Refinements to Hedgefundie's excellent approach

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

jarjarM wrote: Tue Apr 27, 2021 10:14 pm
Hydromod wrote: Tue Apr 27, 2021 9:50 pm
Thanks for the interesting post. Have you look at the look back window sensitivity? I saw you're doing 2 months but wondering if you see any improvement by going shorter look back since you're dealing with LETFs that tend to be more volatile. Thanks.
When I do inverse variance, I tend to use 21 days, although it doesn’t make a huge difference. I went to 42 days for the covariance matrix, but I haven’t tried different durations for that. I suspect that it won’t make much difference between 1, 2, or 3 months, based on inverse volatility testing.
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randyharris
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Re: Refinements to Hedgefundie's excellent approach

Post by randyharris »

RovenSkyfall wrote: Thu Mar 18, 2021 2:54 pm
Hydromod wrote: Tue Feb 23, 2021 4:09 pm
ljford7 wrote: Tue Feb 23, 2021 3:17 pm
Hydromod wrote: Thu Jul 30, 2020 10:12 am I'm prepared to switch over to TMV if it looks like we've entered a rising interest rates environment. IMO significant positive returns and moderately positive correlation is more important than negative returns with moderately negative correlation.

I'm still mulling over exit strategies for a long-term market flatline; this is such a small portion of my total portfolio that I'm inclined to just let it ride for a while, but that's not a decision that needs to be made in a hurry.
Very interesting thread and I learned quite a bit. Just curious, with TMF getting beat up pretty badly lately, did you ever make headway into a system to make the switch to TMV if needed?
Not yet, but it’s starting to be something that is ticking a little bit.
After seeing this paper: https://papers.ssrn.com/sol3/papers.cfm ... id=2741701, I have been stuck on the idea that maybe a UPRO/TMF 200DMA is the best way to avoid losses of TMF, but use it in a downturn. Your prior PV simulations looked to use end of month data, but that doesnt seem specific enough to test the 200dMA. Any thoughts on running this in Matlab with daily data?
You can do 10 month in PV which is virtually the same as 200 day
ScaledWheel
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Re: Refinements to Hedgefundie's excellent approach

Post by ScaledWheel »

I got interested in this approach and read up a bit. Of interest to some here who like testing with their own data but don't want to code up their own implementation, the authors of a recent paper on risk-budgeting [1] have a python package [2] that's easy to use. I especially like the ConstrainedRiskBudgeting class [3] as it allows you to specify constraints on the weights of securities, e.g., if you always want to have more than 10 or 15% of your portfolio in an asset you can set that constraint.

I just need to create some synthetic data for leveraged funds to test it out a bit more.

[1] https://papers.ssrn.com/sol3/papers.cfm ... id=3331184
[2] https://github.com/jcrichard/pyrb
[3] https://github.com/jcrichard/pyrb/blob/ ... on.py#L220
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RovenSkyfall
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Re: Refinements to Hedgefundie's excellent approach

Post by RovenSkyfall »

ScaledWheel wrote: Wed May 12, 2021 10:26 pm I got interested in this approach and read up a bit. Of interest to some here who like testing with their own data but don't want to code up their own implementation, the authors of a recent paper on risk-budgeting [1] have a python package [2] that's easy to use. I especially like the ConstrainedRiskBudgeting class [3] as it allows you to specify constraints on the weights of securities, e.g., if you always want to have more than 10 or 15% of your portfolio in an asset you can set that constraint.

I just need to create some synthetic data for leveraged funds to test it out a bit more.

[1] https://papers.ssrn.com/sol3/papers.cfm ... id=3331184
[2] https://github.com/jcrichard/pyrb
[3] https://github.com/jcrichard/pyrb/blob/ ... on.py#L220
Thank you for the post. Will have to take a look at some point. Please post results you find interesting!

Re: Synthetics, there is a long post about this somewhere around here where you can get access to a well thought out synthetic version of the LETFs.
I saved my money, but it can't save me | The Chariot
ScaledWheel
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Re: Refinements to Hedgefundie's excellent approach

Post by ScaledWheel »

RovenSkyfall wrote: Thu May 13, 2021 8:23 am Thank you for the post. Will have to take a look at some point. Please post results you find interesting!

Re: Synthetics, there is a long post about this somewhere around here where you can get access to a well thought out synthetic version of the LETFs.
I took a quick look at the code and it seems to match the math in the paper, so I'm not too worried about correctness, though I would triple check before making any "real money" decisions behind it.

Regarding the LETFs, it seems easy to generate _if_ you can get access to the index data, which is the hard part. I'm using Hedgefundie's simulated TMF and UPRO data, which goes back to 86, and was easily able to generate TQQQ going back to 99, but gotta figure out how to get daily return data for some of the other indices. Will try and dig around tonight to do so.
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

ScaledWheel wrote: Thu May 13, 2021 11:58 am
RovenSkyfall wrote: Thu May 13, 2021 8:23 am Thank you for the post. Will have to take a look at some point. Please post results you find interesting!

Re: Synthetics, there is a long post about this somewhere around here where you can get access to a well thought out synthetic version of the LETFs.
I took a quick look at the code and it seems to match the math in the paper, so I'm not too worried about correctness, though I would triple check before making any "real money" decisions behind it.

Regarding the LETFs, it seems easy to generate _if_ you can get access to the index data, which is the hard part. I'm using Hedgefundie's simulated TMF and UPRO data, which goes back to 86, and was easily able to generate TQQQ going back to 99, but gotta figure out how to get daily return data for some of the other indices. Will try and dig around tonight to do so.
Simulating leveraged ETFs may be the post
ScaledWheel
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Re: Refinements to Hedgefundie's excellent approach

Post by ScaledWheel »

Hydromod wrote: Thu May 13, 2021 9:21 pm
ScaledWheel wrote: Thu May 13, 2021 11:58 am Regarding the LETFs, it seems easy to generate _if_ you can get access to the index data, which is the hard part. I'm using Hedgefundie's simulated TMF and UPRO data, which goes back to 86, and was easily able to generate TQQQ going back to 99, but gotta figure out how to get daily return data for some of the other indices. Will try and dig around tonight to do so.
Simulating leveraged ETFs may be the post
Thanks, I did find that helpful. It seems to follow the math I was using, though lots of discussions about which borrowing rate to use. As I'm not too concerned with <1% CAGR differences in results, I'm not too worried about that and am just using the 90-day TBill [0] rate with a +0.2% bias added on based off one of the papers I read [1]. Still the major problem is finding an ETF with history going back pre-2000.

A question for you (Hydromod). I think you mentioned in the HFEA thread that you are using a combination of UPRO/TMF/TQQQ/DRN/UTSL for your mix. I can simulate these back to mid-2000's with VNQ:DRN, VPU:UTSL. Did you get data further back than this or no? Ideally, I'd like to have at least two bear markets (2000 and 2009) to look at how the portfolio performs.

Preliminarily, I have found that using basic momentum metrics to set the TMF risk budget is rather successful for increasing exposure to TMF before/during drawdowns for capital preservation. But there is still plenty of work needed to convince myself it's a worthwhile strategy to throw a small amount of money into. And of course this has grown from a small analysis project to a software project :D

[0]: https://fred.stlouisfed.org/series/DTB3
[1]: https://papers.ssrn.com/sol3/papers.cfm ... id=3272486 Believe discussion starts after equation 6
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

ScaledWheel wrote: Mon May 17, 2021 6:51 am Thanks, I did find that helpful. It seems to follow the math I was using, though lots of discussions about which borrowing rate to use. As I'm not too concerned with <1% CAGR differences in results, I'm not too worried about that and am just using the 90-day TBill [0] rate with a +0.2% bias added on based off one of the papers I read [1]. Still the major problem is finding an ETF with history going back pre-2000.

A question for you (Hydromod). I think you mentioned in the HFEA thread that you are using a combination of UPRO/TMF/TQQQ/DRN/UTSL for your mix. I can simulate these back to mid-2000's with VNQ:DRN, VPU:UTSL. Did you get data further back than this or no? Ideally, I'd like to have at least two bear markets (2000 and 2009) to look at how the portfolio performs.

Preliminarily, I have found that using basic momentum metrics to set the TMF risk budget is rather successful for increasing exposure to TMF before/during drawdowns for capital preservation. But there is still plenty of work needed to convince myself it's a worthwhile strategy to throw a small amount of money into. And of course this has grown from a small analysis project to a software project :D

[0]: https://fred.stlouisfed.org/series/DTB3
[1]: https://papers.ssrn.com/sol3/papers.cfm ... id=3272486 Believe discussion starts after equation 6
I use RWR:DRN (start 2001-04-23), XLU:UTSL (1998-12-18), ^NDX:QQQ:TQQQ (1985-01-31/1999-03-10), and VFINX:UPRO (1976-08-31).

TMF is either TLTsim:TLT:TMF (mid 1997) or TMFhf:TMF (1986), where TLTsim is from Simba's daily simulated funds and TMFhf is Hedgefundie's original TMF simulated sequence. I prefer TLTsim, but it doesn't go back as far.

It's useful to omit the DRN part to go back to 1999. The other useful thing is to try 2x and use UOPIX as the actual 2x NASDAQ. Just doing the minimum variance formality looks like it would have handled the events since 1999 pretty well (since 1986 if DRN and UTSL are left out).

I'd be interested in what you are doing for the momentum. The best I've found is to use the unemployment index, which looks like it might have given useful risk budget signals (although not useful for the very fast-moving COVID shock), but that's not momentum.
ScaledWheel
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Re: Refinements to Hedgefundie's excellent approach

Post by ScaledWheel »

Hydromod wrote: Mon May 17, 2021 9:07 pm
ScaledWheel wrote: Mon May 17, 2021 6:51 am Thanks, I did find that helpful. It seems to follow the math I was using, though lots of discussions about which borrowing rate to use. As I'm not too concerned with <1% CAGR differences in results, I'm not too worried about that and am just using the 90-day TBill [0] rate with a +0.2% bias added on based off one of the papers I read [1]. Still the major problem is finding an ETF with history going back pre-2000.

A question for you (Hydromod). I think you mentioned in the HFEA thread that you are using a combination of UPRO/TMF/TQQQ/DRN/UTSL for your mix. I can simulate these back to mid-2000's with VNQ:DRN, VPU:UTSL. Did you get data further back than this or no? Ideally, I'd like to have at least two bear markets (2000 and 2009) to look at how the portfolio performs.

