PP Inspired Leveraged Portfolios

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Re: PP Inspired Leveraged Portfolios

Post by Kbg » Wed Jan 27, 2021 8:20 am

TruDrew wrote:
Tue Jan 26, 2021 8:23 pm
Do you implement VXX instead of VIXY for tax purposes? Since VXX is an ETN and VIXY is an ETF that has to be reported on a k-1. I've had vxx in the past and schwab included it in the 1099 so I was able to use this to offset other short term capital gains. However, I'm not sure how offsetting capital losses with stocks works with VIXY or VIXM since they're reported on a k-1.
This is really tax advice and the standard caveat...I'm not a tax guy but I still do/file my own returns. I think it is a matter of preference on taxes but a matter of instrument structure between VXX and VIXY/M. With the latter two you actually "own" the stuff and the "stuff" is real. The former is a note debt note on a banks books. So there's that. Personally I don't sweat that issue with these funds, but someone might and there are substantive differences structurally that folks should be aware of before they commit their funds.

Now to taxes, what a K-1 really does is give you a tax oriented profit/loss report as one of the many "mini-partners" regarding your %age of the business. Handily, with most good ETF companies (and ProShares does a good job in my view) they give you good instructions and tell you where to enter the entries from the K-1 into the various tax forms (e.g. where the numbers should go). So if you can read, you can do your taxes if that's your thing. If not, you give it to your tax person and they do the work for you. If you are a do your taxes early person you will hate them as they generally don't get released until March.

Substantively you will find the vast majority of gains or losses will end up hitting Form 6781 as you "own" futures, which means your profits and losses will automatically be treated at 60% LTCG and 40% STCG. (IIRC) They will also be marked to market every year so if you don't buy or sell a single share you're still going to get a K-1 and be on the hook for the associated taxes (or deductions for a loss) from that year's "futures trading business." Given that, the way to pay for taxes is just sell enough shares to cover the taxes as that makes no real difference in terms of driving a tax bill.

What makes most sense tax wise of course is completely a personal thing...as to forms a very small side rant.

For ease I would much rather deal with a K-1 and a 6781 form than the monstrosity one has to go through when buying and selling stocks and accounting for dividends which to me is far more of a hassle.

Short version: VXX you control taxes trading a "stock", VIXY/M is marked to market futures tax rules...this can be a good thing or bad. If you are trading VXX more than annually, VIXY/M are going to be far more tax efficient (maybe).

Hmmm...however, given decay in VXX you are probably going to book STCLs every year assuming you buy and sell which is likely to maintain your allocation. This right here would be a good research project I probably ought to do...may change how I think about them from a tax perspective...writing can be very helpful, it can spawn thoughts you haven't thought of.

Maybe Vinnie will chime in on this one.
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Re: PP Inspired Leveraged Portfolios

Post by TruDrew » Fri Jan 29, 2021 7:28 pm

Kbg wrote:
Wed Jan 27, 2021 8:20 am
TruDrew wrote:
Tue Jan 26, 2021 8:23 pm
Do you implement VXX instead of VIXY for tax purposes? Since VXX is an ETN and VIXY is an ETF that has to be reported on a k-1. I've had vxx in the past and schwab included it in the 1099 so I was able to use this to offset other short term capital gains. However, I'm not sure how offsetting capital losses with stocks works with VIXY or VIXM since they're reported on a k-1.
This is really tax advice and the standard caveat...I'm not a tax guy but I still do/file my own returns. I think it is a matter of preference on taxes but a matter of instrument structure between VXX and VIXY/M. With the latter two you actually "own" the stuff and the "stuff" is real. The former is a note debt note on a banks books. So there's that. Personally I don't sweat that issue with these funds, but someone might and there are substantive differences structurally that folks should be aware of before they commit their funds.

Now to taxes, what a K-1 really does is give you a tax oriented profit/loss report as one of the many "mini-partners" regarding your %age of the business. Handily, with most good ETF companies (and ProShares does a good job in my view) they give you good instructions and tell you where to enter the entries from the K-1 into the various tax forms (e.g. where the numbers should go). So if you can read, you can do your taxes if that's your thing. If not, you give it to your tax person and they do the work for you. If you are a do your taxes early person you will hate them as they generally don't get released until March.

Substantively you will find the vast majority of gains or losses will end up hitting Form 6781 as you "own" futures, which means your profits and losses will automatically be treated at 60% LTCG and 40% STCG. (IIRC) They will also be marked to market every year so if you don't buy or sell a single share you're still going to get a K-1 and be on the hook for the associated taxes (or deductions for a loss) from that year's "futures trading business." Given that, the way to pay for taxes is just sell enough shares to cover the taxes as that makes no real difference in terms of driving a tax bill.

What makes most sense tax wise of course is completely a personal thing...as to forms a very small side rant.

For ease I would much rather deal with a K-1 and a 6781 form than the monstrosity one has to go through when buying and selling stocks and accounting for dividends which to me is far more of a hassle.

Short version: VXX you control taxes trading a "stock", VIXY/M is marked to market futures tax rules...this can be a good thing or bad. If you are trading VXX more than annually, VIXY/M are going to be far more tax efficient (maybe).

Hmmm...however, given decay in VXX you are probably going to book STCLs every year assuming you buy and sell which is likely to maintain your allocation. This right here would be a good research project I probably ought to do...may change how I think about them from a tax perspective...writing can be very helpful, it can spawn thoughts you haven't thought of.

