking about one-off situations like Japan. How would the 70% daily-resetting 3x equity exposure had worked in ex-US stocks? Or even total world? I bet you it would be pretty ugly with massive volatility decay.

The US market has been an anomaly. You are going into this assuming it is a good basis for the future. A sound process will work in other markets, and this one doesn't pass that test.

If you are in-fact back-testing to 1955 then good, that is a full cycle for interest rates at-least and is representative of what TMF would've seen, but I still think that period of US equity returns is not a good baseline for what to expect in the future.
Why do you assume that US stocks did that much better than global stocks? If that were the case, even the dumbest investor would have realized by now that the US is the only place where stocks are allowed to grow and US stocks would have a global market cap of 100%.

In fact, these things are pretty cyclical. Sometimes US stocks do better, sometimes international stocks do better.
Image

Just to be clear, I am generally not against international diversification, but in this case there isn't a practical way to do so.
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

MotoTrojan wrote: Thu Apr 08, 2021 11:15 am Hydromods backtest included a sweeping starting point, where-as tradri you are also putting rebalance timing luck into the mix since Portfolio Visualizer is looking at annual calendar rebalances only. I think quarterly is the best mix of trading costs and optimization personally, but as Hydro said, in theory daily is the best.
I do acknowledge that quarterly rebalancing is better than yearly.

Also, I am not using Portfolio Visualizer to simulate the leveraged ETFs. I was using the real leveraged ETFs, so the fund is rebalanced daily. I was just testing how UPRO/TMF would have done with different rebalancing intervals. I am still not convinced that daily is optimal, as monthly rebalancing would have produced lower returns than quartely rebalancing in Portfolio Visualizer. (since the inception of these ETFs)
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

RovenSkyfall wrote: Thu Apr 08, 2021 11:29 am
If you make it through the HFEA threads you will see the posts where people describe the ideal rebalancing (in a frictionless world) as daily. You should be weary of PV for backtesting and the confidence you have with the results as they only look at monthly data and so do not provide a backtest that mirrors reality.

The TMF functions similar to cash in the probability curves I posted earlier, so you exposure to market beta is predominantly due to UPRO. A typical 55/45 HFEA has a leverage of about 1.6 -- somewhere between the unleveraged and the 2xsp500 leverage probability functions. At 70/30 your probability function is going to look more similar to the 2xsp500 probability. If you remember that curve, there is a significant tail risk at 20 years of holding.....
Could you please link the posts that discuss that daily UPRO/TMF rebalancing is optimal?

I was only using Portfolio Visualizer to test different rebalancing intervals since inception of these funds, so the data is accurate. (at least for that time period)

I assume the probability curve you mean is the one in the Mean Variance Optimization thread from Uncorrelated? The problem with that model is that it is only as good as the data you put in. He makes some wild assumptions about simulating UPRO, which results in his models showing that 100% UPRO results in the highest CAGR. According to the Simulating Returns of Leveraged ETFs thread, this isn't true.
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

Rogue_trader wrote: Thu Apr 08, 2021 12:36 pm
How about I share with you the R code? But actually the mystery was solved. Apparently UPRO uses total return swaps and ^GSPC is indeed only prices index. So I need to compare UPRO with total return S&P500 and I did that it lags.
I have never coded in R before, but sure, I'd love to see that.
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

b.lock wrote: Thu Apr 08, 2021 4:44 pm I've been holding a small amount of UPRO (3x leveraged S&P500) in a tax-advantaged account for 3.5 years, and it's up about 170%. This forum is pretty against leveraged ETFs, which is fine except that some of the reasoning is using twisted logic.

When I see posters using cherry picked data it makes me believe them less. For example if you bought UPRO on a specific date 1955 it wouldn't recover until some date in 2020, and that's used to justify the leveraged ETF hate. But the same can be said of the S&P500 in a lot of cases; if you bought right before a crash it will take a long time to get your money back.

If you believe that over time the market will go up, then it makes sense to apply those same strategies to leveraged ETFs.
That's what I thought as well, until I realized that leveraged ETF portfolios behave quite differently than normal portfolios.

You can even see that a 70/30 UPRO/TMF allocation rebalanced quarterly outperformed 100% UPRO since the inception of these funds in Portfolio Visualizer.
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

alex_686 wrote: Thu Apr 08, 2021 7:04 pm
So, 2 interrelated points.

You need to understand the point of "not intended for overnight holding". If you hold UPRO for a year you are going to get a different result then if you bought SPY with 3x leverage. The daily rebalancing is going to give you a radically different character.

Which takes us to the second point, the historical data being used in this thread is mostly useless. You are going to have some insight for periods under 3 years. Maybe 10 years if you use fancy mathematics.

The difference between daily rebalancing and fixed leveraged depends on returns, cost of leverage, volatility, and if prices are mean reverting or trend following. The math behind this is well understood. Their are 2 problems here. The first is that the values of these inputs change frequently. Investment Theory is one of those great subject where the more data you throw at the problem the worse the results are. The second is that there are no classic crashes. Each one is unique.

Be skeptical of models in general. Be extra skeptical of the ones that you find free on the internet.
I would agree that the data & calculations in this particular thread are pretty useless.

But would you also say the historical data for the Simulating Returns of Leveraged ETFs thread is pretty useless? As far as I know, they included the returns, the borrowing cost, the volatility and the path-dependance in their simulations.
Last edited by tradri on Fri Apr 09, 2021 6:07 am, edited 1 time in total.
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

chris319 wrote: Fri Apr 09, 2021 12:19 am The S&P 500 index as we know it today came into existence on March 4, 1957. I have created an alternate version which goes back to 3-4-1957. Using data from 1957 forward the sweet spot is 3x.

What is salient from the 7-page thread on simulating LETF's?
You do you, but I would suggest reading through the thread and see if you can find any inconsistencies or other things to improve the backtest.
chris319
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by chris319 »

I would suggest reading through the thread and seeing if you can find any inconsistencies or other things to improve the backtest.
Simulating an ETF is rather straightforward. There is a paper that describes the math — the link is somewhere in this 12-page thread. Good luck finding it.

One refinement I have made is to add the published ER to the borrowing cost. Borrowing costs are the average LIBOR rate for the period under test which we determined is 4.69%. I'm using .95% as the ER which is typical.