Preliminarily, I have found that using basic momentum metrics to set the TMF risk budget is rather successful for increasing exposure to TMF before/during drawdowns for capital preservation. But there is still plenty of work needed to convince myself it's a worthwhile strategy to throw a small amount of money into. And of course this has grown from a small analysis project to a software project :D

[0]: https://fred.stlouisfed.org/series/DTB3
[1]: https://papers.ssrn.com/sol3/papers.cfm ... id=3272486 Believe discussion starts after equation 6
I use RWR:DRN (start 2001-04-23), XLU:UTSL (1998-12-18), ^NDX:QQQ:TQQQ (1985-01-31/1999-03-10), and VFINX:UPRO (1976-08-31).

TMF is either TLTsim:TLT:TMF (mid 1997) or TMFhf:TMF (1986), where TLTsim is from Simba's daily simulated funds and TMFhf is Hedgefundie's original TMF simulated sequence. I prefer TLTsim, but it doesn't go back as far.

It's useful to omit the DRN part to go back to 1999. The other useful thing is to try 2x and use UOPIX as the actual 2x NASDAQ. Just doing the minimum variance formality looks like it would have handled the events since 1999 pretty well (since 1986 if DRN and UTSL are left out).

I'd be interested in what you are doing for the momentum. The best I've found is to use the unemployment index, which looks like it might have given useful risk budget signals (although not useful for the very fast-moving COVID shock), but that's not momentum.
What has looked good in backtesting, but nothing definitive yet, is to use some multiplier of the relative strength index [0] of the SP500 to set the risk budget for TMF. The idea being that I want to reduce the risk budget of TMF during drawdowns and get more exposure to equities. I'm also playing with adding min(0, EMA_slope) term to increase equity exposure even further.

[0]: https://www.investopedia.com/terms/r/rsi.asp
ScaledWheel
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Re: Refinements to Hedgefundie's excellent approach

Post by ScaledWheel »

Hydromod wrote: Mon May 17, 2021 9:07 pm I'd be interested in what you are doing for the momentum. The best I've found is to use the unemployment index, which looks like it might have given useful risk budget signals (although not useful for the very fast-moving COVID shock), but that's not momentum.
At the end of the day, there really is not much of an upside in using basic momentum metrics for portfolio weighting once you have more than a couple funds. Image below is a telltale chart with the base as HFEA (55/45). All portfolios are rebalanced at the beginning of the quarter.

Personally I am using the red portfolio with momentum-based risk budgeting (RB). Since I am running a script to get my portfolio weights on rebalancing, I am just adding in the momentum piece as I like that it increases TMF budgets at highs and decreases TMF budgets during drawdowns. Although I will say the impact does appear to be marginal.

I set the TMF risk budget as

Code: Select all

(RSI + EMA50_slope) / 3
, where "3" is just a scaling factor in order to set a "baseline" TMF risk budget. A scaling factor of 3 sets a baseline budget of about 0.2 whereas a scaling factor of 2 gives a baseline budget of around 0.33.

I am using SPY to calculate these momentum metrics.

This portfolio subset accounts for about 10% of my overall portfolio and is in my ROTH. I am also putting 20% of new taxable investments into this strategy, as well ass my ROTH contributions.

Image
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

ScaledWheel wrote: Tue Jun 01, 2021 3:27 pm At the end of the day, there really is not much of an upside in using basic momentum metrics for portfolio weighting once you have more than a couple funds. Image below is a telltale chart with the base as HFEA (55/45). All portfolios are rebalanced at the beginning of the quarter.
I think you aren't being quite fair in your approach, which may be throwing off your conclusions.

I assign the risk budget by categories (equities and treasuries), then equally divide the category risk by the number of assets in each category to assign the asset risk budget.

If you are assigning a risk budget r to TMF, the other funds should have a risk budget of (1 - r)/Nequity, where the sum of risk budget factors = 1. That should keep the risk budget balanced as you add and subtract funds.

When I run these combinations with 2/3 total risk to equities, 1/3 total risk to TMF, using my risk budget approach with minimum variance, for the last 17 years (just a bit shorter than your period) I get about
  • UPRO/TQQQ/TNA/EDC/TMF:
    29% CAGR
  • UPRO/TQQQ/TNA/TMF:
    37% CAGR
  • UPRO/TQQQ/TMF:
    38% CAGR
  • UPRO/TMF:
    33% CAGR
Ratio of gain over the period relative to UPRO/TMF:
  • UPRO/TQQQ/TNA/EDC/TMF:
    0.6
  • UPRO/TQQQ/TNA/TMF:
    1.65
  • UPRO/TQQQ/TMF:
    1.87
EDC did quite poorly during this period, which dragged down performance. It's weird that you are getting outperformance with EDC.

I think that you are getting the outperformance by adding equity funds without proportionately reducing the risk to each equity. This is great in a bull market but terrible in a bear.

I have the risk assigned to each as
  • UPRO/TQQQ/TNA/EDC/TMF:
    1/6, 1/6, 1/6, 1/6, 1/3
  • UPRO/TQQQ/TNA/TMF:
    2/9, 2/9, 2/9, 1/3
  • UPRO/TQQQ/TMF:
    1/3, 1/3, 1/3
  • UPRO/TMF:
    2/3, 1/3
I suspect that your momentum results will look quite a bit different if you assign the risk budget by category.

Hope this helps.
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

A little revisit to this question in the HEDGEFUNDIE main thread, nodding to the good discussion afterwards
millennialblues wrote: Fri Mar 12, 2021 5:37 pm my question:
what do people think of this mix? it tries to target specific sectors to capture more non-correlations, details in notes.

40 TQQQ (3x Nasdaq) - high flyer stocks, lots of risk
10 CURE (3x Healthcare) - non-correlated stocks, much lower risk
10 SOXL/other (in this case, 3x semiconductors) - quarterly or annual selection based on sector-play

10 FAS (3x Finance) - for cyclical inflation periods, like 2021

15 TMF (3x 20+ Treasuries)
10 TYD (3x 7-10 Year)
5 VIXY to protect against massive volatility
I was able to create synthetic 3x funds for testing:
  • FAS using XLF extended with FIDSX
  • SOXL using SOXX extended with FSELX
  • CURE using XLV
  • UTSL using XLU extended with FKUTX
  • DRN using RWR extended with VGSIX extended with RFI
  • TMF using HEDGEFUNDIE's sequence
The TMF sequence limits (1986) except XLV starts end of 1998 and RFI starts late 1993.

I know the thoughts are typically to avoid sector plays, but the thought of low correlation is attractive.

I'm using a risk-budgeting approach that assigns a fraction of the risk to the equity class and the rest to the bond class, with each asset in a class assigned an equal weight. The weights are assigned using a minimizing function, accounting for correlations with a lookback of 3 months and for volatility with a lookback of 2 months. I rebalance frequently (2 weeks to a month). There is no estimate of returns, just correlation and volatility.

The nice thing about the risk-budgeting approach is that the only values I supply are the category risk budgets: with equities and bonds, that's only one tuning parameter. I typically assign equities 2/3 to 3/4 of the risk budget, and bonds the rest. All of the weights are then calculated automatically for each periodic rebalance, accounting for correlations. This tends to bump up TMF whenever volatilities are high and drop TMF when volatilities are small.

I consider this approach as maintaining a constant risk allocation instead of a constant asset allocation.

In this spirit, typically I've found that the TYD allocation is around 2.35 times larger than the TMF allocation when both are used.

Once I figured out the ETF extensions, I started playing with the longer histories to check for glitches.

It turns out that UTSL/FAS/SOXL/TMF, at least as synthetic histories, survived very nicely from 1986 on, as did URTY/TQQQ/TMF. Both sequences had positive returns for every period of 2 years or longer, with essentially the same CAGR since 1986 (44 percent, although of course there are likely expenses in the synthetic histories that are not properly accounted for). There was no issue with FAS during the GFC or TQQQ during 2000, because the regime of elevated volatilities drove the allocation towards TMF. Similar behavior was obtained with the 1x versions. Merging the two fund sets had very little overall impact.

The overall correlations between UTSL, FAS, and SOXL were 0.32 to 0.55; all had negative correlations to TMF. The overall correlations between URTY and TQQQ were 0.74.

On shorter sequences, adding CURE or DRN didn't seem to improve returns, and adding TYD smoothed out the sequence but tended to lower overall returns.

My conclusion is that diversification really works, even with sector plays, as long as the assets maintain positive returns over time. I'm convinced that maintaining the risk budget works better than maintaining an asset allocation. Gold doesn't add returns, so I haven't found it useful.

It may be necessary to assign a higher risk budget to equities going forward, give low bond returns, or accept lower returns. In some of the cases, there is a definite flattening of the portfolio returns over time, perhaps due to inaccuracies in calculating the synthetic LETF or perhaps due to lowering rates of return.
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

I was able to go a bit further back in time with some of the key funds, using mutual-fund surrogates. So now I can back test starting in 1986 and go to present, just about the entire HEDGEFUNDIE period.

To place this in context, I'm trying to mitigate sequence of returns risks more than trying to maximize CAGR.

I'm currently running a risk-based mix of UPRO/TQQQ/UTSL/DRN/TMF. These funds have relatively low correlations over the entire period: UPRO is correlated with TQQQ/UTSL/DRN/TMF at around 80%, 60%, 65%, and -28%.

I have the combined equities having 75% of the portfolio risk budget and TMF having 25% of the portfolio risk budget. Each of the four included equities has 25% of the equity risk budget, or 18.75% of the portfolio risk budget. These risk budget factors are the only tuning factors, other than the rebalance frequency and lookback duration.

The backtest funds are synthesized with the following sequences
  • S&P 500: 1x => VFINX/SPY, 2x => VFINX/ULPIX, 3x => VFINX/UPRO
  • NASDAQ: 1x => ^NDX/QQQ, 2x => ^NDX/UOPIX, 3x => ^NDX/QQQ/TQQQ
  • Utilities: 1x => FKUTX/XLU, 2x => FKUTX/XLU/UPW, 3x => FKUTX/XLU/UTSL
  • Real Estate: 1x => FRESX/VGSIX/RWR, 2x => FRESX/VGSIX/URE, 3x => FRESX/VGSIX/DRN
  • Long-term treasuries: 1x => VUSTX/TLT, 2x => VUSTX/TLT/UBT, 3x => VUSTX/TLT/TMF
The early NASDAQ funds are based on the price index, not total returns, so returns are underestimated. The ULPIX and UOPIX funds are 2x ETFS that initiated in 1998, so they followed the 2000 crash.