Maybe Vinnie will chime in on this one.
That makes sense thanks for that explaining all of that. Makes me feel better about holding the etf instead of the ETN. Also from how I'm understanding this, it sounds like VIXY/M is not subjected to the wash sale rule since you wouldn't have to sell in order to realize some losses along the way with the marked to market treatment.

i agree that writing helps. That's why I like this forum :D.

Recently i ran my own back test using excel for VIXY/M and an equity allocation because portfoliovisualizer only looks at month end prices for rebalancing instead of the possible day or week fluctuations that can bring an asset outside of rebalance bands. In my opinion, this is especially important for volatility products since they are known to pop.
Has this been a limitation you've run into with portfoliovisualizer as well and your portfolios containing volatility products? Or is there a way to get daily prices in here. Otherwise, does anyone know of another site that could just as easily provide this information like portfoliovisualizer?
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Re: PP Inspired Leveraged Portfolios

Post by Kbg » Mon Feb 01, 2021 10:03 am

You can get daily data from Tiingo. If you come up with any promising ideas on a good rebalancing method let me know and I’ll give them a look and report what I find. You can also get simulated data for these ETFs that go back before they were even created but you have to buy it. I have some so happy to evaluate that stuff as well.
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Re: PP Inspired Leveraged Portfolios

Post by jalanlong » Sat Feb 20, 2021 10:33 pm

Kbg wrote:
Thu Dec 31, 2020 3:13 pm
UST/TQQQ/VGSH 70/20/10 (The bullet)

VGSH/TQQQ/TMF/DGP 44/25/12.5/18.5 (The barbell) - Note the change from UGLD to DGP and the change in weighting of gold etfs and cash.

VGSH 35%, UST 30%, TQQQ 25%, DGP 5%, VIXY 5% (Newbie 1)

BND 70%, TQQQ 25%, VIXY 5% (Newbie 2)

A very good year for RP that's for sure, and I'm going to change the official portfolio again to a simple 70% BND/25% TQQQ/5% VIXY. This is a result of a lot of VIX ETF study. Here are the performance stats for the above portfolios for 2020 from 1/1/20 - 12/30/20. I'll report both with annual and quarterly rebalances. If one decides to include a long vol ETF in their trading I suggest taking a serious look on when to rebalance it (in 90% of the cases this ends up meaning buying more). It is a key component of this particular approach.

Bullet - 28.04/51.76%

Barbell - 40.25/62.45%

Newbie 1 - 35.76/66.20%

Newbie 2 - 32.34/60.02%

Personal - 38.6%

2020 by consensus is probably not a great one in most peoples' eyes, but from an investing perspective it was a very good one.
Any reason you chose BND? The 7-10 Treasury ETF (IEF) backtests slightly better. Just wondering
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Re: PP Inspired Leveraged Portfolios

Post by ppnewbie » Sun Feb 21, 2021 12:23 am

Sorry for the annoying question here. Can I get a quick recap on the newbie 2 rules. Rebalance bands and frequency of rebalancing.
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Re: PP Inspired Leveraged Portfolios

Post by Kbg » Tue Jun 08, 2021 9:00 am

I think when VIXY is down to 2.5% or quarterly whichever you prefer. It's easy to let VIXY shrink to nothing because it does such a good job of burning through a bunch of money. However, that kind of defeats the purpose of having a hedge in the first place. If I can remember I'll make an update to the portfolio stats early July.
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Re: PP Inspired Leveraged Portfolios

Post by Kbg » Tue Jun 08, 2021 9:17 am

"Any reason you chose BND? The 7-10 Treasury ETF (IEF) backtests slightly better. Just wondering"

BND is pretty safe so far as a bond index fund goes. It's like 60%+ treasuries. For me it's a pure risk/reward call. The corporates in BND bump up that fund's returns over IEF slightly. My backtesting shows you get a smidge overall better return in the portfolio for a smidge more risk with BND. I'm very much HB in that I don't try to predict returns, but I do expect assets to behave in certain ways which I do believe is quite predictable. I see absolutely nothing that suggests to me the risk/reward tradeoff between BND/IEF will change, so at the end of the day it's a personal risk preference call. IEF does a nice job of responding/performing better during stock market dives, which is a nice feature. However, over longer time periods BND is going to outperform. Additionally, BND's duration is 6.4 vs. 7.8 for IEF. Currently, I favor shorter duration but technically they are both firmly in the "intermediate term bond" category.

I wouldn't sweat it too much either way, go with what you like. You'll be fine.
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Re: PP Inspired Leveraged Portfolios

Post by hydromod » Fri Jun 18, 2021 1:10 pm

Hi

I just ran across this forum the other day. I'm one of those on the boglehead forum following the leveraged ETF discussions, and it gave me great comfort that folks have been working this angle since 2011. I'll admit that there are a number of excitable folks hearing about 3x LETFs, but there are more cautious folks too...

I've been working variants of the so-called Hedgefundie Excellent Adventure (HFEA) since mid 2019 with a small percentage of my portfolio, all in a Roth account. The Roth allows frequent rebalancing without worrying about tax consequences, and for good or ill the portfolio is completely boxed off from my main portfolio.

The original version of the HFEA was a 40/60 UPRO/TMF portfolio with quarterly rebalancing, based on the expectation that future monetary policy will be fairly similar to the period since the early 1980s. So approximately risk balanced but missing parts of the PP. The original poster (Hedgefundie) moved to 55/45 UPRO/TMF after lots of discussion about poor expected treasury yields. Hedgefundie no longer posts, unfortunately, he felt like some folks were a little too contentious on the forum.