For SPX I'm using GSPC, the actual index, back to March 4, 1957 and not VFINX which has its own expense ratio baked into the data.

No simulation will ever be perfect because there are so many unknowns. This will get us close enough.
Financial decisions based on emotion often turn out to be bad decisions.
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

chris319 wrote: Fri Apr 09, 2021 6:30 am
Simulating an ETF is rather straightforward. There is a paper that describes the math — the link is somewhere in this 12-page thread. Good luck finding it.

One refinement I have made is to add the published ER to the borrowing cost. Borrowing costs are the average LIBOR rate for the period under test which we determined is 4.69%. I'm using .95% as the ER which is typical.

For SPX I'm using GSPC, the actual index, back to March 4, 1957 and not VFINX which has its own expense ratio baked into the data.

No simulation will ever be perfect because there are so many unknowns. This will get us close enough.
How are you so sure that the overnight rate only has to be subtracted once? Clearly 2x and 3x leveraged ETFs have different borrowing costs.

GSPC doesn't include dividends: https://quant.stackexchange.com/questio ... y-and-gspc
AnilG
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by AnilG »

This paper might be of interest to you.

Path-Dependence of Leveraged ETF Returns∗ Marco Avellaneda and Stanley Zhang,
SIAM J. FINANCIAL MATH. 2010 Vol. 1, pp. 586–603
Abstract. It is well known that leveraged exchange-traded funds (LETFs) do not reproduce the corresponding
multiple of index returns over extended (quarterly or annual) investment horizons. For instance, in 2008 and early 2009, most LETFs underperformed the corresponding static strategies. In this paper, we study this phenomenon in detail. We give an exact formula linking the return of a leveraged fund with the corresponding multiple of the return of the unleveraged fund and its realized variance. This formula is tested empirically over quarterly horizons for 56 leveraged funds (44 double-leveraged and 12 triple-leveraged) using daily prices since January 2008 or since inception, according to the fund considered. The results indicate excellent agreement between the formula and the empirical data. The study also shows that leveraged funds can be used to replicate the returns of the underlying index, provided we use a dynamic rebalancing strategy. Empirically, we find that rebalancing frequencies required to achieve this goal are moderate—on the order of one week between rebalancings. Nevertheless, this need for dynamic rebalancing leads to the conclusion that LETFs as currently designed may be unsuitable for buy-and-hold investors.
Also, there are two excellent books on LETF mentioned in original HedgeFundie thread that are worth reading for anyone who want to understand LETFs more deeply.

Leveraged Exchange- Traded Funds
A Comprehensive Guide to Structure, Pricing, and Performance
Narat Charupat and Peter Miu

Tim Leung • Marco Santoli
Leveraged Exchange-Traded Funds
Price Dynamics and Options Valuation

tradri wrote: Fri Apr 09, 2021 5:39 am
That's what I thought as well, until I realized that leveraged ETF portfolios behave quite differently than normal portfolios.

You can even see that a 70/30 UPRO/TMF allocation rebalanced quarterly outperformed 100% UPRO since the inception of these funds in Portfolio Visualizer.
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tradri
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

AnilG wrote: Fri Apr 09, 2021 7:25 am This paper might be of interest to you.

Path-Dependence of Leveraged ETF Returns∗ Marco Avellaneda and Stanley Zhang,
SIAM J. FINANCIAL MATH. 2010 Vol. 1, pp. 586–603
Abstract. It is well known that leveraged exchange-traded funds (LETFs) do not reproduce the corresponding
multiple of index returns over extended (quarterly or annual) investment horizons. For instance, in 2008 and early 2009, most LETFs underperformed the corresponding static strategies. In this paper, we study this phenomenon in detail. We give an exact formula linking the return of a leveraged fund with the corresponding multiple of the return of the unleveraged fund and its realized variance. This formula is tested empirically over quarterly horizons for 56 leveraged funds (44 double-leveraged and 12 triple-leveraged) using daily prices since January 2008 or since inception, according to the fund considered. The results indicate excellent agreement between the formula and the empirical data. The study also shows that leveraged funds can be used to replicate the returns of the underlying index, provided we use a dynamic rebalancing strategy. Empirically, we find that rebalancing frequencies required to achieve this goal are moderate—on the order of one week between rebalancings. Nevertheless, this need for dynamic rebalancing leads to the conclusion that LETFs as currently designed may be unsuitable for buy-and-hold investors.
Also, there are two excellent books on LETF mentioned in original HedgeFundie thread that are worth reading for anyone who want to understand LETFs more deeply.

Leveraged Exchange- Traded Funds
A Comprehensive Guide to Structure, Pricing, and Performance
Narat Charupat and Peter Miu

Tim Leung • Marco Santoli
Leveraged Exchange-Traded Funds
Price Dynamics and Options Valuation

tradri wrote: Fri Apr 09, 2021 5:39 am
That's what I thought as well, until I realized that leveraged ETF portfolios behave quite differently than normal portfolios.

You can even see that a 70/30 UPRO/TMF allocation rebalanced quarterly outperformed 100% UPRO since the inception of these funds in Portfolio Visualizer.
Thank you. Will take a look at the paper and the books. :beer
Hydromod
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by Hydromod »

tradri wrote: Fri Apr 09, 2021 4:47 am
Hydromod wrote: Thu Apr 08, 2021 11:03 am
I did some fairly exhaustive testing a while back.

It turns out that end of month and end of quarter have historically been especially favorable rebalancing points. These are what PV uses. Using other parts of the quarter gave worse results than monthly.

Daily rebalancing would have been best without trading costs and slippage, but disappoint when these are accounted for.

Whether this behavior persists going forward, who knows.
So if I understand you correctly, you are saying that it makes a difference whether one rebalances at the 31st day of the month of each quarter instead of on the 15th or any other day? How is that possible? Doesn't this create a massive arbitrage opportunity?

Could you show me the data and calculations that show that daily rebalancing would be superior theoretically?
You're right, one day by itself being superior would have been obliterated.