The mutual funds do not have open/high/low data, so the variability during the day of a trade is missed. Some of the mutual funds were active and aren't a perfect match, but that's the best I've been able to come up with.

The three following figures all represent the same period. I changed the figures a bit from previous cases.

The allocation figure provides a cumulative average for each asset; the right boundary would correspond to the average allocation over the entire period. The equities do not have the same average allocation, because the allocation adjusts for relative volatility.

The drawback figure is complementary to the drawdown figure, showing how many years prior the fund first hit the current adjusted price level. I especially like this for interpreting drawdowns of LETF portfolios, because a substantial drawdown may not be consequential for sequence of returns if it has only returned the last six months to a year of returns.

In the following figures, rebalancing is every 10 days. That's overkill to a large extent, but it makes sure that end-of-month and end-of-quarter rebalancing bonus effects are washed out over time. You would only do this in a tax-advantaged account.

Lookback is 3 months for correlations and 2 months for volatility.

The gray lines are for the portfolio, the colored lines represent individual funds. Green is the LTT LETF, other colors are different equities.

1x funds

Image

CAGR: 10.4%, arith return: 10.8%, std dev: 8.5%, arith return/std dev: 1.26
estimated optimum leverage: 14.8
average TLT ~40%

2x funds

Image

CAGR: 23.3%, arith return: 24.7%, std dev: 16.8%, arith return/std dev: 1.47
estimated optimum leverage: 8.8
average UBT ~40%

3x funds

Image

CAGR: 50.2%, arith return: 53.4%, std dev: 25.5%, arith return/std dev: 2.1
estimated optimum leverage: 8.2
average TMF ~40%

The arithmetic return assumes Gaussian returns, which is clearly not right but it gives a reference.

The ratio of arithmetic return to standard deviation is almost the Sharpe ratio, except the risk-free return is not subtracted. Neglecting the risk-free return means that the Sharpe ratio may be significantly smaller for the 1x portfolio but the 2x and 3x are probably pretty close.

The estimated optimum leverage is the Sharpe ratio divided by volatility, is only valid for a Gaussian portfolio, and clearly should be considered way too high in practice. Again this is provided just for inter-comparison discussion purposes.

Averaged over the period from 1986 to present, all of these portfolios end up as essentially a 1x, 2x, or 3x 60/40 portfolio, although over time the equity LETFs ranged from 30 to 80 percent of the adaptive portfolio. So time-averaged equities average 60, 120, and 180 percent of the corresponding unlevered equity-only portfolio. I suspect that the volatility of the equity-only portion of the portfolio is probably less than the volatility of the S&P 500 component.

Of these, I find the 2x figure especially interesting because the 2x S&P and NASDAQ funds are actual funds starting in 1998, with real consequences during 2000 and 2008. Even with the very extended and large drawdowns, including the extended large real estate drawdown starting in 2008, the minimum variance algorithm adjusted the ULPIX and UOPIX allocations down during the crisis so that the overall portfolio didn't suffer very much.

The values for these returns should be taken with a large grain of salt, but the trends puzzle me.

In this example, the CAGR increases as approximately 2.2^L, where the leverage factor is L. The volatility is approximately proportional to L. This gives an increasing Sharpe ratio with increasing leverage.

The implied optimum LETF leverage is given by the LETF leverage times the calculated implied optimum leverage:
  • 1x: overall implied LETF leverage is 1 x 14.8 = 14.8
  • 2x: overall implied LETF leverage is 2 x 8.8 = 17.6
  • 3x: overall implied LETF leverage is 3 x 8.2 = 24.6
Clearly the optimum leverage would be applied to the portfolio, if there was an equivalent ETF that replicated the portfolio, not to the underlying LETFs used to build the portfolio. Nobody in their right mind would apply additional leverage to the 3x LETF portfolio, but it is very interesting that the implied optimal leverage increases as the actual leverage increases. This opposite happens when the asset allocations are held fixed.

I've done the same type of exercise with sector ETFs (utilities, semiconductors, financials, health, consumer) and LTTs, with similar results. I've tested with ITTs, which seems to really dilute returns because LTTs are more than twice as effective at balancing volatility than ITTs.

I think that part of the explanation for the portfolio behavior is that the expected return is essentially constant regardless of volatility, but volatility clustering allows some projection of future volatility. So the adaptive allocation process harvests the return during the lower-volatility periods for each asset, which cuts overall portfolio volatility without cutting returns. I didn't do the comparison here, but I've seen a cut in portfolio volatility of 20% relative to a fixed allocation. Willthrill81 uses a similar argument for substituting time averages for allocation fractions with tactical asset allocation.

I think that having several volatile but low-correlation assets further calms the overall portfolio volatility as a sort of central tendency thing.

I suspect that the relatively low correlation combined with large fluctuations may make volatility pumping more effective as the leverage increases.

But I think the main contribution to the improvement with increasing leverage must be because compounding has a better chance to work if the same average (and positive) return is harvested with less overall volatility. The overall return is

R = (1 + L(mu + x)) / (1 + (mu + x)), where L is the leverage, mu is expected daily return, and x is the deviation from the expected daily return (with x having an expected value of zero).

If x is zero, you get compounding with an exponentially increasing deviation with increasing leverage.

If abs(x) is usually much larger than mu, volatility decay kills returns. That's why folks seek out low-volatility portfolios.

It seems like the minimum variance approach is cutting enough volatility to make a significant difference in compounding, especially for the 3x portfolio. Running a diversified set of 3x equities instead of just UPRO also cuts portfolio volatility.

Here's rooting for TMF to maintain (i) negative correlation to equities (or at least near-zero correlation), (ii) similar volatility, and (iii) non-negative returns! :moneybag
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Re: Refinements to Hedgefundie's excellent approach

Post by AlphaLess »

Hydromod wrote: Tue Jun 08, 2021 12:19 am A little revisit to this question in the HEDGEFUNDIE main thread, nodding to the good discussion afterwards
millennialblues wrote: Fri Mar 12, 2021 5:37 pm my question:
what do people think of this mix? it tries to target specific sectors to capture more non-correlations, details in notes.

40 TQQQ (3x Nasdaq) - high flyer stocks, lots of risk
10 CURE (3x Healthcare) - non-correlated stocks, much lower risk
10 SOXL/other (in this case, 3x semiconductors) - quarterly or annual selection based on sector-play

10 FAS (3x Finance) - for cyclical inflation periods, like 2021

15 TMF (3x 20+ Treasuries)
10 TYD (3x 7-10 Year)
5 VIXY to protect against massive volatility
I was able to create synthetic 3x funds for testing:
  • FAS using XLF extended with FIDSX
  • SOXL using SOXX extended with FSELX
  • CURE using XLV
  • UTSL using XLU extended with FKUTX
  • DRN using RWR extended with VGSIX extended with RFI
  • TMF using HEDGEFUNDIE's sequence
The TMF sequence limits (1986) except XLV starts end of 1998 and RFI starts late 1993.

I know the thoughts are typically to avoid sector plays, but the thought of low correlation is attractive.

I'm using a risk-budgeting approach that assigns a fraction of the risk to the equity class and the rest to the bond class, with each asset in a class assigned an equal weight. The weights are assigned using a minimizing function, accounting for correlations with a lookback of 3 months and for volatility with a lookback of 2 months. I rebalance frequently (2 weeks to a month). There is no estimate of returns, just correlation and volatility.

The nice thing about the risk-budgeting approach is that the only values I supply are the category risk budgets: with equities and bonds, that's only one tuning parameter. I typically assign equities 2/3 to 3/4 of the risk budget, and bonds the rest. All of the weights are then calculated automatically for each periodic rebalance, accounting for correlations. This tends to bump up TMF whenever volatilities are high and drop TMF when volatilities are small.

I consider this approach as maintaining a constant risk allocation instead of a constant asset allocation.

In this spirit, typically I've found that the TYD allocation is around 2.35 times larger than the TMF allocation when both are used.

Once I figured out the ETF extensions, I started playing with the longer histories to check for glitches.

It turns out that UTSL/FAS/SOXL/TMF, at least as synthetic histories, survived very nicely from 1986 on, as did URTY/TQQQ/TMF. Both sequences had positive returns for every period of 2 years or longer, with essentially the same CAGR since 1986 (44 percent, although of course there are likely expenses in the synthetic histories that are not properly accounted for). There was no issue with FAS during the GFC or TQQQ during 2000, because the regime of elevated volatilities drove the allocation towards TMF. Similar behavior was obtained with the 1x versions. Merging the two fund sets had very little overall impact.

The overall correlations between UTSL, FAS, and SOXL were 0.32 to 0.55; all had negative correlations to TMF. The overall correlations between URTY and TQQQ were 0.74.

On shorter sequences, adding CURE or DRN didn't seem to improve returns, and adding TYD smoothed out the sequence but tended to lower overall returns.

My conclusion is that diversification really works, even with sector plays, as long as the assets maintain positive returns over time. I'm convinced that maintaining the risk budget works better than maintaining an asset allocation. Gold doesn't add returns, so I haven't found it useful.