There's a bunch of splinter variants to the HFEA, some using TQQQ instead of or augmenting UPRO, some using EDV and reducing the UPRO fraction, some deleveraging or over-leveraging in various ways.

Folks seem to have come to the conclusion that it's better to use the 3x LETFs titrated with 1x ETFs to deleverage, rather than directly using 2x LETFs, for cost purposes.

I made some behavioral mistakes during 2020 (not disastrous but eye-opening), so I've been thinking hard about how to handle the 3x LETFs going forward.

I've thought about 3x permanent portfolio, all-weather portfolio, and golden butterfly, among others. I'm definitely interested in a relatively smooth ride compared to shooting for the moon.

I've personally settled on a flavor of risk-parity approach that attempts to maintain a relatively constant proportion of risk among the assets while minimizing variance given that constraint, and rebalance frequently. In effect, this approach deleverages equities during high volatility and re-leverages during calmer periods. I really like that the main tuning parameters are just the relative fraction of risk between equities, bonds, and gold (when it is included in the portfolio); I can mix and match 1x, 2x, and 3x funds in backtesting without inadvertently changing the risk profile.

Backtesting to the 1980s with daily returns (using synthetic extensions for earlier years) suggests that this would have shifted around the allocations quite a bit over time, but would have consistently maintained positive rolling two-year CAGRs over essentially the entire duration.

I'm currently in a UPRO/TQQQ/UTSL/DRN/TMF portfolio with 2/3 of risk to equities, but I'm considering running a URTY/TQQQ/DRN/TMF portfolio to (i) simplify, reduce correlations, and take advantage of barbelling, and (ii) assigning 3/4 of risk to equities to slightly boost returns.

My thought is that the lack of a 3x gold takes gold out of the portfolio, because a 2x gold isn't volatile enough to balance the 3x funds without taking up too much of the allocation.

My thought is that TMF is not going to provide much return going forward in general, but is the safety net. Backtesting with cash taking the place of TMF suggests that volatility-based leveraging/deleveraging may have been quite effective even in 2000 and 2008, so any flight to safety effect in TMF is a bonus rather than a requirement.

My thought is that TYD is also not going to provide much return, any rebalancing with TMF is small, and TYD takes too much of the portfolio because it isn't volatile enough to counterbalance the 3x equities.

With that introduction, I'm curious as to what folks here think of this approach, if people are using such adaptive allocations, and any experience that people might have in that regard.

Thanks
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Re: PP Inspired Leveraged Portfolios

Post by StrategyDriven » Fri Jun 18, 2021 1:47 pm

Welcome Hydromod,

The past 10+ years have been incredible for these leveraged adaptive asset allocation / min variance type strategies. My issue is that if you extended them back in time they nearly blow up with up to 90% drawdowns. I don't see anything wrong with some allocation to this type of strategy but I think people like Private Farmer have been terrifically lucky to go all in and on margin with regard to the timing of their investing heavily in these strategies, it worked out, but may not have in a different time period.
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Re: PP Inspired Leveraged Portfolios

Post by hydromod » Fri Jun 18, 2021 4:56 pm

Oh, I fully appreciate how these funds can dive. My pet example is UOPIX, which is a 2x NASDAQ starting in 1998. Real horror show a couple of years after initiation.

That's in part why I'm keen on the adaptive risk-budget weighting based on volatility. I haven't seen the portfolio volatility in backtesting nearly as much as the individual assets, simply because the equity fraction tended to drop a lot prior to and during crashes.

My big test is 1987 in that regard. 2000 and 2008 not so much.

No guarantees going forward of course.

I can see putting a quarter of my portfolio to a 3x scheme; but that's overall not that big of an overall leverage.
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Re: PP Inspired Leveraged Portfolios

Post by Mark Leavy » Fri Jun 18, 2021 5:10 pm

Volatility is completely unreliable for predicting market crashes.

I wouldn't depend on volatility weighting as a safeguard against going bust. When the event happens, it will be too late. Maximum historical drawdown is a better measure, but also not foolproof. I would add a healthy margin of safety on top of that.
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Re: PP Inspired Leveraged Portfolios

Post by StrategyDriven » Fri Jun 18, 2021 5:10 pm

hydromod wrote:
Fri Jun 18, 2021 4:56 pm
Oh, I fully appreciate how these funds can dive. My pet example is UOPIX, which is a 2x NASDAQ starting in 1998. Real horror show a couple of years after initiation.

That's in part why I'm keen on the adaptive risk-budget weighting based on volatility. I haven't seen the portfolio volatility in backtesting nearly as much as the individual assets, simply because the equity fraction tended to drop a lot prior to and during crashes.

My big test is 1987 in that regard. 2000 and 2008 not so much.

No guarantees going forward of course.

I can see putting a quarter of my portfolio to a 3x scheme; but that's overall not that big of an overall leverage.
My MAX PAIN strategy sustained a 67% drawdown in backtesting back in Oct of 1987, good to know these things ahead of time I think.

- to clarify my comment about 'good to know these things ahead of time I think', I realize that could read funny, I don't mean that you will know what is going to happen, but it's good to know what happened in long term backtesting so that you are aware of what may happen in the future.

Link to drawdown info
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Re: PP Inspired Leveraged Portfolios

Post by StrategyDriven » Fri Jun 18, 2021 5:15 pm

Mark Leavy wrote:
Fri Jun 18, 2021 5:10 pm
Volatility is completely unreliable for predicting market crashes.