For rebalancing, it's more like there has been a continuum of better to worse (not that one day is vastly better than all other days). Towards the change of quarter/month seems to do better than days close to the middle. This isn't my observation alone, I've seen it discussed in at least two or three places outside of this forum (for example here). It's been observed that there is something of a cycle in both stocks and treasuries across the month, and the two are out of phase. My suspicion is that rebalancing is more or less favorable depending on when one rebalances during the two cycles.

I don't have a theoretical calculation for the daily rebalancing, but I believe it to be because of the negative correlation between stocks and treasuries. Rebalancing from high to low every time a pair switches position gives a boost to the portfolio as a whole. The negative correlation that people discuss with stocks and treasuries is based on daily fluctuations. Rebalancing 252 times a year gives access to this boost 252 times, rebalancing weekly 52 times, month 12 times, etc., assuming that the negative correlation is the same at each time scale. So rebalancing daily gives 5 times the boost as weekly, 21 times the boost as monthly, etc.

I suspect that the weekly and monthly negative correlations are weaker than the daily negative correlations, so that would make the effect even smaller. At the longer time scales, corresponding idea would target the larger swings from market cycles, which is a different and harder thing (i.e., ideally one rebalances at peaks and troughs, but you don't know when you are at the peak and trough).

I went through a variety of calculations in the Refinements to Hedgefundie's excellent approach thread when I first started looking into investing. Basically I was trying to educate myself on what to expect, and gave myself the incentive of documenting it in a relatively compact thread away from the main discussion of many many comments. You may find some of it interesting.

There's a few entries that talk about the correlation effect. I found that the boost from daily rebalancing dropped pretty rapidly with the interval. Recently I've started trying to simulate actual trades, including the bid-ask spread, and it appears that the slippage from trades may eat up the daily rebalancing bonus. I haven't documented that yet.

Hope this helps.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by alex_686 »

tradri wrote: Fri Apr 09, 2021 5:50 am I would agree that the data & calculations in this particular thread are pretty useless.

But would you also say the historical data for the Simulating Returns of Leveraged ETFs thread is pretty useless? As far as I know, they included the returns, the borrowing cost, the volatility and the path-dependance in their simulations.
I am pretty skeptical about leverage and modeling - but then again I have been paid to be a glass-half-empty type of guy and worry about how this stuff blows up. I was on the margin desk during the dot.com boom and bust. I found then that leveraged portfolios crashed every which way. And while I am not a math PhD working as a financial quant I do work with them.

What you want to do is construct a model explaining how this thing works. Then, as one set of tests, back test it.

All crashes are unique. Mean reversion does not exist. Inputs can shift suddenly from one stable state to another. Longer historical periods tends to give you worse statistical results. Most people don't understand statistics. Models work until they don't work, where they fail miserably.

Risky assets tend to produce higher returns than less risky results. By extending the time period you are saying that you have a higher risk tolerance. Going back to 1929 is basically saying that you have infinite risk tolerance and thus risk can be ignored. This is wrong on multiple levels.

If slightly different starting dates gives you different results then you can't use the ending values. Solutions range from the Sharpe ratio, Sortino ratio, or Monte Carlo simulations.

I know that the primary drivers are going to be returns, cost of leverage, volatility, and if prices are mean reverting or trend following. These inputs change. If your data spans a secular periods where these values change then you are going to get garbage results.

If the current inputs are different then historical inputs than you can't use historical data in your model today. Validate your model - yes.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
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RovenSkyfall
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by RovenSkyfall »

DMoogle wrote: Thu Apr 08, 2021 11:35 pm
britcoal wrote: Thu Apr 08, 2021 11:25 pm Apologies to all - I have not read the entire thread - but I do want to ask a question. I see the dangers of using 3X leveraged ETFs 100% all the time.. but what about using 3X leveraged ETFs whenever one sees a 30%+ drop in the market? Yes, there is still risk, but if things don't return to normal we're all pretty screwed, right? It seems like a good time to take advantage of a discount and multiply that. I suppose there is the danger of a prolonged downturn..
Two flaws in your thinking: (1) you're basically trying to time the bottom - is 30% the bottom, or will it drop down to 40%? Or more? (2) it sounds like you're assuming that the market will "recover," i.e. reach its previous price point quickly. The 2008/2009 crash did, and so did the pandemic crash last year, but that is not always the case. It's a bit of a cliche at this point, but look at Japan as an example.
Buying low also assumes you are holding cash waiting for that to happen. You will need to calculate the opportunity loss of holding that cash rather than having it invested...
I saved my money, but it can't save me | The Chariot
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RovenSkyfall
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by RovenSkyfall »

tradri wrote: Fri Apr 09, 2021 5:04 am
MotoTrojan wrote: Thu Apr 08, 2021 11:05 am
I am showing relative performance compared to S&P500. Returns aren't absolute for your strategy, they are relative to the S&P500.

Small-value did well over 14% if you go back to the 1955 window as you have shown, but again, relative returns is all you can expect.
Could you show me the evidence that suggests that small cap value would have done that much better in the past?

I haven't done a ton of research in that area, but Ben Felix recently published a video on multifator investing which showed a table showing that most factor premiums delivered about 2+% more than the opposite factor, meaning that they outperformed even less than that when comparing it to a total stock market index. (https://youtu.be/jKWbW7Wgm0w at 9:12)

Also, I am a bit skeptical that historical backtesting is as useful in that particular case, as much more people are looking for value (and other factors) today then they were before Warren Buffet got famous.
This is a super deep topic as well and more academic research than LETFs. You can get started here: viewtopic.php?f=10&t=282533&p=5928964#p5928964
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by RovenSkyfall »

tradri wrote: Fri Apr 09, 2021 5:31 am
RovenSkyfall wrote: Thu Apr 08, 2021 11:29 am
If you make it through the HFEA threads you will see the posts where people describe the ideal rebalancing (in a frictionless world) as daily. You should be weary of PV for backtesting and the confidence you have with the results as they only look at monthly data and so do not provide a backtest that mirrors reality.

The TMF functions similar to cash in the probability curves I posted earlier, so you exposure to market beta is predominantly due to UPRO. A typical 55/45 HFEA has a leverage of about 1.6 -- somewhere between the unleveraged and the 2xsp500 leverage probability functions. At 70/30 your probability function is going to look more similar to the 2xsp500 probability. If you remember that curve, there is a significant tail risk at 20 years of holding.....
Could you please link the posts that discuss that daily UPRO/TMF rebalancing is optimal?
Here is where Hydromod posted this.