It may be necessary to assign a higher risk budget to equities going forward, give low bond returns, or accept lower returns. In some of the cases, there is a definite flattening of the portfolio returns over time, perhaps due to inaccuracies in calculating the synthetic LETF or perhaps due to lowering rates of return.
If you are looking for complexify your already complex life, this is a great strategy.
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

AlphaLess wrote: Wed Aug 25, 2021 12:07 pm If you are looking for complexify your already complex life, this is a great strategy.
No doubt that I would never have come up with this if I haven't been working from home for the last 1+ years. :wink:

Once it is in place, it boils down to running a few scripts on the weekend to download some closing values and estimate the current allocations, then every few weeks tweak the allocations/rebalance if something has gotten too far out of whack. It's definitely not set and forget.
AlphaLess
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Re: Refinements to Hedgefundie's excellent approach

Post by AlphaLess »

Hydromod wrote: Wed Aug 25, 2021 12:17 pm
AlphaLess wrote: Wed Aug 25, 2021 12:07 pm If you are looking for complexify your already complex life, this is a great strategy.
No doubt that I would never have come up with this if I haven't been working from home for the last 1+ years. :wink:

Once it is in place, it boils down to running a few scripts on the weekend to download some closing values and estimate the current allocations, then every few weeks tweak the allocations/rebalance if something has gotten too far out of whack. It's definitely not set and forget.
You are severely underestimating the amount of time you are wasting thinking about this, typing boglehead messages, etc.
I don't carry a signature because people are easily offended.
secondopinion
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Re: Refinements to Hedgefundie's excellent approach

Post by secondopinion »

Hydromod wrote: Wed Aug 25, 2021 12:17 pm
AlphaLess wrote: Wed Aug 25, 2021 12:07 pm If you are looking for complexify your already complex life, this is a great strategy.
No doubt that I would never have come up with this if I haven't been working from home for the last 1+ years. :wink:

Once it is in place, it boils down to running a few scripts on the weekend to download some closing values and estimate the current allocations, then every few weeks tweak the allocations/rebalance if something has gotten too far out of whack. It's definitely not set and forget.
If one is willing to put the effort and risk, it could pay off massively over time (or not). Of course, doing active management is sometimes a side job; no shame in this since I already take a few hours a week to semi-actively manage my portfolio.
Passive investing: not about making big bucks but making profits. Active investing: not about beating the market but meeting goals. Speculation: not about timing the market but taking profitable risks.
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Re: Refinements to Hedgefundie's excellent approach

Post by secondopinion »

AlphaLess wrote: Wed Aug 25, 2021 12:31 pm
Hydromod wrote: Wed Aug 25, 2021 12:17 pm
AlphaLess wrote: Wed Aug 25, 2021 12:07 pm If you are looking for complexify your already complex life, this is a great strategy.
No doubt that I would never have come up with this if I haven't been working from home for the last 1+ years. :wink:

Once it is in place, it boils down to running a few scripts on the weekend to download some closing values and estimate the current allocations, then every few weeks tweak the allocations/rebalance if something has gotten too far out of whack. It's definitely not set and forget.
You are severely underestimating the amount of time you are wasting thinking about this, typing boglehead messages, etc.
Wasting, maybe not. But it is not a minor amount of time regardless. That is partially why I do not bother to explain my strategy.
Passive investing: not about making big bucks but making profits. Active investing: not about beating the market but meeting goals. Speculation: not about timing the market but taking profitable risks.
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

secondopinion wrote: Wed Aug 25, 2021 12:35 pm
AlphaLess wrote: Wed Aug 25, 2021 12:31 pm
Hydromod wrote: Wed Aug 25, 2021 12:17 pm
AlphaLess wrote: Wed Aug 25, 2021 12:07 pm If you are looking for complexify your already complex life, this is a great strategy.
No doubt that I would never have come up with this if I haven't been working from home for the last 1+ years. :wink:

Once it is in place, it boils down to running a few scripts on the weekend to download some closing values and estimate the current allocations, then every few weeks tweak the allocations/rebalance if something has gotten too far out of whack. It's definitely not set and forget.
You are severely underestimating the amount of time you are wasting thinking about this, typing boglehead messages, etc.
Wasting, maybe not. But it is not a minor amount of time regardless. That is partially why I do not bother to explain my strategy.
No underestimating the time I've spent, believe me. Extended thinking time to look at a topic from many sides is part of the territory with many years of higher education. I expect and hope that the time will be tailing off going forward though.

In many ways it's been more about the intellectual challenge of linking my outside insights on probability and risk to finance than anything else.
secondopinion
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Re: Refinements to Hedgefundie's excellent approach

Post by secondopinion »

Hydromod wrote: Wed Aug 25, 2021 1:42 pm
secondopinion wrote: Wed Aug 25, 2021 12:35 pm
AlphaLess wrote: Wed Aug 25, 2021 12:31 pm
Hydromod wrote: Wed Aug 25, 2021 12:17 pm
AlphaLess wrote: Wed Aug 25, 2021 12:07 pm If you are looking for complexify your already complex life, this is a great strategy.
No doubt that I would never have come up with this if I haven't been working from home for the last 1+ years. :wink:

Once it is in place, it boils down to running a few scripts on the weekend to download some closing values and estimate the current allocations, then every few weeks tweak the allocations/rebalance if something has gotten too far out of whack. It's definitely not set and forget.
You are severely underestimating the amount of time you are wasting thinking about this, typing boglehead messages, etc.
Wasting, maybe not. But it is not a minor amount of time regardless. That is partially why I do not bother to explain my strategy.
No underestimating the time I've spent, believe me. Extended thinking time to look at a topic from many sides is part of the territory with many years of higher education. I expect and hope that the time will be tailing off going forward though.

In many ways it's been more about the intellectual challenge of linking my outside insights on probability and risk to finance than anything else.
There is nothing wrong with thinking on things if you enjoy it. I enjoy what I do, so I really do not worry about it.
Passive investing: not about making big bucks but making profits. Active investing: not about beating the market but meeting goals. Speculation: not about timing the market but taking profitable risks.
perfectuncertainty
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Re: Refinements to Hedgefundie's excellent approach

Post by perfectuncertainty »

Hydromod wrote: Wed Aug 25, 2021 12:17 pm
AlphaLess wrote: Wed Aug 25, 2021 12:07 pm If you are looking for complexify your already complex life, this is a great strategy.
No doubt that I would never have come up with this if I haven't been working from home for the last 1+ years. :wink:

Once it is in place, it boils down to running a few scripts on the weekend to download some closing values and estimate the current allocations, then every few weeks tweak the allocations/rebalance if something has gotten too far out of whack. It's definitely not set and forget.
How can a mere mortal like me use this?
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

perfectuncertainty wrote: Sat Aug 28, 2021 1:23 pm
Hydromod wrote: Wed Aug 25, 2021 12:17 pm
AlphaLess wrote: Wed Aug 25, 2021 12:07 pm If you are looking for complexify your already complex life, this is a great strategy.
No doubt that I would never have come up with this if I haven't been working from home for the last 1+ years. :wink:

Once it is in place, it boils down to running a few scripts on the weekend to download some closing values and estimate the current allocations, then every few weeks tweak the allocations/rebalance if something has gotten too far out of whack. It's definitely not set and forget.
How can a mere mortal like me use this?
I run a Matlab script that pulls the data from Yahoo and then performs the calculation. Others have created python versions.

I also made an Excel spreadsheet that performs the calculations, with a little manual updating. It's a little flaky; I've run across issues with the STOCKHISTORY function, which sometimes omits a day here and there. Also, grabbing from Yahoo finance is more robust, because you really want the adjusted close to account for splits and dividends.

In the Excel version, you have to manually update the covariance matrix and manually start the solver. Not hard, just a little tedious. The answers tend to be very similar to the Matlab ones, to the third decimal place or so, in the limited testing I've done.

I suspect that something very similar would work in Google sheets; I just haven't tried the solver function.

If you are running just two funds, you can use the STOCKHISTORY function to get the data and then calculate the risk-budget inverse volatility values directly; the same thing works in Google sheets with GOOGLEFINANCE to get the data.
princessandra
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Re: Refinements to Hedgefundie's excellent approach

Post by princessandra »

Thank you for sharing your work. You mentioned that you used a minimum variance approach in determining the weights of the assets. However, the formulas that I found don't really differentiate between the lookback periods of volatility versus lookback periods of coorelation (if I understand it correctly)... Are you using a formula that you developed yourself?

Is there a reason you choose 3 months lookback for coorelation and 2 months for volatility?
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

princessandra wrote: Fri Dec 31, 2021 1:16 pm Thank you for sharing your work. You mentioned that you used a minimum variance approach in determining the weights of the assets. However, the formulas that I found don't really differentiate between the lookback periods of volatility versus lookback periods of correlation (if I understand it correctly)... Are you using a formula that you developed yourself?

Is there a reason you choose 3 months lookback for correlation and 2 months for volatility?
I'm not using a rigorous approach. I'm trying to get the most recent period I can get away with for estimating volatility, because I am prepared to rebalance fairly frequently. My feeling is that correlation is more persistent but requires a longer period for a given accuracy level.

I just estimate once for correlation and once each for the individual fund volatilities.

I'm not too worried about rigor because (i) the period is really too short for anything more than gross estimates anyway and (ii) I update the statistics every week to capture the gross changes.
jarjarM
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Re: Refinements to Hedgefundie's excellent approach

Post by jarjarM »

princessandra wrote: Fri Dec 31, 2021 1:16 pm Thank you for sharing your work. You mentioned that you used a minimum variance approach in determining the weights of the assets. However, the formulas that I found don't really differentiate between the lookback periods of volatility versus lookback periods of coorelation (if I understand it correctly)... Are you using a formula that you developed yourself?

Is there a reason you choose 3 months lookback for coorelation and 2 months for volatility?
A quick chime in: you should check out the white paper written by smartly on combining momentum with minimal variance. There's discussion length of correlation look back (6 months) and volatility (1 month). Maybe of interest.

adaptive asset allocation
kjm
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Re: Refinements to Hedgefundie's excellent approach

Post by kjm »

Since we're on the topic of momentum... thoughts on using simple momentum to select the equity component of an HFEA-esque portfolio? You'd keep the equity to LTT ratio at approximately 1 to 1. Rather than using an S&P 500 index fund for your equity exposure, you'd select an equity style factor based on momentum. Here's an example using RYOCX, NAESX, and VUSTX.

https://bit.ly/32W1yp6

Compared to SPY, VUSTX over the same period.

https://bit.ly/3sO1vGL

In practice, I would select between large cap growth and small cap value. QQQ/IJS for 1x. QLD/SAA for 2x. TQQQ/TNA for 3x. There's no 3x small cap value ETF as far as I'm aware. You'd expect one style factor to do better than the other depending on the interest rate environment. And in fact, we just saw this in action with small cap value outperforming earlier in the year with rates rising and large cap growth catching up later in the year as rates stabilized.