I wouldn't depend on volatility weighting as a safeguard against going bust. When the event happens, it will be too late. Maximum historical drawdown is a better measure, but also not foolproof. I would add a healthy margin of safety on top of that.
yep, the problem with volatility is that it's a reactionary number. By the time it goes up, the sh*t has already hit the fan.
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Re: PP Inspired Leveraged Portfolios

Post by hydromod » Fri Jun 18, 2021 5:40 pm

StrategyDriven wrote:
Fri Jun 18, 2021 5:10 pm
My MAX PAIN strategy sustained a 67% drawdown in backtesting back in Oct of 1987, good to know these things ahead of time I think.

Link to drawdown info
That's quite a nice linked document there! I agree you want to know about how much pain to expect.

Do you find that the trend following seems to be a bit wobbly in the last five or ten years? It seems to me as though the market is responding much faster than in prior decades.

I found that it would have made a big difference exactly when rebalancing took place in 1987. Some of the bogleheads people were fixated on results based on quarterly rebalancing with a fixed start date, which gives pretty optimistic returns when aligned on quarters. I was trying all sorts of combinations of start date and rebalancing frequency.

Out of curiosity, how do you project back to 1979? I use VFINX and VUSTX, but I don't know how to go back for URTY/MIDU/EDV.

I'm a bit concerned that my synthetic LETF returns seem optimistic, even accounting for ER and borrowing costs and trading slippage.
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Re: PP Inspired Leveraged Portfolios

Post by StrategyDriven » Fri Jun 18, 2021 6:07 pm

hydromod wrote:
Fri Jun 18, 2021 5:40 pm
StrategyDriven wrote:
Fri Jun 18, 2021 5:10 pm
My MAX PAIN strategy sustained a 67% drawdown in backtesting back in Oct of 1987, good to know these things ahead of time I think.

Link to drawdown info
That's quite a nice linked document there! I agree you want to know about how much pain to expect.

Do you find that the trend following seems to be a bit wobbly in the last five or ten years? It seems to me as though the market is responding much faster than in prior decades.

I found that it would have made a big difference exactly when rebalancing took place in 1987. Some of the bogleheads people were fixated on results based on quarterly rebalancing with a fixed start date, which gives pretty optimistic returns when aligned on quarters. I was trying all sorts of combinations of start date and rebalancing frequency.

Out of curiosity, how do you project back to 1979? I use VFINX and VUSTX, but I don't know how to go back for URTY/MIDU/EDV.

I'm a bit concerned that my synthetic LETF returns seem optimistic, even accounting for ER and borrowing costs and trading slippage.
It is not my experience that the past 5 or 10 years have been wobbly, my decade by decade results are remarkably similar over the decades and so far this decade isn't deviating significantly. What it seems to me is that we've had more very fast drops and sometimes very fast recoveries. Certainly the Oct 1987 drop was super fast, but it seems more common lately.

Regarding the fixed start date with quarterly rebalancing, I prefer annual and decade metrics to look at, they may be arbitrary to some, but they repeating and easy to compare to me and they are completely objective. I disclose full metrics back to 1980 for all strategies for example, even when it shows a 67% drawdown, I don't think everybody is so forthright and try to pretty up what they show.

D1984 on this form was gracious enough to get me daily return data for most of the components in my strategies and that was used to extend the LETF. No idea what his connections and sources are, but it was an incredible gift to get that data. I've got a couple components that could use improving (noted in the deck) but it's very solid and realistic data, not perfect, in my opinion.
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Re: PP Inspired Leveraged Portfolios

Post by hydromod » Fri Jun 18, 2021 6:34 pm

StrategyDriven wrote:
Fri Jun 18, 2021 6:07 pm
It is not my experience that the past 5 or 10 years have been wobbly, my decade by decade results are remarkably similar over the decades and so far this decade isn't deviating significantly. What it seems to me is that we've had more very fast drops and sometimes very fast recoveries. Certainly the Oct 1987 drop was super fast, but it seems more common lately.

Regarding the fixed start date with quarterly rebalancing, I prefer annual and decade metrics to look at, they may be arbitrary to some, but they repeating and easy to compare to me and they are completely objective. I disclose full metrics back to 1980 for all strategies for example, even when it shows a 67% drawdown, I don't think everybody is so forthright and try to pretty up what they show.

D1984 on this form was gracious enough to get me daily return data for most of the components in my strategies and that was used to extend the LETF. No idea what his connections and sources are, but it was an incredible gift to get that data. I've got a couple components that could use improving (noted in the deck) but it's very solid and realistic data, not perfect, in my opinion.
I end up going to the opposite extreme for metrics, but it isn't good for summary presentations like you are doing. I end up plotting a CDF based on every possible fixed x-year return (i.e., for each starting date that fits x years in the data). x might be 3, 5 or 10 years, which seems to me to be a reasonable investing time frame for comparisons and completely start-date independent. Perhaps I like that because my background is risk from the science/engineering side. For your purposes, the annual and decade metrics are quite fine. I tend to like using tell-tale plots, which are the deviation from a reference portfolio, because that lets me see where an algorithm is having systematic issues.

There's work afoot in the bogleheads forum to estimate various leveraged funds, with spreadsheets having daily/monthly/annual steps. I've felt very lucky to have access to that, but the daily returns generally don't go back as far as you have. I think monthly goes back to 1955 or so. The compilers have had issues finding dividend information, if I understand correctly. You have definitely received a gift.