I was only using Portfolio Visualizer to test different rebalancing intervals since inception of these funds, so the data is accurate. (at least for that time period)
Just making sure you knew.

I assume the probability curve you mean is the one in the Mean Variance Optimization thread from Uncorrelated? The problem with that model is that it is only as good as the data you put in. He makes some wild assumptions about simulating UPRO, which results in his models showing that 100% UPRO results in the highest CAGR. According to the Simulating Returns of Leveraged ETFs thread, this isn't true.
Regarding the probability density function you can see it here. These are the distribution of outcomes of holding different amounts of leveraged SP500.

Which assumptions about UPRO are you referencing? To be clear, maximizing for CAGR only applies to the individuals with a CRRA y=1 (which is not most people). That is why Uncorrelated suggested the MVO. If you are looking to only maximize CAGR, you would reference the y=1 mark for your holdings, which is not 100% UPRO.
When you run a backtest, the ending balance (which is related to the CAGR) is calculated as:
ending balance = X1 * X2 * X3 * ... * Xn.
Or equivalently:
log(ending balance) = log(X1) + log(X2) + log(Xx) + ... + log(Xn)
Whereas the expected utility is calculated as:
expected utility = average(U(X1) + U(X2) + U(X3) + ... + U(Xn))
With U being the utility function. When your coefficient of relative risk aversion γ is 1, U(x) = log(x). Therefore, finding the max CAGR by repeatedly running backtests is equivalent to optimizing for max utility with γ = 1. That's why I said that this framework is intended to replace backtests: observing the CAGR value of a backtest is only meaningful if γ = 1, but it is very unlikely your personal coefficient of relative risk aversion is equal to 1!
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

AnilG wrote: Fri Apr 09, 2021 7:25 am This paper might be of interest to you.

Path-Dependence of Leveraged ETF Returns∗ Marco Avellaneda and Stanley Zhang,
SIAM J. FINANCIAL MATH. 2010 Vol. 1, pp. 586–603
Abstract. It is well known that leveraged exchange-traded funds (LETFs) do not reproduce the corresponding
multiple of index returns over extended (quarterly or annual) investment horizons. For instance, in 2008 and early 2009, most LETFs underperformed the corresponding static strategies. In this paper, we study this phenomenon in detail. We give an exact formula linking the return of a leveraged fund with the corresponding multiple of the return of the unleveraged fund and its realized variance. This formula is tested empirically over quarterly horizons for 56 leveraged funds (44 double-leveraged and 12 triple-leveraged) using daily prices since January 2008 or since inception, according to the fund considered. The results indicate excellent agreement between the formula and the empirical data. The study also shows that leveraged funds can be used to replicate the returns of the underlying index, provided we use a dynamic rebalancing strategy. Empirically, we find that rebalancing frequencies required to achieve this goal are moderate—on the order of one week between rebalancings. Nevertheless, this need for dynamic rebalancing leads to the conclusion that LETFs as currently designed may be unsuitable for buy-and-hold investors.
As far as I can tell, the dynamic rebalancing strategy that is proposed in the paper isn't really applicable to a UPRO/TMF strategy.

First of all, their goal is to match the underlying index as closely as possible, as opposed to achieving the maximum CAGR long-term.
They achieve this by combining long/short ETFs, and conclude that weekly rebalancing keeps the tracking error low.

Is this a fair assessment of their dynamic hedging strategy, and if yes, how exactly does this apply to the optimal rebalancing interval of a UPRO/TMF portfolio?
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by chris319 »

How are you so sure that the overnight rate only has to be subtracted once? Clearly 2x and 3x leveraged ETFs have different borrowing costs.
Oh yeah, I forgot to mention that for a 3x fund the borrowing cost is doubled. I found the explanation for this elsewhere and it is valid.

The borrowing cost, not the borrowing rate.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

Hydromod wrote: Fri Apr 09, 2021 7:52 am
You're right, one day by itself being superior would have been obliterated.

For rebalancing, it's more like there has been a continuum of better to worse (not that one day is vastly better than all other days). Towards the change of quarter/month seems to do better than days close to the middle. This isn't my observation alone, I've seen it discussed in at least two or three places outside of this forum (for example here). It's been observed that there is something of a cycle in both stocks and treasuries across the month, and the two are out of phase. My suspicion is that rebalancing is more or less favorable depending on when one rebalances during the two cycles.

I don't have a theoretical calculation for the daily rebalancing, but I believe it to be because of the negative correlation between stocks and treasuries. Rebalancing from high to low every time a pair switches position gives a boost to the portfolio as a whole. The negative correlation that people discuss with stocks and treasuries is based on daily fluctuations. Rebalancing 252 times a year gives access to this boost 252 times, rebalancing weekly 52 times, month 12 times, etc., assuming that the negative correlation is the same at each time scale. So rebalancing daily gives 5 times the boost as weekly, 21 times the boost as monthly, etc.

I suspect that the weekly and monthly negative correlations are weaker than the daily negative correlations, so that would make the effect even smaller. At the longer time scales, corresponding idea would target the larger swings from market cycles, which is a different and harder thing (i.e., ideally one rebalances at peaks and troughs, but you don't know when you are at the peak and trough).

I went through a variety of calculations in the Refinements to Hedgefundie's excellent approach thread when I first started looking into investing. Basically I was trying to educate myself on what to expect, and gave myself the incentive of documenting it in a relatively compact thread away from the main discussion of many many comments. You may find some of it interesting.

There's a few entries that talk about the correlation effect. I found that the boost from daily rebalancing dropped pretty rapidly with the interval. Recently I've started trying to simulate actual trades, including the bid-ask spread, and it appears that the slippage from trades may eat up the daily rebalancing bonus. I haven't documented that yet.

Hope this helps.
This end-of-month phenomenon is quite interesting, although we'll have to see whether it will persist in the future. Anyways, it can't hurt to rebalance on the 30th/31st of each quarter, so one might as well use it.

I'm still not entirely convinced on daily rebalancing being theoretically superior though. While I acknowledge your argument that keeping your asset allocation as constant as possible should be superior, isn't there also an argument for "letting it ride" a bit? That way you can let UPRO compound for a little bit longer when the stock market goes up, while being able to "buy the dip" when UPRO crashes over the course of a quarter, right?