I'm currently doing something like this in my 401k with 80% in QQQ or AVUV depending on momentum and 20% TMF.
TheDoctor91
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Re: Refinements to Hedgefundie's excellent approach

Post by TheDoctor91 »

Stumbled upon something similar early this year :)

Let's just say that the backtests are...earth shattering. Let's see how live goes.
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

jarjarM wrote: Fri Dec 31, 2021 8:04 pm
princessandra wrote: Fri Dec 31, 2021 1:16 pm Thank you for sharing your work. You mentioned that you used a minimum variance approach in determining the weights of the assets. However, the formulas that I found don't really differentiate between the lookback periods of volatility versus lookback periods of coorelation (if I understand it correctly)... Are you using a formula that you developed yourself?

Is there a reason you choose 3 months lookback for coorelation and 2 months for volatility?
A quick chime in: you should check out the white paper written by smartly on combining momentum with minimal variance. There's discussion length of correlation look back (6 months) and volatility (1 month). Maybe of interest.

adaptive asset allocation
This white paper seems vaguely familiar. I suspect that I read through it sometime in the past few years. It may well have given me tacit permission to consider different look backs when I finally started implementing the minimum variance method.

I suspect that there is a tradeoff between accurately estimating the statistics and getting less accurate statistics that are more representative during transitions in market behavior. The six-month correlation look back is trying to get relatively accurate correlations, which is good during stable periods. I can't say that I've dug into the effect of look back duration on correlation very intensively though.
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

kjm wrote: Fri Dec 31, 2021 8:30 pm Since we're on the topic of momentum... thoughts on using simple momentum to select the equity component of an HFEA-esque portfolio? You'd keep the equity to LTT ratio at approximately 1 to 1. Rather than using an S&P 500 index fund for your equity exposure, you'd select an equity style factor based on momentum. Here's an example using RYOCX, NAESX, and VUSTX.
I'm not really a fan of using momentum-based methods, although certainly there are very nice backtests. Your backtest case converted to 3x is very nice, especially with an 8-month timing period (model), but I guess that I don't really have the temperament to wholesale switch in and out of different assets; I like the concept of keeping a static risk budget but letting that set the allocation. Also, I find that there is more difficulty in calibrating as the number of parameters goes up. Even further, I'm worried that the rapidity of market responses is increasing over time, which means that continual recalibration may be needed going forward.

As an approximate comparison to the momentum model, I'd use inverse volatility and minimum variance. These aren't quite what I do; the inverse volatility approach neglects correlations and both assume equal risk budget for each component (I'd have a smaller allocation to treasuries and larger to equities). The volatility-based models tend to have steadier increases, albeit not as dramatic as the better momentum cases.

Whenever I try mechanistic models, I like to try on various funds. It seems to me that things that would have worked on S&P and NASDAQ indexes start to fall apart when used on different index funds (e.g., Japan, European markets, etc.). Also, implementing trades tends to add significant drag.

With that said, I'm intrigued by the concept of adaptively adjusting the risk budget weights based on some sort of momentum. A glaring example would have been in switching between TMF and TMV, depending on which is doing better in the current regime. This would have worked spectacularly over the 1955 to present period, with TMV dominant 1955 to 1982 and TMF dominant since. I've seen similar ideas for gold vs. treasuries.

In the context of equity style factor switching, I'd be tempted to implement a momentum approach by adjusting the risk budget weights. Currently I just set the two overall equity/treasury risk budget weights, then evenly divide the equity risk budget among all equity funds and evenly divide the treasury risk budget among all treasury funds. In the momentum approach, perhaps the risk budget could be biased by recent momentum; maybe the ratio between risk component budgets might be the same as the ratio of recent returns.
zkn
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Re: Refinements to Hedgefundie's excellent approach

Post by zkn »

Interesting thread. Hydromod, do you plan to summarize your analysis and conclusions? Since your analysis evolves over time and some posts seem to be ad hoc analyses in response to requests, it would be useful and more readable to see the methods, analyses and conclusions summarized in one place.

It's curious to see this analysis done in the context of leveraged ETFs, as I imagine some of the effects of rebalancing would be resulting from cancelling-out leverage reset (a kind of rebalancing) within the leveraged ETFs. In other words, a lot of rebalancing is being done internally in the funds so the deliberate rebalance between funds is only the other half of the picture. Furthermore, the benefits to reducing volatility on improving compounding returns is elevated because the leverage is so high.

I'm reluctant with approaches that are too flexible in fitting data due to problems of overfitting, but I have been entertaining the idea of taking into account volatility targeting, momentum, and/or macro signals when rebalancing. Since rebalancing is necessary, it would not be introducing more costs and it would be a relatively minor "sin". Some thoughts:

1) Volatility targeting: I noticed another poster mentioned this. If we consider investing as a series of (daily/monthly/quarterly/whatever) bets that our investments go up, it makes sense that the most statistically optimal strategy would be to keep the bet sizes relatively constant each time. But if the stakes (volatility) change, then adjusting bet size inversely to the stakes (volatility) would make more sense. In practice it seems to work even better than that, because of the low volatility anomaly we don't expect higher returns in stocks when we can forecast increased volatility, so volatility targeting allows us to both have a more statistically efficient approach and harvest the low volatility effect. Here is a paper demonstrating the effect for equities. For predicting volatility, I like the ensemble predictor calculated as an average of the exponentially weighted moving average, a GARCH model estimate, implied volatility, and 30-day historical volatility from the book Positional Option Trading by Sinclair (chapter 3 on forecasting volatility). This could also be used for minimum variance portfolio rebalancing (or any rebalancing where volatility estimates need to be updated).

2) Trend following is often called a defensive strategy because historically it has performed well when stocks or bonds have done badly. However, trend following strategies such as managed futures are expensive to add to a portfolio. So maybe considering trend when rebalancing introduces some trend following effects, like a poor man's managed futures. For example, delaying rebalancing from bonds into stocks when stocks have negative momentum and bonds have positive momentum. This is also likely to be consistent with volatility targeting of the stock part since stock volatility would likely be elevated. Just an idea at this stage because I haven't seen a study quite like what I am thinking (or analyzed it myself).

3) Macro signals. I understand from skimming this thread that unemployment has been examined but there is a wider range of indicators of macroeconomic regimes that have shown to have some benefit in asset allocation. This chapter describes growth, inflation and market stress "nowcasts" using unemployment and other indicators. There is a firm 42 Macro that follows this kind of methodology and updates their forecasts as data comes in. I like to pay attention to this primarily to evaluate the probability of the stock-bond correlation going positive.

Now how it all fits together, I don't know :happy
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Re: Refinements to Hedgefundie's excellent approach

Post by comeinvest »

Great thread. Do you think the results of this thread regarding periodic rebalancing and rebalancing bands would equally apply to (m)HFEA implemented with futures? (Except that the timing within the month/quarter then cannot be chosen as the roll period is about a week.)
TheDoctor91
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Re: Refinements to Hedgefundie's excellent approach

Post by TheDoctor91 »

Does anyone know the formula for calculating the portfolio weights using adaptive asset allocation minimum variance or the other approaches? Or a script, or excel spreadsheet?
jarjarM
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Re: Refinements to Hedgefundie's excellent approach

Post by jarjarM »

TheDoctor91 wrote: Tue Jan 04, 2022 2:13 pm Does anyone know the formula for calculating the portfolio weights using adaptive asset allocation minimum variance or the other approaches? Or a script, or excel spreadsheet?
There's an excel sheet and detail formula in the 2nd thread. You'll have to dig for it a bit though.
laurenthu
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Re: Refinements to Hedgefundie's excellent approach

Post by laurenthu »

I made a Google Colab Jupyter Notebook to help get the right weighting based on the risk budgetting approach. You can find it here: https://colab.research.google.com/drive ... sp=sharing
This should help you get there, all is automatic and it is based on TQQQ SOXL FAS RETL equity and TMF as bonds. It budgets 25% risk for TMF and then the rest split amongst the 3X equity ETFs. It is 2 months rolling from today's date.
Any question please let me know!
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Re: Refinements to Hedgefundie's excellent approach

Post by LadyGeek »

laurenthu, Welcome! Comments:

- The code required a Google account sign-in with the Firefox browser. (I did not test the code in Firefox.) The code runs in Chrome without a Google account sign-in.
- There is a minor typo in the optimal weight table title. "optinal weigths" should be "optimal weights"
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

I’ve been noticing questions on how the best strategy for contributing when contributions are not aligned with a quarterly rebalance. This is especially the case on the r/LETFs subreddit. There are arguments that it should be (i) at the current allocation, (ii) the maximum-rebalance allocation, and (iii) the desired allocation. I was curious so I took a look.

The first thing to realize is that the new contributions have absolutely no impact on returns for any existing funds until the rebalance occurs. Each new contribution is its own little bucket, which loses its identity to become part of the portfolio once the rebalance occurs.

The second thing is that rebalancing occurs costs. Slippage occurs during trades, and there are tax consequences in taxable. Of course, the tax consequences are typically incurred for shares with long-term gains rather than the new contribution when using some intelligent rebalancing scheme.

In effect, each contribution is an independent bet on returns until the next rebalance, reduced by the corresponding costs during rebalance.

When the rebalance costs are expected to dominate over returns, then a clear winning strategy is to contribute in a way that minimizes the rebalance costs. One would hope that this is not usually the case, though.

When the rebalance costs are small, then the question is whether there is room for an optimal allocation based on the day of the quarter that the contribution occurs.

I used UPRO and TMF sequences, augmented with simulated values back to 1986. Then I partitioned the sequences into 141 quarters. The idea is to allow consistent durations between contribution and rebalance, but the calendar quarters don’t all have the same number of days. I aligned each of the 63 starting days in the first quarter with a corresponding day in each subsequent quarter.

There are a few degrees of freedom: (i) the rebalance day in the quarter, (ii) the number of days before the rebalance that the contribution is made, and (iii) the allocations for the contribution.

The orthodox HFEA rebalance is on the first or last day of the calendar quarter. The contribution might be on any day. The allocation is the control parameter.

The first figure shows the cumulative distribution function of returns before rebalance, assuming that the rebalance is on the last day of the quarter. Each line represents a different day of the quarter for the contribution, with the red lines representing early in the quarter and the blue lines representing near the end of the quarter. The observed spread in returns for the contribution until rebalance is largest for the longest duration. The reported returns are in excess of the risk-free rate (a small correction for this short duration).

The six subplots show different combinations of UPRO and TMF, ranging from fully UPRO to fully TMF. The overall spread in returns is tighter when UPRO and TMF are mixed, and is largest when the contribution goes fully to UPRO.