As a matter of curiousity, how do you model slippage from trades? I've noticed that slippage tends to ding returns noticeably with some of my more frequent rebalancing extravaganzas, especially with 1x funds.
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Re: PP Inspired Leveraged Portfolios

Post by hydromod » Fri Jun 18, 2021 9:58 pm

Just as a point of comparison with the MAX PAIN approach, here's an attempt with what I have data for, leaving out MIDU and EDV.

Image

I think the synthetic data are optimistic, but what gets my attention is the relatively mild portfolio drawdowns even though the LETFs had severe ones.

If I compare with the corresponding 1x funds, I also get muted drawdowns for the portfolio. I think that the 1x portfolio also may be performing a little poorer in a relative sense because of trade slippage, which isn't as proportionately large for the 3x LETFs.

Image

I hope folks find this interesting - it's getting a flavor of steady returns that is a bit similar to what you all have been doing for so long with the leveraged PP, using some of the same LETFs, but using a bit different theoretical approach.
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Re: PP Inspired Leveraged Portfolios

Post by hydromod » Sat Jun 19, 2021 12:37 pm

vincent_c wrote:
Fri Jun 18, 2021 10:24 pm
Honestly this is a bit hard to follow.

Can you write down your strategy in the simplest and shortest way possible? Also, are you looking for advice or critique or neither? Are you open to discussion to actually figure out whether this is a smart thing to do, or is this something that is just for fun and it all resorts to something personal?

I’ve followed the HFEA threads myself but there are just so many problems with the strategies I’ve seen that a lot of times I think people are distracted by the data and analysis that they forget the basic stuff like whether there are cheaper ways to acheive the same things with lower risk etc.
Yeah, I dumped too much at once. I blew through the thread so quickly once I found it that I got over-excited...

My background is numerical and risk modeling in the sciences, not at all finance, so I'm still in the learning stage for sure but I do have the math and modeling background to follow and test stuff. I write my own Matlab code for testing, and check against portfolio visualizer.

I've been trying to soak up the ways that people approach finance, especially the modeling part, to pick out a useful way to suit my own personality and financial situation. So the back and forth regarding strategy on the HFEA threads have been illuminating for me. I even started a thread here to capture my learning process a bit.

I'm quite interested in applying a sound levered strategy going forward within a smallish siloed Roth account, currently about 5 percent of an overall portfolio. The fairly typical portfolio outside of that account should handle retirement needs adequately, so the Roth account is partly for frills, partly for legacy, and partly for intellectual interest. This Roth account is the only place I have access to levered funds. Because it is hard to get significant money into the Roth account, which constrains rebalancing, I'm conceptually treating the silo as an entire portfolio that I want to grow rapidly but safely.

If the testing performs well in real life, once I leave employment I would be tempted to roll a good chunk of my 403b into the 3x strategy and perhaps use a similar 1x approach with most of the rest. A goal is to reduce sequence of returns risks during decumulation without cutting returns too drastically.

I'm mostly interested in getting feedback on the levered portfolio strategy itself, not so much on how it interacts with the total portfolio. The strategy is really a combination of things I've seen, but it seems just a bit different from most strategies that people use so I thought it might be of interest for you all as offering a different perspective for a similar end.

I'm also trying to write out exactly what is going on to clarify the ideas in my mind.

I will say that I'm comfortable with trading ETFs and I think I have a good feel for the different behaviors between 1x, 2x, and 3x ETFs, and the risks associated with levered ETFs. Options and futures and such are all Greek to me, and I'd have to see a compelling reason to dive into such things.

Approach

With all that said, the strategy is really quite simple. I use a minimum variance optimizer for a portfolio of N assets, given a historical variance-covariance matrix for the assets, to develop the weights for the assets that would minimize the portfolio variance given the variance-covariance matrix. The optimizer is constrained by the requirement that the weights are between 0 and 1, and sum to 1. I don't provide expected returns.

A useful twist is that I also assign a risk weight to each asset as another constraint. The risk weight constrains the proportion of portfolio volatility derived from each asset.

A key implementation point is that I assign the risk weight according to category (e.g., equities, bonds, gold), assign each asset to a category, and evenly spread the risk weight among all assets in a category. For example, the equities risk weight might be 0.75 and bonds risk weight is 0.25. If I have three equities (UPRO, URTY, TQQQ) and two bonds (TMF, TYD), each equity has a risk weight of 0.25 and each bond has a risk weight of 0.125.

Each time I rebalance, I recalculate the weights based on the most current estimate of the variance-covariance matrix. The weights may adjust quite a lot as volatilities change over time.

Assigning risk weights in this way allows me to compare returns and volatilities for different fund combinations on an apples-to-apples risk basis. All I tune is the fraction of risk assigned to each category, the lookback period for calculating the variance-covariance matrix, and the rebalancing frequency strategy.

When I calculate the portfolio returns, I try to account for trading slippage from the bid-ask spread and for variation of the asset funds during the trading day, randomly sampling between the high and low values for the day for each fund.

I find that the strategy is not all that sensitive to
  • the overall risk budget for equities between 1/2 and 3/4 (usually higher CAGR for higher equity risk budget)
  • the lookback period for the variance-covariance matrix (I find two or three months seems to work pretty well)
  • the rebalancing frequency (I find 10 to 20 trading days tends to give reasonably smooth results)
This is a much higher trading frequency than would be very practical in a taxable account, and would likely run into tax issues.