Also, if rebalancing as often as possible is theoretically superior, why does a monthly rebalanced UPRO/TMF portfolio perform worse than a quarterly rebalanced UPRO/TMF portfolio in Portfolio Visualizer? Is this only unique to the time period 2009-2021?
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

alex_686 wrote: Fri Apr 09, 2021 8:01 am I am pretty skeptical about leverage and modeling - but then again I have been paid to be a glass-half-empty type of guy and worry about how this stuff blows up. I was on the margin desk during the dot.com boom and bust. I found then that leveraged portfolios crashed every which way. And while I am not a math PhD working as a financial quant I do work with them.

What you want to do is construct a model explaining how this thing works. Then, as one set of tests, back test it.

All crashes are unique. Mean reversion does not exist. Inputs can shift suddenly from one stable state to another. Longer historical periods tends to give you worse statistical results. Most people don't understand statistics. Models work until they don't work, where they fail miserably.

Risky assets tend to produce higher returns than less risky results. By extending the time period you are saying that you have a higher risk tolerance. Going back to 1929 is basically saying that you have infinite risk tolerance and thus risk can be ignored. This is wrong on multiple levels.

If slightly different starting dates gives you different results then you can't use the ending values. Solutions range from the Sharpe ratio, Sortino ratio, or Monte Carlo simulations.

I know that the primary drivers are going to be returns, cost of leverage, volatility, and if prices are mean reverting or trend following. These inputs change. If your data spans a secular periods where these values change then you are going to get garbage results.

If the current inputs are different then historical inputs than you can't use historical data in your model today. Validate your model - yes.
I think the model/strategy that most closely resembles this, is Ray Dalio's risk parity strategy, right?
You basically try to find uncorrelated assets that have a good Sharpe ratio and increase returns with leverage.

Can you explain to me why longer historical periods give worse statistical results?
I do agree though, that following a strategy that has only produced higher returns over 100 years and over no other time period, is probably not ideal for us mortals.

Changing the end date for 70/30 UPRO/TMF in the backtest spreadsheet to 2010 does lower the CAGR to 11.76%, but it's still higher than a 1x S&P 500. Taking a recent example, 2000-2010 (the lost decade), I get a CAGR of 1.61%, which is also higher than the 1x S&P 500.

The time-period for the backtest starts in 1955, at a time when interest rates were similarly low as today, so I think this backtest encompasses many market/interest rate environments.

Would you say that's enough validation for trusting the model? :beer
Last edited by tradri on Fri Apr 09, 2021 12:48 pm, edited 2 times in total.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by chris319 »

Does rebalancing include the sale of any assets? If so, a sale is a taxable event and has to be taken into account which a simulation doesn't do. You can't assume everyone is in a tax-deferred account. In taxable accounts taxes are a very real consideration.

Dividends are easily dealt with. The published yield of UPRO is 0.10%. Just divide by 252 and add it in daily.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

RovenSkyfall wrote: Fri Apr 09, 2021 8:45 am
Regarding the probability density function you can see it here. These are the distribution of outcomes of holding different amounts of leveraged SP500.

Which assumptions about UPRO are you referencing? To be clear, maximizing for CAGR only applies to the individuals with a CRRA y=1 (which is not most people). That is why Uncorrelated suggested the MVO. If you are looking to only maximize CAGR, you would reference the y=1 mark for your holdings, which is not 100% UPRO.
Yes, it seems that only holding 2x or 3x leveraged S&P 500 isn't the best idea to increase the CAGR long-term.

Now that you mention that y=1 is the point where the CAGR is the highest, this Mean Variance framework makes total sense. I thought that higher expected utility means higher CAGR, but going off the y=1 leveraged portfolio, it also says that around 70/30 UPRO/TMF should produce the highest CAGR. I originally assumed the UPRO model wasn't incorporating the borrowing costs, but it seems that it did that correctly.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

chris319 wrote: Fri Apr 09, 2021 11:48 am Oh yeah, I forgot to mention that for a 3x fund the borrowing cost is doubled. I found the explanation for this elsewhere and it is valid.

The borrowing cost, not the borrowing rate.
Great, now we are on the same page.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

chris319 wrote: Fri Apr 09, 2021 12:18 pm Does rebalancing include the sale of any assets? If so, a sale is a taxable event and has to be taken into account which a simulation doesn't do. You can't assume everyone is in a tax-deferred account. In taxable accounts taxes are a very real consideration.

Dividends are easily dealt with. The published yield of UPRO is 0.10%. Just divide by 252 and add it in daily.
In the beginning one can probably rebalance with new money, but later on yes. However, taxes are only paid if gains are being made, so the net results should still be higher than a lower-return strategy.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by chris319 »

In the beginning one can probably rebalance with new money, but later on yes. However, taxes are only paid if gains are being made, so the net results should still be higher than a lower-return strategy.
The added funds will affect your cost basis and this in turn affects CAGR and gets into IRR. It also assumes additional funds are available for rebalancing. Then there is the matter of capital losses. They can't be glossed over, either. This gets very complicated so I'm not interested in any switching strategies.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

chris319 wrote: Fri Apr 09, 2021 12:51 pm
The added funds will affect your cost basis and this in turn affects CAGR and gets into IRR. It also assumes additional funds are available for rebalancing. Then there is the matter of capital losses. They can't be glossed over, either. This gets very complicated so I'm not interested in any switching strategies.
I don't think rebalancing is that big of a deal, considering that the majority of investors own more than one fund and therefore have to do that from time to time.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by Hydromod »

tradri wrote: Fri Apr 09, 2021 11:57 am I'm still not entirely convinced on daily rebalancing being theoretically superior though. While I acknowledge your argument that keeping your asset allocation as constant as possible should be superior, isn't there also an argument for "letting it ride" a bit? That way you can let UPRO compound for a little bit longer when the stock market goes up, while being able to "buy the dip" when UPRO crashes over the course of a quarter, right?

I think there are two different things here: (i) short-term anticorrelated fluctuations and (ii) market fluctuations. I didn't argue one way or the other on how to address market fluctuations. If I were doing daily rebalancing, I would use time-varying weights, like inverse volatility, that are based on the latest month or two to dynamically change the allocation across the cycle. That kind of tactical approach typically did better than constant weights in my backtesting.