Image

The second figure shows statistics for the same cases, broken down by day of quarter (rebalance is on day 63). The left plots show mean and median return; the right plots show standard deviation of return and the coefficient of variation (the last few days are not shown, because the mean return is very small). In this case, the six lines correspond to the six subfigures in the first figure, with the cyan line corresponding to 100/0 UPRO/TMF and the orange line corresponding to 0/100 UPRO/TMF.

The expected and median return (for a given day, calculated across all quarters) steadily drops as the contribution occurs closer to the rebalance date. There appears to be a mildly stronger return for high allocations to UPRO early in the quarter and to TMF late in the quarter. As might be expected, the standard deviation is smallest for an intermediate mix of UPRO and TMF.

These cases suggest that the most consistent returns are likely at roughly the allocation mix, assuming the allocation is somewhere between 40/60 and 60/40 UPRO/TMF.

Image

The general picture is consistent when the rebalancing occurs on day 22 (third figure) or day 43 (fourth figure), corresponding to the start of the 2nd and 3rd months of the quarter. There is a hint that a higher UPRO allocation would have provided slightly larger mean and median returns in the early part of the quarter for both of these cases, again at the cost of a higher variability. This is accentuated even more when rebalancing is in the middle of the quarter (fifth figure); TMF performance appears to have been significantly degraded when rebalancing occurred at this time. Similarly poor TMF performance is seen when rebalancing in the middle of each of the three months, perhaps associated with treasury auctions occurring in the middle of months.

Image

Image

Image

As the takeaway, I don’t really see much benefit to going away from the default allocation when contributing, unless one is stretching for returns. It won’t make much difference to the overall HFEA returns, once the contributions are small compared to the total portfolio. Some may want to simply add 100% UPRO, and let rebalancing shortly afterwards do its thing for risk mitigation.

A possible reason for going away from the default contribution is if one does volatility calculations that suggest future volatility is either higher or lower than normal. If future volatility is predicted to be low, this would favor 100% UPRO; conversely, if future volatility is predicted to be high, this would favor 100% TMF to mitigate volatility decay.
akxc
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Re: Refinements to Hedgefundie's excellent approach

Post by akxc »

Great work in this thread Hydromod!

I was wondering whether you have compared your results in these analyses your have done in the overlap period between the simulated dataset and the real data on UPRO/TMF. During the examination I posted in the main HFEA thread between rebalancing on different days of the quarters I did a comparison between the simulated/real data during the 2009-2019 overlap period. I noticed that the real data had a slightly higher dispersion in the end results than the simulated data. For example, the simulated data would generally underestimate underperformance/overperformance of the worst/best rebalance days. In the end the simulated data underestimated the benefit daily rebalancing would give you by about 20-30 basis points if I recall. Haven't looked a whole lot into this, and was just wondering if you've looked into this as well, as perhaps the simulated data could have quirks that may not matter to the overall return of quarterly rebalance HFEA strategy but show up in the analyses you have been working on.
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

akxc wrote: Mon Jan 10, 2022 6:43 pm I was wondering whether you have compared your results in these analyses your have done in the overlap period between the simulated dataset and the real data on UPRO/TMF. During the examination I posted in the main HFEA thread between rebalancing on different days of the quarters I did a comparison between the simulated/real data during the 2009-2019 overlap period. I noticed that the real data had a slightly higher dispersion in the end results than the simulated data. For example, the simulated data would generally underestimate underperformance/overperformance of the worst/best rebalance days. In the end the simulated data underestimated the benefit daily rebalancing would give you by about 20-30 basis points if I recall. Haven't looked a whole lot into this, and was just wondering if you've looked into this as well, as perhaps the simulated data could have quirks that may not matter to the overall return of quarterly rebalance HFEA strategy but show up in the analyses you have been working on.
I haven't looked too much at comparing UPROSIM and TMFSIM during the overlap period. I generally create my own set now, using the same methodology, and I have done some comparisons to see how well they match with the actual data. My favorite is to do something like 50/50 UPRO/SPXU or 50/50 TQQQ/SQQQ with both simulated and real datasets, which really highlights the implementation details.

I do think that the simulated series are optimistic in terms of overall returns, especially when borrowing interest rates were higher.

I'm most interested in mitigating volatility effects, where underestimating daily dispersion by a little doesn't affect the algorithms much. I haven't really checked on daily dispersion; if I were in a position to be trying to harvest the daily pumping, I'd be more rigorous. I'm not all that tempted, because M1 isn't really suited for that kind of activity. Also, it is hard to achieve the rebalance at the close-of-day price, and I suspect that there would be nuances when rebalancing at other times if UPRO and TMF respond at different rates during the day.
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

laurenthu wrote: Fri Jan 07, 2022 4:36 am I made a Google Colab Jupyter Notebook to help get the right weighting based on the risk budgetting approach. You can find it here: https://colab.research.google.com/drive ... sp=sharing
This should help you get there, all is automatic and it is based on TQQQ SOXL FAS RETL equity and TMF as bonds. It budgets 25% risk for TMF and then the rest split amongst the 3X equity ETFs. It is 2 months rolling from today's date.
Any question please let me know!
I checked this out a bit. It's generally matching to 2+ places with my Matlab code, given the same input period. I have some further details in the reddit forum here.

I would expect at least 3 places match between the solvers, but for practical purposes it appears that there would be little difference in the allocations once rounded for rebalancing purposes.
no simpler
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Re: Refinements to Hedgefundie's excellent approach

Post by no simpler »

This public strategy on Composer switches the original HFEA to "risk off" when trailing 10 day max drawdown of SPY is more than 5%:
https://app.composer.trade/symphony/GRJ ... u/details

Here's the description of the logic:
Image

It seems to have a better return to max drawdown characteristics:
Image

Anyhow, the software isn't quite as flexible as Python or Matlab, but it's quite a bit faster to play with things and get feedback. You can also do inverse vol weighting.
AlphaLess
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Re: Refinements to Hedgefundie's excellent approach

Post by AlphaLess »

I have not followed this thread for a while.

Could someone tell me what is the latest and greatest?

Does someone have an ACTUAL strategy performance?
I don't carry a signature because people are easily offended.
no simpler
Posts: 116
Joined: Sat Jul 13, 2019 4:54 pm

Re: Refinements to Hedgefundie's excellent approach

Post by no simpler »

AlphaLess wrote: Sat Jan 22, 2022 12:02 pm I have not followed this thread for a while.

Could someone tell me what is the latest and greatest?

Does someone have an ACTUAL strategy performance?
Not sure I totally understand - what do you mean by "actual"? you mean live trading on real money?
AlphaLess
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Location: Kentucky

Re: Refinements to Hedgefundie's excellent approach

Post by AlphaLess »

no simpler wrote: Sat Jan 22, 2022 12:06 pm
AlphaLess wrote: Sat Jan 22, 2022 12:02 pm I have not followed this thread for a while.

Could someone tell me what is the latest and greatest?

Does someone have an ACTUAL strategy performance?
Not sure I totally understand - what do you mean by "actual"? you mean live trading on real money?
Yes, as that is the only thing that matters.
I don't carry a signature because people are easily offended.
J-Kole
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Re: Refinements to Hedgefundie's excellent approach

Post by J-Kole »

Hydromod wrote: Mon Aug 12, 2019 11:13 pm I took a couple of hours and implemented the moving average in the same risk-budget style as the UEI example I showed. I ramp the budget allocation up a fixed delta each day that the daily value is above the moving average, and ramp down a fixed delta each day that the daily value is below the moving average. I can allow this to occur like an on/off switch or gradually over months. I can use either UPRO or UPRO/3 as the signal.

Basically the different options I tried give fairly consistent average 5-yr CAGR in the range of 20 to 23% and max drawdowns in the range of 45 to 66%, compared to the nominal 40/60 with 17.4% and max drawdown of 66%. This is roughly in the range of the UEI options I checked. I think they are giving fairly similar signals regarding timing. Again limiting the maximum risk budget to 80% helped mitigate Black Monday drawdowns.

There may not be much more that can be easily gained with just these two fixed assets.
Hydromod, if the 200-MA strategy gives the same results as buy and hold can you please explain this reddit post because from the chart it looks like the 200-MA mitigated huge drawdowns in the 00's, 08's, and 20's.
https://www.reddit.com/r/LETFs/comments ... long_with/

Additionally, if Hedgefudie exited his position during the 2020 crash using the 200-SMA, he could have reduced his drawdown and got out with around 30k in profits above his initial investment of 100k.
viewtopic.php?t=288192

I've been researching the strategy and just confused why it won't work. Thank you.
Last edited by J-Kole on Wed Jan 26, 2022 12:00 pm, edited 2 times in total.
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

J-Kole wrote: Wed Jan 26, 2022 11:57 am Hydromod, if the 200-MA strategy gives the same results as buy and hold can you please explain this reddit post because from the chart it looks like the 200-MA mitigated huge drawdowns in the 00's, 08's, and 20's.
https://www.reddit.com/r/LETFs/comments ... long_with/

Additionally, if Hedgefudie exited his position during the 2020 crash using the 200-SMA, he could have reduced his drawdown and got out with around 30k in profits above his initial investment of 100k.
viewtopic.php?t=288192

I've been researching the strategy and just confused why it won't work. Thank you.
My experience is that I can't get a moving-average signal to reliably give a statistical predictive edge on future returns. Remember, for a method to be worthwhile you have to be able to determine when to get out AND when to get in at a more favorable price, and you have to be successful at both more times than not. You can get out fine, but you've lost if you are late getting back in. And every time you make a trade, there's some slippage during the trades, which means you have to be successful enough to overcome the slippage from both trading overhead and failures to get the timing right.

It's dangerous to look too far back with these approaches, namely before computers were king and when trades might take days to execute with associated brokerage fees. This tended to be better for getting predictive power from moving averages, because the overhead from trades made folks slower to react and folks weren't so used to such math. It may not have been too far back where it would have even been possible to trade with such approaches.

With the current high-powered algorithmic wizards and instantaneous trading I think that any edge from moving averages has long been arbitraged away. It's so easy that anyone can do it, and many can do it faster and cheaper than random individual trader; when enough do it, then the edge disappears.