My strong suspicion is that a band approach would work about as well for determining trading, perhaps with a relative band of 15 percent or so.

I don't believe any part of this approach is new, but perhaps the pieces haven't been combined in quite this way.

Interpretation

I think that the approach seems to handle one of the aspects of 3x LETFs that people are most concerned about, which is volatility. The figures in my previous entry show quite mild portfolio drawdowns relative to the individual funds, for example. My estimated annualized volatility for QQQ alone and the URTY/TQQQ/TMF portfolio I showed in my previous entry are 0.26 and 0.29, respectively, from 1986 to present.

I think that the performance ends up taking advantage of two features: (i) volatility clustering and (ii) constant expected return.

Volatility clustering allows some predictability for future volatility based on recent volatility.

In some of my testing, I tried to see if I could also use recent volatility or recent market trends to predict future returns for the S&P 500 and NASDAQ. I found no predictability at all. I interpret this to mean that the expected returns are essentially the same, regardless of volatility. Of course, volatility is so large that maybe it's just too hard to measure expected returns. An implication is that expected returns may be essentially constant over time. At first I was disappointed that I couldn't find an edge (not that I expected to), but if it is actually the case that expected returns are constant over time then that may be a feature, not a bug.

In essence, asset allocation determines the risk budget. When the asset allocation is fixed over time, the risk fraction changes over time as volatility changes. The fixed asset allocation has to handle the high-volatility periods as well as the low-volatility periods, with the same expected return throughout.

When the risk budget determines the asset allocation, the asset is emphasized during low-volatility times and de-emphasized in high-volatility times. If the average asset allocation is the same over some period of time, and the expected return is the same over time, then it naturally follows that adjusting the asset allocation to emphasize periods of low volatility must naturally result in overall lower portfolio volatility without affecting expected returns.

This adaptive allocation naturally gives a smoothing effect to the portfolio. So it tends to lag (relatively) during bulls and gain (relatively) during bears. An adventurous sort might adjust the risk budget factor dynamically, increasing the equity risk during low volatility and decreasing during high volatility.

One flaw with the HFEA approach that people have often pointed to is the anticipated loss of the tailwind from treasury rates dropping. I suspect strongly that this adaptive approach would still perform adequately even with cash instead of TMF, albeit with smaller returns and higher volatility. A zero-return TMF may still provide the benefit of enhanced crash protection compared to cash.

Ok, I'll step down from the soapbox now.

Hopefully you found it thought-provoking and useful, and I especially welcome comments that pick up things that I screwed up or overlooked. These have been very useful on the boglehead forum. I try to be careful but such errors are quite possible.
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Re: PP Inspired Leveraged Portfolios

Post by Mark Leavy » Sat Jun 19, 2021 12:56 pm

All of the mathematical techniques you describe above are predicated on Gaussian distributions of returns. The math is not stable for other distributions. Gaussian models are a deadly simplification for financial planning. And higher order models scaffolded onto those simplifications are even more deadly.
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Re: PP Inspired Leveraged Portfolios

Post by modeljc » Sat Jun 19, 2021 1:58 pm

hydromod wrote:
Sat Jun 19, 2021 12:37 pm
vincent_c wrote:
Fri Jun 18, 2021 10:24 pm
Honestly this is a bit hard to follow.

Can you write down your strategy in the simplest and shortest way possible? Also, are you looking for advice or critique or neither? Are you open to discussion to actually figure out whether this is a smart thing to do, or is this something that is just for fun and it all resorts to something personal?

I’ve followed the HFEA threads myself but there are just so many problems with the strategies I’ve seen that a lot of times I think people are distracted by the data and analysis that they forget the basic stuff like whether there are cheaper ways to acheive the same things with lower risk etc.
Yeah, I dumped too much at once. I blew through the thread so quickly once I found it that I got over-excited...

My background is numerical and risk modeling in the sciences, not at all finance, so I'm still in the learning stage for sure but I do have the math and modeling background to follow and test stuff. I write my own Matlab code for testing, and check against portfolio visualizer.

I've been trying to soak up the ways that people approach finance, especially the modeling part, to pick out a useful way to suit my own personality and financial situation. So the back and forth regarding strategy on the HFEA threads have been illuminating for me. I even started a thread here to capture my learning process a bit.

I'm quite interested in applying a sound levered strategy going forward within a smallish siloed Roth account, currently about 5 percent of an overall portfolio. The fairly typical portfolio outside of that account should handle retirement needs adequately, so the Roth account is partly for frills, partly for legacy, and partly for intellectual interest. This Roth account is the only place I have access to levered funds. Because it is hard to get significant money into the Roth account, which constrains rebalancing, I'm conceptually treating the silo as an entire portfolio that I want to grow rapidly but safely.

If the testing performs well in real life, once I leave employment I would be tempted to roll a good chunk of my 403b into the 3x strategy and perhaps use a similar 1x approach with most of the rest. A goal is to reduce sequence of returns risks during decumulation without cutting returns too drastically.

I'm mostly interested in getting feedback on the levered portfolio strategy itself, not so much on how it interacts with the total portfolio. The strategy is really a combination of things I've seen, but it seems just a bit different from most strategies that people use so I thought it might be of interest for you all as offering a different perspective for a similar end.

I'm also trying to write out exactly what is going on to clarify the ideas in my mind.