Also, if rebalancing as often as possible is theoretically superior, why does a monthly rebalanced UPRO/TMF portfolio perform worse than a quarterly rebalanced UPRO/TMF portfolio in Portfolio Visualizer? Is this only unique to the time period 2009-2021?

This has been a point of discussion for quite some time. I tried to take out the coincidences that happen to line up. If you look at all possible starting points within the month and quarter for the all possible cases of the same fixed duration (say 5 years or 10 years) from 1986 to 2019 (the HEDGEFUNDIE simulated dataset), the median monthly case does better than the median quarterly case. It's pretty much monotonic from days to weeks to months to years, really.

However, PV only looks at end-of-month and end-of-quarter returns. It seems to me that the rebalancing variation across the quarter has been larger than the rebalancing variation across the month, although both are lined up favorably in PV.

I must admit I didn't check if there were systematic differences between the 1st, 2nd, and 3rd months of a quarter. Now I wonder if that would make a difference.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

Hydromod wrote: Fri Apr 09, 2021 12:55 pm
tradri wrote: Fri Apr 09, 2021 11:57 am I'm still not entirely convinced on daily rebalancing being theoretically superior though. While I acknowledge your argument that keeping your asset allocation as constant as possible should be superior, isn't there also an argument for "letting it ride" a bit? That way you can let UPRO compound for a little bit longer when the stock market goes up, while being able to "buy the dip" when UPRO crashes over the course of a quarter, right?

I think there are two different things here: (i) short-term anticorrelated fluctuations and (ii) market fluctuations. I didn't argue one way or the other on how to address market fluctuations. If I were doing daily rebalancing, I would use time-varying weights, like inverse volatility, that are based on the latest month or two to dynamically change the allocation across the cycle. That kind of tactical approach typically did better than constant weights in my backtesting.

Also, if rebalancing as often as possible is theoretically superior, why does a monthly rebalanced UPRO/TMF portfolio perform worse than a quarterly rebalanced UPRO/TMF portfolio in Portfolio Visualizer? Is this only unique to the time period 2009-2021?

This has been a point of discussion for quite some time. I tried to take out the coincidences that happen to line up. If you look at all possible starting points within the month and quarter for the all possible cases of the same fixed duration (say 5 years or 10 years) from 1986 to 2019 (the HEDGEFUNDIE simulated dataset), the median monthly case does better than the median quarterly case. It's pretty much monotonic from days to weeks to months to years, really.

However, PV only looks at end-of-month and end-of-quarter returns. It seems to me that the rebalancing variation across the quarter has been larger than the rebalancing variation across the month, although both are lined up favorably in PV.

I must admit I didn't check if there were systematic differences between the 1st, 2nd, and 3rd months of a quarter. Now I wonder if that would make a difference.
So....as long as this end-of-quarter phonemon persists, there shouldn't be a problem exploiting that, right?
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by Hydromod »

tradri wrote: Fri Apr 09, 2021 1:00 pm So....as long as this end-of-quarter phonemon persists, there shouldn't be a problem exploiting that, right?
Sure. At least it's a basis for picking a day without having to worry much. Even if it was purely coincidence, and disappears today, I don't see why it would hurt. Unless too many people decide to arbitrage somehow...
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by RovenSkyfall »

Hydromod wrote: Fri Apr 09, 2021 1:08 pm
tradri wrote: Fri Apr 09, 2021 1:00 pm So....as long as this end-of-quarter phonemon persists, there shouldn't be a problem exploiting that, right?
Sure. At least it's a basis for picking a day without having to worry much. Even if it was purely coincidence, and disappears today, I don't see why it would hurt. Unless too many people decide to arbitrage somehow...
Hydromod, you might know the answer to this. I seems like everyone in HFEA is using a concave rebalancing method, when in theory a convex rebalancing method might produce greater returns. As far as you know has anyone looked into this? The article that made me think of it is this: https://www.tandfonline.com/doi/abs/10. ... .v44.n1.16
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by MotoTrojan »

tradri wrote: Fri Apr 09, 2021 5:13 am
MotoTrojan wrote: Thu Apr 08, 2021 11:10 am
If it only works in one market, that suggests it is not a well founded strategy but is just overfitting. I am not talking about one-off situations like Japan. How would the 70% daily-resetting 3x equity exposure had worked in ex-US stocks? Or even total world? I bet you it would be pretty ugly with massive volatility decay.

The US market has been an anomaly. You are going into this assuming it is a good basis for the future. A sound process will work in other markets, and this one doesn't pass that test.

If you are in-fact back-testing to 1955 then good, that is a full cycle for interest rates at-least and is representative of what TMF would've seen, but I still think that period of US equity returns is not a good baseline for what to expect in the future.
Why do you assume that US stocks did that much better than global stocks? If that were the case, even the dumbest investor would have realized by now that the US is the only place where stocks are allowed to grow and US stocks would have a global market cap of 100%.

In fact, these things are pretty cyclical. Sometimes US stocks do better, sometimes international stocks do better.
Image

Just to be clear, I am generally not against international diversification, but in this case there isn't a practical way to do so.
When dealing with leverage there is more to it than "they both went up". I'll let you backtest the ex-US stocks though.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by MotoTrojan »

tradri wrote: Fri Apr 09, 2021 5:20 am
MotoTrojan wrote: Thu Apr 08, 2021 11:15 am Hydromods backtest included a sweeping starting point, where-as tradri you are also putting rebalance timing luck into the mix since Portfolio Visualizer is looking at annual calendar rebalances only. I think quarterly is the best mix of trading costs and optimization personally, but as Hydro said, in theory daily is the best.
I do acknowledge that quarterly rebalancing is better than yearly.