If I remember correctly, I could find some predictive capability in the S&P up to early 2015. It seems to me that the cycles have been speeding up over time, and now the market responds so quickly that these long-term cycle signals are mushed together with shorter-term responses. More recently, the cycles tend to generate a lot of false signals; moving averages don't help with determining which signal is real and which is false. Lots of false signals are bad, because they swamp the few large real signals. Discouragingly, the S&P gave the best results of any index funds that I tried.

That's my opinion about why it won't work reliably. I applaud those that are successful at such methods, but I think that all-in/all-out based on moving averages is just a losing proposition in the face of slippages.

After all that is said, some folks claim that moving averages can be used as a proxy for future volatility. There is some statistical benefit from adjusting a portfolio to a lower equity allocation during periods of high volatility, not necessarily for increased long-term returns but for lower overall volatility (which gives better risk-based returns and presumably a higher safe withdrawal rates during decumulation), so maybe some success can be claimed because of this volatility timing.

That's the targeted benefit of the risk-budget minimum variance approach I've been describing, just using a more precise estimate for volatility.
TheDoctor91
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Re: Refinements to Hedgefundie's excellent approach

Post by TheDoctor91 »

Hydromod wrote: Wed Jan 26, 2022 3:35 pm
J-Kole wrote: Wed Jan 26, 2022 11:57 am Hydromod, if the 200-MA strategy gives the same results as buy and hold can you please explain this reddit post because from the chart it looks like the 200-MA mitigated huge drawdowns in the 00's, 08's, and 20's.
https://www.reddit.com/r/LETFs/comments ... long_with/

Additionally, if Hedgefudie exited his position during the 2020 crash using the 200-SMA, he could have reduced his drawdown and got out with around 30k in profits above his initial investment of 100k.
viewtopic.php?t=288192

I've been researching the strategy and just confused why it won't work. Thank you.
My experience is that I can't get a moving-average signal to reliably give a statistical predictive edge on future returns. Remember, for a method to be worthwhile you have to be able to determine when to get out AND when to get in at a more favorable price, and you have to be successful at both more times than not. You can get out fine, but you've lost if you are late getting back in. And every time you make a trade, there's some slippage during the trades, which means you have to be successful enough to overcome the slippage from both trading overhead and failures to get the timing right.

It's dangerous to look too far back with these approaches, namely before computers were king and when trades might take days to execute with associated brokerage fees. This tended to be better for getting predictive power from moving averages, because the overhead from trades made folks slower to react and folks weren't so used to such math. It may not have been too far back where it would have even been possible to trade with such approaches.

With the current high-powered algorithmic wizards and instantaneous trading I think that any edge from moving averages has long been arbitraged away. It's so easy that anyone can do it, and many can do it faster and cheaper than random individual trader; when enough do it, then the edge disappears.

If I remember correctly, I could find some predictive capability in the S&P up to early 2015. It seems to me that the cycles have been speeding up over time, and now the market responds so quickly that these long-term cycle signals are mushed together with shorter-term responses. More recently, the cycles tend to generate a lot of false signals; moving averages don't help with determining which signal is real and which is false. Lots of false signals are bad, because they swamp the few large real signals. Discouragingly, the S&P gave the best results of any index funds that I tried.

That's my opinion about why it won't work reliably. I applaud those that are successful at such methods, but I think that all-in/all-out based on moving averages is just a losing proposition in the face of slippages.

After all that is said, some folks claim that moving averages can be used as a proxy for future volatility. There is some statistical benefit from adjusting a portfolio to a lower equity allocation during periods of high volatility, not necessarily for increased long-term returns but for lower overall volatility (which gives better risk-based returns and presumably a higher safe withdrawal rates during decumulation), so maybe some success can be claimed because of this volatility timing.

That's the targeted benefit of the risk-budget minimum variance approach I've been describing, just using a more precise estimate for volatility.
I’ve found the same, a lot more whiplashes now, but i wonder if over the very long term if a moving strategy should still work.

Being able to take the pain in the meantime is a lot more difficult.
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

This is a very long entry. The TL;DR is that in the past it appeared that it was statistically possible to identify assets out of a potential group that will perform better than the remaining assets over the next few weeks to a quarter based on recent months, but this edge has been slender at best over the last decade or two. Typically, incorporating the top third to half as a group was necessary for outperformance; selecting on absolute returns degraded performance. At times, using the best third of a diversified set of 1x or 3x equity assets significantly outperformed the 1x or 3x S&P index, but the S&P index has tended to match this set over the last decade or two. The implication is that using such a strategy going forward may have extended periods somewhat underperforming the 1x or 3x S&P index due to trading slippage, but there may be relatively short periods allowing overall outperformance.

Diversification is a way of smoothing out portfolio performance. A diversified portfolio has a mix of high- and low-performing assets, and rebalancing tends to be a sell-high/buy-low proposition as long as the assets take turns outperforming. With diversification, the portfolio will never perform as well as the best-performing asset nor as poorly as the worse-performing asset. Diversified index funds such as SPY/VFINX are already diversified across the market, which is why a simple S&P/bond portfolio makes a good investment in the first place. However, there are periods when the S&P 500 has lagged for extended periods.

I’m interested in examining the criteria for picking diversified portfolios, because I want to build a robust portfolio with volatile 3x LETFs. I am seeking to maintain returns high enough to attain a permanent withdrawal rate much higher than the commonly quoted 3.5 to 4 percent, which requires high returns with (relatively) low volatility. At the moment, the 3x LETFs are less than 10 percent of my portfolio, are siloed off from the remainder, and would not be tapped into for a decade or two. My plan is to work out how to safely handle these assets while that part of the portfolio is small enough that it is not going to make or break retirement.

Part of my plan is to explicitly allocate volatility across assets using a risk-budget minimum variance approach to determine a time-varying asset allocation that tends to minimize portfolio volatility, as I’ve described before. I like this approach for determining asset allocations because (i) it has tended to mitigate slow crashes (but not the fast ones) and (ii) it’s performed acceptably well with respect to both absolute and risk-adjusted returns in backtests regardless of which assets are thrown together.

The asset allocation strategy is only part of a portfolio allocation scheme, because it works with the assets that it is given but has nothing to say about what assets are used. Backtesting using the S&P or NASDAQ indices combined with long-term treasuries has historically performed well, but these are picked based on 20/20 hindsight. This entry is looking at potential asset selection strategies to go with the asset allocation strategy.

Most asset selection approaches select assets based on performance over some prior period. Some tactical asset allocation strategies invoke the concept of momentum, confirming/updating sectors as often as weekly or monthly based on recent performance (e.g., over the last N months), while the buy-and-hold crowd tend to select based on some longer period (e.g., over the last N decades) and only gradually adjust the allocations. Periodically adjusting which sectors are invested in has the potential of maintaining a better-performing mix of assets, at the cost of needing to project acceptable allocations until the next adjustment. Rapid (less than annual evaluations) have the potential for churn and added complexity. Slow (multiyear/multidecade evaluations) have the potential for long-term lagging with a poor asset selection.

To get a handle on this tradeoff, I looked at the consequences of periodically selecting a subset from a collection of potential assets based on their recent prior history and evaluating the total-return performance over the next period for (i) the selected group, (ii) the non-selected group, (iii) the overall collection, and (iv) the S&P index. To be actionable, I would expect that, on average over many periods, the average next-period return for the selected assets would have higher returns than the average next-period return for the overall collection. There would be no point in using prior histories otherwise. The minimum variance approach would be responsible for adjusting allocations to improve risk-adjusted returns.
To test whether there might be some benefit to considering potential switches in asset allocations on a relatively frequent basis, it is necessary to (i) assemble a collection of assets, (ii) decide on a methodology for selecting assets based on historical returns, and (iii) decide on a methodology for evaluating predictions.

I assembled several mixes of 1x and 3x funds. The 1x funds cover a variety of US equity index funds by market cap and sector, international equity index funds, REITs, bonds and treasuries, and precious metals. I mixed and matched these somewhat; sometimes lumping everything together and sometimes evaluating just broad categories. The 3x funds include the popular categories (UPRO is S&P 500, TQQQ is NASDAQ, DRN is REIT, UMDD is midcap, URTY is small cap, EURL is European, EDC is emerging markets, SOXL is semiconductors, CURE is healthcare, FAS is financials, UTSL is utilities, RETL is retail, WANT is consumer discretionary, NAIL is home construction). These are sectors that have current 3x LETFs and a reasonably long history. All sequences were augmented with simulated daily returns based on existing mutual funds, typically Vanguard or Fidelity funds. These likely have some survivor bias on returns.

I used a simple but representative methodology for selecting assets. I used every possible starting day during the test period. For each evaluation day, I calculated the equivalent CAGR for a set of N different previous periods, each a multiple of one 21-day month, and averaged the N CAGR values. These were ranked from lowest to highest, and the top fraction were selected. The examples use lookbacks of 3, 5, 7, and 9 months; for each of these four cases, the equivalent CAGR was calculated, then the four values were weighted equally. This approach effectively weights the shortest periods higher, because they are part of all longer periods. I didn’t get dramatically different rankings if the CAGR values were weighted by the period duration or the inverse of the period duration, or if I picked somewhat different months. I selected whole numbers of months for lookbacks to avoid potential issues with systematically different performance during different parts of a month.

I used the average CAGR for the next period as the comparison metric. The next period might be two weeks or one 21-day month, for example.
I tried using the top third to top half of the ranked assets. These gave generally similar results with respect to average predicted CAGR. If I selected fewer assets, their subsequent average CAGR tended to be worse. If I selected just the assets with positive results (a typical tactical asset allocation strategy), the subsequent average CAGR also tended to be worse.

The following plots give a flavor of the predictive capability. Each one considers the period where the simulated record is complete for each asset, with every day of the period used to select a group of assets. In order, these include (i) a mix of LETFS including both 3x risk assets and a variety of 1x (VFITX and TLT), 2x (UGL), and 3x (TMF and TYD) safety assets, using a one-month (21-day) prediction; (ii-v) the same case without the safety assets, using 10-, 21-, 42-, and 63-day prediction; and (vi) a mix of 1x risk assets.

In each figure, the top plot shows the cumulative distribution function for three different metrics: (i) average CAGR of the selected group minus the average CAGR of the non-selected group, (ii) average CAGR of the selected group minus the average CAGR for the entire collection of ETFs, and (iii) average CAGR of the selected group minus the CAGR for UPRO. The additional labeling provides (i) number of assets to select in the top group (or middle group), (ii) total assets considered, (iii) prediction period, and (iv) the number of days for a lookback case (divide by 21 to get months). The squares on the curves represent the log-average over all of the samples; the median is found where the curve crosses the horizontal 0.5 line. The horizontal axis expresses daily return as equivalent CAGR.