I will say that I'm comfortable with trading ETFs and I think I have a good feel for the different behaviors between 1x, 2x, and 3x ETFs, and the risks associated with levered ETFs. Options and futures and such are all Greek to me, and I'd have to see a compelling reason to dive into such things.

Approach

With all that said, the strategy is really quite simple. I use a minimum variance optimizer for a portfolio of N assets, given a historical variance-covariance matrix for the assets, to develop the weights for the assets that would minimize the portfolio variance given the variance-covariance matrix. The optimizer is constrained by the requirement that the weights are between 0 and 1, and sum to 1. I don't provide expected returns.

A useful twist is that I also assign a risk weight to each asset as another constraint. The risk weight constrains the proportion of portfolio volatility derived from each asset.

A key implementation point is that I assign the risk weight according to category (e.g., equities, bonds, gold), assign each asset to a category, and evenly spread the risk weight among all assets in a category. For example, the equities risk weight might be 0.75 and bonds risk weight is 0.25. If I have three equities (UPRO, URTY, TQQQ) and two bonds (TMF, TYD), each equity has a risk weight of 0.25 and each bond has a risk weight of 0.125.

Each time I rebalance, I recalculate the weights based on the most current estimate of the variance-covariance matrix. The weights may adjust quite a lot as volatilities change over time.

Assigning risk weights in this way allows me to compare returns and volatilities for different fund combinations on an apples-to-apples risk basis. All I tune is the fraction of risk assigned to each category, the lookback period for calculating the variance-covariance matrix, and the rebalancing frequency strategy.

When I calculate the portfolio returns, I try to account for trading slippage from the bid-ask spread and for variation of the asset funds during the trading day, randomly sampling between the high and low values for the day for each fund.

I find that the strategy is not all that sensitive to
  • the overall risk budget for equities between 1/2 and 3/4 (usually higher CAGR for higher equity risk budget)
  • the lookback period for the variance-covariance matrix (I find two or three months seems to work pretty well)
  • the rebalancing frequency (I find 10 to 20 trading days tends to give reasonably smooth results)
This is a much higher trading frequency than would be very practical in a taxable account, and would likely run into tax issues.

My strong suspicion is that a band approach would work about as well for determining trading, perhaps with a relative band of 15 percent or so.

I don't believe any part of this approach is new, but perhaps the pieces haven't been combined in quite this way.

Interpretation

I think that the approach seems to handle one of the aspects of 3x LETFs that people are most concerned about, which is volatility. The figures in my previous entry show quite mild portfolio drawdowns relative to the individual funds, for example. My estimated annualized volatility for QQQ alone and the URTY/TQQQ/TMF portfolio I showed in my previous entry are 0.26 and 0.29, respectively, from 1986 to present.

I think that the performance ends up taking advantage of two features: (i) volatility clustering and (ii) constant expected return.

Volatility clustering allows some predictability for future volatility based on recent volatility.

In some of my testing, I tried to see if I could also use recent volatility or recent market trends to predict future returns for the S&P 500 and NASDAQ. I found no predictability at all. I interpret this to mean that the expected returns are essentially the same, regardless of volatility. Of course, volatility is so large that maybe it's just too hard to measure expected returns. An implication is that expected returns may be essentially constant over time. At first I was disappointed that I couldn't find an edge (not that I expected to), but if it is actually the case that expected returns are constant over time then that may be a feature, not a bug.

In essence, asset allocation determines the risk budget. When the asset allocation is fixed over time, the risk fraction changes over time as volatility changes. The fixed asset allocation has to handle the high-volatility periods as well as the low-volatility periods, with the same expected return throughout.

When the risk budget determines the asset allocation, the asset is emphasized during low-volatility times and de-emphasized in high-volatility times. If the average asset allocation is the same over some period of time, and the expected return is the same over time, then it naturally follows that adjusting the asset allocation to emphasize periods of low volatility must naturally result in overall lower portfolio volatility without affecting expected returns.

This adaptive allocation naturally gives a smoothing effect to the portfolio. So it tends to lag (relatively) during bulls and gain (relatively) during bears. An adventurous sort might adjust the risk budget factor dynamically, increasing the equity risk during low volatility and decreasing during high volatility.

One flaw with the HFEA approach that people have often pointed to is the anticipated loss of the tailwind from treasury rates dropping. I suspect strongly that this adaptive approach would still perform adequately even with cash instead of TMF, albeit with smaller returns and higher volatility. A zero-return TMF may still provide the benefit of enhanced crash protection compared to cash.

Ok, I'll step down from the soapbox now.

Hopefully you found it thought-provoking and useful, and I especially welcome comments that pick up things that I screwed up or overlooked. These have been very useful on the boglehead forum. I try to be careful but such errors are quite possible.
What level of returns did the back testing produce? +20% or more?
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Re: PP Inspired Leveraged Portfolios

Post by hydromod » Sat Jun 19, 2021 5:17 pm

Mark Leavy wrote:
Sat Jun 19, 2021 12:56 pm
All of the mathematical techniques you describe above are predicated on Gaussian distributions of returns. The math is not stable for other distributions. Gaussian models are a deadly simplification for financial planning. And higher order models scaffolded onto those simplifications are even more deadly.
I agree that daily returns are not Gaussian. A Laplacian (double exponential) is better, but still inadequate to explain the tails. I agree that there are problems in precisely representing actual distributions and in calculating their parameters, and I agree that tail events (positive and negative) occur many orders of magnitude more frequently than a Gaussian distribution predicts.

But I'm missing out on what you are recommending, I guess.