Also, I am not using Portfolio Visualizer to simulate the leveraged ETFs. I was using the real leveraged ETFs, so the fund is rebalanced daily. I was just testing how UPRO/TMF would have done with different rebalancing intervals. I am still not convinced that daily is optimal, as monthly rebalancing would have produced lower returns than quartely rebalancing in Portfolio Visualizer. (since the inception of these ETFs)
I know you are using the real ETFs, but Portfolio Visualizer monthly only trades at the end of each calendar month, while quarterly does the end of each calendar quarter, etc... There is a lot of chance/luck involved in those times still based on past history that has no reason to repeat itself. Hydromod also used daily-resetting data (same as you with actual ETF data), but tested it with daily, monthly, quarterly, etc... rebalances that swept through every possible day (starting Jan 1, Jan 2, Jan 3, Jan 4, etc...). Portfolio Visualizer can't do that, which is why it's results can't be trusted. It is pretty amazing how big of a dispersion in returns you can get depending on what day of the year you start your quarterly or annual rebalance is what I am saying.

Daily rebalancing is typically the best option in any trading strategy, including value, momentum, etc... but only on paper because trading costs get ya.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by Hydromod »

RovenSkyfall wrote: Fri Apr 09, 2021 1:19 pm Hydromod, you might know the answer to this. I seems like everyone in HFEA is using a concave rebalancing method, when in theory a convex rebalancing method might produce greater returns. As far as you know has anyone looked into this? The article that made me think of it is this: https://www.tandfonline.com/doi/abs/10. ... .v44.n1.16
I will be the first to admit that my finance background was almost nonexistent prior to about 2 years ago. I took a quick scan through to see what the difference between the two approaches might be, because I hadn't heard these terms in this context before.

I don't recall seeing anything like a convex approach before, although it's occurred to me that using a floor of some sort might be useful if one is trying to do some sort of trend following.

Sorry I can't be of help.

I do appreciate the link, and I'll need to think further on this.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

MotoTrojan wrote: Fri Apr 09, 2021 1:40 pm When dealing with leverage there is more to it than "they both went up". I'll let you backtest the ex-US stocks though.
If you want accurate backtests, you should really ask siamond. I am a newbie when it comes to this.

Still, I don't see a reason why results should be drastically different, given the similarities in returns: https://www.hartfordfunds.com/practice- ... ycles.html

In fact, there are many (good) arguments for investing in global stocks, so I won't be surprised if a (hypothetical) global UPRO/TMF produces better results long-term.

According to this video, global stocks had higher returns with lower volatility: https://www.youtube.com/watch?v=RR7e1Y-HJxQ at 6:00
So if this works for the US, it most likely works for global stocks/long-term government bonds.
Last edited by tradri on Fri Apr 09, 2021 4:30 pm, edited 2 times in total.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by tradri »

MotoTrojan wrote: Fri Apr 09, 2021 1:43 pm
I know you are using the real ETFs, but Portfolio Visualizer monthly only trades at the end of each calendar month, while quarterly does the end of each calendar quarter, etc... There is a lot of chance/luck involved in those times still based on past history that has no reason to repeat itself. Hydromod also used daily-resetting data (same as you with actual ETF data), but tested it with daily, monthly, quarterly, etc... rebalances that swept through every possible day (starting Jan 1, Jan 2, Jan 3, Jan 4, etc...). Portfolio Visualizer can't do that, which is why it's results can't be trusted. It is pretty amazing how big of a dispersion in returns you can get depending on what day of the year you start your quarterly or annual rebalance is what I am saying.

Daily rebalancing is typically the best option in any trading strategy, including value, momentum, etc... but only on paper because trading costs get ya.
Let's not forget that a 70/30 UPRO/TMF portfolio has produced a 14.31% CAGR when rebalanced annually. (according to the backtest spreadsheet)
These are already fantastic results, so quarterly rebalancing is just the icing on the cake.
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Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by alex_686 »

tradri wrote: Fri Apr 09, 2021 12:11 pm I think the model/strategy that most closely resembles this, is Ray Dalio's risk parity strategy, right?
You basically try to find uncorrelated assets that have a good Sharpe ratio and increase returns with leverage.

Can you explain to me why longer historical periods give worse statistical results?
I do agree though, that following a strategy that has only produced higher returns over 100 years and over no other time period, is probably not ideal for us mortals.

Changing the end date for 70/30 UPRO/TMF in the backtest spreadsheet to 2010 does lower the CAGR to 11.76%, but it's still higher than a 1x S&P 500. Taking a recent example, 2000-2010 (the lost decade), I get a CAGR of 1.61%, which is also higher than the 1x S&P 500.

The time-period for the backtest starts in 1955, at a time when interest rates were similarly low as today, so I think this backtest encompasses many market/interest rate environments.

Would you say that's enough validation for trusting the model? :beer
Not familiar enough with Ray Dalio's stratagy.

There are 2 reasons why longer periods don't work.

First, as I have said before, the inputs of the model vary over time. If you cross periods you are going to get garbage results. Statistical models assume constant relationships, volatility, correlation, etc. Throw those out because you are crossing different secular eras then you need to throw out the results as well.

So that extra 1.61% in my mind is statistically insignificant. Data mine enough and you will get results. That does not mean anything.

Second, longer time periods makes the assumption that you have infinite risk tolerance. In my experience that is a poor assumption.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
alex_686
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Joined: Mon Feb 09, 2015 1:39 pm

Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by alex_686 »

A little off tangent, but...

One of the road marks in my life was the hedge fund Long Term Capital Management. You had the smartest guys in the room, including 2 Nobel laureates, losing a couple of billion dollars over 6 weeks and nearly blowing up the economy because their market models, which included a fair amount of leverage, which were more or less guaranteed that their portfolio was risk free.

It is a great story. Treat leverage with a healthy level of respect.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
DMoogle
Posts: 549
Joined: Sat Oct 31, 2020 10:24 pm

Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by DMoogle »

alex_686 wrote: Fri Apr 09, 2021 8:23 pm A little off tangent, but...

One of the road marks in my life was the hedge fund Long Term Capital Management. You had the smartest guys in the room, including 2 Nobel laureates, losing a couple of billion dollars over 6 weeks and nearly blowing up the economy because their market models, which included a fair amount of leverage, which were more or less guaranteed that their portfolio was risk free.

It is a great story. Treat leverage with a healthy level of respect.
From their Wikipedia page:
At the beginning of 1998, the firm had equity of $4.7 billion and had borrowed over $124.5 billion with assets of around $129 billion, for a debt-to-equity ratio of over 25 to 1.[17] It had off-balance sheet derivative positions with a notional value of approximately $1.25 trillion, most of which were in interest rate derivatives such as interest rate swaps. The fund also invested in other derivatives such as equity options.
So if you only look at debt to equity, they were 25:1. If you include notional value of derivatives, they were 250:1 leveraged.