The middle plot shows the cumulative gain for the high group for each metric.

The bottom plot shows a dot whenever the asset is selected. Assets that were extended with a prior mutual fund have an ‘ex’ at the end of the name. The color represents rank in the lookback set, with red dots at the top of the selected group and light gray just making it into the top group. The number at the right axis indicates the fraction of possible days that the asset is in the top group, and the selected group on the last day is indicated by red circles.

Image

Image

Image

Image

Image

Image

Comparing these figures, I come up with several takeaways.
  • The benefit of an individual prediction is subtle at best. The net effect accrues over many repetitions, where any individual prediction is typically very positive or very negative relative to the compared behavior. Over the different five-year periods, the momentum effect produced a win rate between roughly 45 and 55 percent.
  • Momentum considerations did seem to have had modest predictive power with respect to selecting a group of assets that would outperform the remainder of the assets. The predictive power was variable over time, but by far the most outperformance occurred 1998 to 2002.
  • The predictions including safety assets tended to have a lower mean win rate relative to UPRO than the equity-only predictions. During 2000-2010, including the safety assets resulted in outperformance relative to UPRO; otherwise, the performance was roughly consistent with UPRO.
  • Predictions with 3x LETFs tended to have a solid win rate relative to UPRO from 1998 to 2015, but more recently outperformance has faded away. Interestingly, UPRO was the least selected LETF over the entire period, and is usually within the middle group.
  • Increasing the prediction period from 10 days to 21, 42, and 63 days tended to substantially shrinking the dispersion in results (i.e., become more consistent). Reducing dispersion is an expected consequence of volatility decreasing as the averaging period increases (i.e., changes during 10 days tend to be much noisier than changes during three months).
The most-selected assets differed among the five-year periods. For the equity-only case with a one-month prediction, the assets selected at least half of the time were TQQQ/SOXL/FAS (1995 to 2000), NAIL/DRN/SOXL (2000 to 2005), EDC/DRN/EURL/UTSL (2005 to 2010), WANT/RETL (2010 to 2015), WANT/SOXL/TQQQ/NAIL (2015 to 2020), and TQQQ/SOXL/WANT (2017 to 2022).

All in all, I would conclude that selecting a group of assets based on recent months has had periods where there has been an edge in performance relative to the rest of the group, but outperformance has been minimal for the last 20 years. Outperformance with respect to the S&P has been a bit better, but has been relatively flat for approaching 10 years (20 years for 1x assets).

This situation can be interpreted in various ways, depending on whether one considers the most recent decade or two to be a new normal. It can be argued that the advent of sophisticated trading strategies has by now removed the momentum edge, so that selecting assets from a group based on recent trend behavior will be unlikely to significantly outperform the group even before slippage from trading (although the selected assets may slightly outperform the S&P, probably associated with higher volatility). On the other hand, it can be argued that selecting assets based on recent behavior has not been detrimental to performance (before trading) and there may be periods in the future where selecting assets will substantially outperform during trending markets. In other words, using such a strategy is likely to somewhat underperform the S&P due to trading slippage going forward, but there may be relatively short periods of outperformance that compensate.

In short, you pays your money and takes your choice.
laurenthu
Posts: 10
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Re: Refinements to Hedgefundie's excellent approach

Post by laurenthu »

This is fantastic work thanks a lot for sharing!
Do I understand correctly that your conclusion from that work is that it's better to have a great basket of 3X ETFs and keep working with that basket, rather than using the momentum factors to select that basket? I am using your TQQQ / SOXL / FAS / RETL risk budget basket and it makes great sense to me, and although they might not be the best each time they are also adding value because of their low correlation.


This is also a good segway to this strategy I have been eyeing recently: https://allocatesmartly.com/financial-m ... -strategy/
This combines 2 things I like - momentum and low correlation. I wonder if we could plug the momentum combined with low correlation idea to a risk budget portfolio, and get great results.
The mechanism would look like this:
Get the top 6 momentum assets from the basket here: S&P 500 (represented by SPY), Nasdaq 100 (QQQ), US real estate (VNQ), US mortgage real estate (REM), intermediate-term US Treasuries (IEF), long-term US Treasuries (TLT), US TIPS (TIP), Europe stocks (VGK), Japan stocks (EWJ), international small cap stocks (SCZ), emerging market stocks (EEM), international real estate (RWX), international treasuries (BWX), commodities (DBC) and gold (GLD).
(momentum on 3 months period, we can refine later)
Get the least correlated 3 assets from the top 6
Do a risk budget portfolio by attributing 75% of the budget to equity assets, and 25% to bond assets from the selection

One of the difficulty will be to determine what we should do if there is no bond asset or no equity asset selected. Also not all of these ETFs have 3X equivalent - shame - but the same mechanisms could still be applied.
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

I'd say that my tentative conclusion is that I can't currently justify going away from holding a good basket of 3x ETFs and working with that. It looks like a good momentum strategy has helped in the past, and in the future potentially could help outperform during certain periods without hurting much most of the time, but the devil is in the details.

If I went to a momentum approach, my tentative conclusion is that I'd use it to select the risk assets only. I'd probably maintain a set of safety assets (at least TMF) and just let the minimum variance approach do its job. I haven't done enough to have any conclusions on whether I could justify using some sort of momentum approach on safety assets. The early example of using momentum to switch between TMF and TMV prior to 1982 is still itching at me, though.

I did a few more tests with different durations. It looks like the six-month predictions are just a bit better than the three-month predictions over the last decade or so, but performance degrades for nine-month predictions and even more for a year. So what this implies is that a momentum strategy might be well served by holding assets for at least three to six months before giving up on them, especially when filtered through the minimum-variance methodology.

I've been reading the Allocate Smartly stuff for a while and I like the discussions of different strategies. That linked article was one of several influences on this test, although I've been curious for some time.

The proposed idea of selecting the least-correlated assets seems like a sound idea for reducing the number of assets. I haven't tested it, though. In practice TQQQ and SOXL are highly correlated and were often selected together, so this strategy would likely have eliminated one most of the time. The minimum-variance approach will tend to account for correlations, so holding four to six assets may not be too onerous to manage and should slightly reduce portfolio volatility.

Selecting the lowest-volatility assets from the momentum set is another approach that might have some benefit. I've seen an idea of using the lowest-volatility middle-of-the-pack approach for selecting assets someplace, I can't remember where, and apparently it did pretty well. The minimum variance approach gets at this idea a bit. I'll have to test this.
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

laurenthu wrote: Thu Feb 10, 2022 5:02 am This is fantastic work thanks a lot for sharing!
Do I understand correctly that your conclusion from that work is that it's better to have a great basket of 3X ETFs and keep working with that basket, rather than using the momentum factors to select that basket? I am using your TQQQ / SOXL / FAS / RETL risk budget basket and it makes great sense to me, and although they might not be the best each time they are also adding value because of their low correlation.

This is also a good segway to this strategy I have been eyeing recently: https://allocatesmartly.com/financial-m ... -strategy/
This combines 2 things I like - momentum and low correlation. I wonder if we could plug the momentum combined with low correlation idea to a risk budget portfolio, and get great results.
The mechanism would look like this:
Get the top 6 momentum assets from the basket here: S&P 500 (represented by SPY), Nasdaq 100 (QQQ), US real estate (VNQ), US mortgage real estate (REM), intermediate-term US Treasuries (IEF), long-term US Treasuries (TLT), US TIPS (TIP), Europe stocks (VGK), Japan stocks (EWJ), international small cap stocks (SCZ), emerging market stocks (EEM), international real estate (RWX), international treasuries (BWX), commodities (DBC) and gold (GLD).
(momentum on 3 months period, we can refine later)
Get the least correlated 3 assets from the top 6
Do a risk budget portfolio by attributing 75% of the budget to equity assets, and 25% to bond assets from the selection

One of the difficulty will be to determine what we should do if there is no bond asset or no equity asset selected. Also not all of these ETFs have 3X equivalent - shame - but the same mechanisms could still be applied.
I did some further testing of the idea of selecting a low-correlation basket from the favored momentum assets. I was expecting that the low-correlation case would do better, but instead the high-correlation basket seemed to do better in general. Go figure.

I've been playing with different momentum weights recently. It seems like equally weighting a 3-month and a 9-month momentum does especially well while selecting from the actual ETFs (leveraged or not). Now that I see that, it occurs to me that these durations track a faster response and a slower response while minimizing seasonal effects.

For testing I use a basket with 3x LETFs having significant AUM + UGL + DBC.

So far, the best behavior comes by selecting around 40 percent of the basket with this weighted relative momentum, updating weekly, and allocating based on the risk-based minimum variance approach. It seems to do better if the momentum selection considers all assets (including bonds and gold). There are periods with no safe assets, which allows the equities to run during a bull, but over 1991 to present the weekly checking seems to have allowed the safe assets to pop in before too much damage was done. For example, 2020 and 2022 look like they would have had around 40 percent drawdowns.

The one additional twist is that adding TMV as an option helped considerably over the test periods, and I suspect that TMV may be a very useful asset going forward. It looks like adding negative leveraged equities may smooth the portfolio responses somewhat at the cost of substantially reduced returns, which may be a good tradeoff for the more risk-adverse.

At first blush, a weekly check would seemingly have low predictive capabilities, but often an asset is selected for an extended period and this gives the momentum selection bias a chance to play out. I'm getting the impression that it's rare that there is wholesale swapping of assets, although that occurs with events (2000, 2008, 2020, 2022).

A particularly valuable test IMO is how the strategy has done since 2015 or so, because this period has had distinctly choppier markets that have been rather challenging for momentum approaches. The preliminary indications are that this approach would have done pretty well even during this period (neglecting slippage).

I haven't tested for trading slippage yet, Sharpe ratios, etc., but I'm very encouraged so far. If this pans out with more rigorous testing, I will be very tempted to follow a similar strategy going forward. It tends to maintain a well diversified portfolio (40% of candidate assets are included) that continually adjusts to the current market trends while balancing risks among the assets according to their volatility and correlation. Still, I can't recommend the approach without more detailed testing on slippage costs etc.
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