In my mind, financial planning implies predicting conditions for the next few decades. What I'm talking about is using recent observations of volatility to estimate portfolio weights based on expectations that volatility will be fairly similar over the next couple of weeks, then readjusting based on new observations. Are you implying that this is a deadly practice in general? Even with a portfolio containing just low-volatility stocks and short-term treasuries? What is the threshold for deadly simplification?

I'd say a Gaussian is decent for say 9 out of 10 days, and not too bad for all but a few days every few months. So using tools based on a Gaussian approach are not likely to be too bad most of the time, and future parameter uncertainty is probably a bigger issue most of the time.

To me, the strategy is trying to deal with most levels of variability with the minimization part, which is decent for the smaller levels of volatility (i.e., almost all of the time). Even simpler models, which only consider variability but not correlation, do reasonably well in backtesting.

Mitigating very large events, in my mind, goes down to (i) selecting the funds that are used based on one's personal risk tolerance and (ii) setting the risk budget between equities and bonds.
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Re: PP Inspired Leveraged Portfolios

Post by hydromod » Sat Jun 19, 2021 5:45 pm

modeljc wrote:
Sat Jun 19, 2021 1:58 pm
What level of returns did the back testing produce? +20% or more?
Returns strongly depend on the selected funds and the risk budget allocation. You can get an idea from the two figures I plotted, which shows rolling 5-year CAGRs for a 1x and a 3x portfolio - the gray lines are the overall portfolio, the colored lines are the individual funds. In both, the LTT allocation averages roughly 50 percent over time. These represent pretty moderate allocations to equities.

The 1x portfolio (IWM/QQQ/TLT) tended to give rolling 5-year returns between 5 and 15 percent, and 10.6 percent CAGR over the entire duration with an annualized volatility of 9.8 percent.

The 3x portfolio (URTY/TQQQ/TMF) tended to give rolling 5-year CAGRs mostly between 20 and 80 percent, and ~50 percent CAGR over the entire duration with an annualized volatility of 29 percent. I take the higher range of returns with a very hefty grain of salt, though, because these include synthetic returns and I suspect that actual funds would have had additional costs that are not incorporated. The last ten years or so, with the actual funds, had rolling 5-year CAGRs between 20 and 40 percent (except for a few months in 2020) and an overall CAGR somewhere in the neighborhood of 30 percent.

The portfolios with 3x LETFs typically show a declining trend in returns after 2010, when the actual funds started becoming available. I don't know if this is because of optimistic assumptions or it would actually have been observed.
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Re: PP Inspired Leveraged Portfolios

Post by Mark Leavy » Sat Jun 19, 2021 8:40 pm

hydromod wrote:
Sat Jun 19, 2021 5:17 pm
...

Mitigating very large events, in my mind, goes down to (i) selecting the funds that are used based on one's personal risk tolerance and (ii) setting the risk budget between equities and bonds.
No issues hydromod. I'm just an old jaded engineer. When I see people making risk mitigation decisions with variance and co-variance matrices I tend to run the other direction as fast as I can.

For a lot of reasons.

Not just the tail risk but because variance is always a trailing statistic. And variance is meaningless for a non normal distribution.

It's possible I misread your scenario and you actually have very safe allocations based on asset diversification. It seems that is what you are implying. If so, my apologies and best of luck.
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Re: PP Inspired Leveraged Portfolios

Post by StrategyDriven » Sat Jun 19, 2021 9:00 pm

hydromod wrote:
Fri Jun 18, 2021 6:34 pm
As a matter of curiousity, how do you model slippage from trades? I've noticed that slippage tends to ding returns noticeably with some of my more frequent rebalancing extravaganzas, especially with 1x funds.
I do not account for slippage. I do track ETF prices for full month and don't account for any rebalancing at the start of the new month simply out of convenience, this way I can just use the more easily available monthly total performance data. I personally do my trades at noon the last day of the month so I'm super close to actual reported data, but even trading the opening morning as AllocateSmartely did a study a while back, it has a negligible impact over time, flip a coin as to whether any specific month turns out better or not, tends to neutralize over time.
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Re: PP Inspired Leveraged Portfolios

Post by hydromod » Sat Jun 19, 2021 10:14 pm

Mark Leavy wrote:
Sat Jun 19, 2021 8:40 pm
hydromod wrote:
Sat Jun 19, 2021 5:17 pm
...

Mitigating very large events, in my mind, goes down to (i) selecting the funds that are used based on one's personal risk tolerance and (ii) setting the risk budget between equities and bonds.
No issues hydromod. I'm just an old jaded engineer. When I see people making risk mitigation decisions with variance and co-variance matrices I tend to run the other direction as fast as I can.

For a lot of reasons.

Not just the tail risk but because variance is always a trailing statistic. And variance is meaningless for a non normal distribution.

It's possible I misread your scenario and you actually have very safe allocations based on asset diversification. It seems that is what you are implying. If so, my apologies and best of luck.
Yes, it's always hard to judge level of insight at first, especially on a touchy topic. Old scientist/engineer myself.

I've tried looking at more rigorous representations, but it would take a bit of coding to do and I suspect that I'd end up with fairly similar asset allocations in the end.

I try to update frequently to handle stale variance estimates. And shrug fatalistically because it's only an estimate; it won't be right, but hopefully it will bias things in the right direction more frequently than in the wrong direction.

I'm not positive that folks would necessarily find my asset allocation "very" safe. But I do try for low correlations and balance between assets to reduce portfolio risks.
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