We're currently talking max 3:1 leverage of a more traditional, balanced portfolio.

This isn't a gripe on you btw - these are certainly riskier strategies than typical Bogleheads asset allocations. Just sometimes people poke their heads in these threads to say silly stuff like "all leverage is dumb, you can't beat the market."
Hydromod
Posts: 1051
Joined: Tue Mar 26, 2019 10:21 pm

Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by Hydromod »

I'm pretty convinced that a risk parity portfolio with 2 to 8 3x LETFs across several asset categories (equities, REITs, treasuries) could do well long term. Keys are picking funds with relatively low correlation, rebalancing as trailing volatility changes, and being careful about balancing risk between categories.

The idea is sort of a leveraged Golden Butterfly with adaptive weighting. A version of a leveraged Golden Butterfly is posted by Optimized Portfolio. Something like an inverse volatility weighted UPRO/TNA/TMF/UGL combination (close to a Golden Butterfly) would have consistently returned 40% annual (for moving 3-year periods) from 1998 to 2015 and 20% annual since, with a maximum drawdown period of maybe 1.5 years. This had barely a hiccup circa 2000 and a little glitch circa 2008; the biggest disturbance was 2020.

Leaving out UGL would have boosted overall CAGR by a few percent.

Plain ol' TQQQ/TMF would have screamed since 1998 (I calculated ~55% CAGR with a minimal blip circa 2000).

I'm limited to starting in 1998 to 2003 for most of the funds I've been looking at. The earlier return numbers are a bit suspect because I've spliced in synthetic versions prior to the fund initiation.

I try to account for slippage during trades; slippage is especially suspect going back in time.

Portfolios with more LETFs won't necessarily scream like TQQQ/TMF would have, but some of the combinations I've been testing seem to have delivered moving 3-year returns consistently >20% annualized for close to 20 years, with maximum drawdown ~50%.

The idea I'm working off of is to assign risk weights to categories, and use inverse volatility for funds inside the same category. An example that seems to backtest well: REITs (3x = DRA) have 20% of the risk weight as equities; treasuries (3x = TMF) have 70%; and gold (2x = UGL) 30%. TMF might vary between 30% and 75% of the entire portfolio, depending on the various volatilities.

I am very curious to see if a minimum variance optimizer accounting for correlations and perhaps moving estimates of expected return would do better.

Some folks would claim that adaptive weighting is market timing. Perhaps, but it's a mechanistic approach that is backward-looking rather than trying to explicitly project future market behavior.

Hopefully I can post some details in the next few weeks as I get things worked out and start implementing the approach in earnest with a small part of my portfolio. I'm torn between shooting for the moon with TQQQ/TMF alone versus shooting for stable returns with a diverse set of funds. Maybe I'll run side-by-side comparisons.
jarjarM
Posts: 2511
Joined: Mon Jul 16, 2018 1:21 pm

Re: Are 3x leveraged ETFs the long-term winning strategy?

Post by jarjarM »

Hydromod wrote: Fri Apr 09, 2021 10:42 pm I'm pretty convinced that a risk parity portfolio with 2 to 8 3x LETFs across several asset categories (equities, REITs, treasuries) could do well long term. Keys are picking funds with relatively low correlation, rebalancing as trailing volatility changes, and being careful about balancing risk between categories.

The idea is sort of a leveraged Golden Butterfly with adaptive weighting. A version of a leveraged Golden Butterfly is posted by Optimized Portfolio. Something like an inverse volatility weighted UPRO/TNA/TMF/UGL combination (close to a Golden Butterfly) would have consistently returned 40% annual (for moving 3-year periods) from 1998 to 2015 and 20% annual since, with a maximum drawdown period of maybe 1.5 years. This had barely a hiccup circa 2000 and a little glitch circa 2008; the biggest disturbance was 2020.

Leaving out UGL would have boosted overall CAGR by a few percent.

Plain ol' TQQQ/TMF would have screamed since 1998 (I calculated ~55% CAGR with a minimal blip circa 2000).

I'm limited to starting in 1998 to 2003 for most of the funds I've been looking at. The earlier return numbers are a bit suspect because I've spliced in synthetic versions prior to the fund initiation.

I try to account for slippage during trades; slippage is especially suspect going back in time.

Portfolios with more LETFs won't necessarily scream like TQQQ/TMF would have, but some of the combinations I've been testing seem to have delivered moving 3-year returns consistently >20% annualized for close to 20 years, with maximum drawdown ~50%.

The idea I'm working off of is to assign risk weights to categories, and use inverse volatility for funds inside the same category. An example that seems to backtest well: REITs (3x = DRA) have 20% of the risk weight as equities; treasuries (3x = TMF) have 70%; and gold (2x = UGL) 30%. TMF might vary between 30% and 75% of the entire portfolio, depending on the various volatilities.

I am very curious to see if a minimum variance optimizer accounting for correlations and perhaps moving estimates of expected return would do better.

Some folks would claim that adaptive weighting is market timing. Perhaps, but it's a mechanistic approach that is backward-looking rather than trying to explicitly project future market behavior.

Hopefully I can post some details in the next few weeks as I get things worked out and start implementing the approach in earnest with a small part of my portfolio. I'm torn between shooting for the moon with TQQQ/TMF alone versus shooting for stable returns with a diverse set of funds. Maybe I'll run side-by-side comparisons.
I would be interested in seeing some comparisons. I started the HFEA with UPRO/TMF/UGLD. Now I have TQQQ/UPRO/URTY (TNA little brother)/TMF across my portfolio. I’m looking at the proper ratio to add for EDZ and my rebalance platform is based on min variance. The one issue I do see is that the 3x LETFs doesn’t always survive, both DZK and UGLD were closed in the last couple of years. So even if we determine the proper ratio, we may not have trading instruments unless you want to move to options/futures.

The original smartly paper on TAA is based on 10 diverse funds with limited correlations so I would love to emulate it to a certain extent. Thanks for bringing up this topic of discussion.
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