Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

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JZah
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by JZah »

Hi Hydromod,

I am very intrigued by your adventure; both on this thread and others. I learnt about it through stumbling across HFEA, then mHFEA, then your ideas and evolution from a simple fund to the more active ~22 asset fund you have made public.

I really like these ideas and wanted to write some of my own code. I was wondering, before I use a whole bunch of time to get the back test data, if you wouldn't mind either helping me with a link to the data or if you have a CSV file or the like that you could share? I would greatly appreciate it and if I come up with any developments I will be sure to share them in kind.

Perhaps DM me?
Football2408
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Football2408 »

Just caught up on this post about your rebalancing analysis. Interesting. The “luck” of rebalancing quarterly in an HFEA posts has been talked about before. To me it seems that anything longer than monthly (or better 2x a month minimum) and there is going to be a decent amount of timing luck, depending on how volatile the asset and portfolios are. I have decided to do two different “tranches” and rebalance each on a monthly basis, so effectively rebalancing 50% of the portfolio every two weeks depending on momentum and vol.

have you added any other strategies to compliment your current construct? Looking at it, this type of strategy might go well with a tail hedge allocation (CAOS, CYA, TAIL). Or something that is essentially the inverse of momentum high vol (BTAL) or a value tilted buy and hold strategy. Or perhaps a combination sleeve of the above with other traditional alts and hedges(gold, long vix products, OTM puts).
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

Football2408 wrote: Sun Dec 10, 2023 5:21 pm Just caught up on this post about your rebalancing analysis. Interesting. The “luck” of rebalancing quarterly in an HFEA posts has been talked about before. To me it seems that anything longer than monthly (or better 2x a month minimum) and there is going to be a decent amount of timing luck, depending on how volatile the asset and portfolios are. I have decided to do two different “tranches” and rebalance each on a monthly basis, so effectively rebalancing 50% of the portfolio every two weeks depending on momentum and vol.

have you added any other strategies to compliment your current construct? Looking at it, this type of strategy might go well with a tail hedge allocation (CAOS, CYA, TAIL). Or something that is essentially the inverse of momentum high vol (BTAL) or a value tilted buy and hold strategy. Or perhaps a combination sleeve of the above with other traditional alts and hedges(gold, long vix products, OTM puts).
I did a little bit of analysis after the last rebalancing post. I (i) aligned the sequence starting in 2007 with February 15 and with March 30, (ii) calculated the volatility and correlations based on the daily, weekly, monthly, etc. for these sequences, (iii) generated sets of normally distributed realizations obeying the stats, and (iv) calculated the rebalancing effect for each assuming no net returns for each asset. Half a quarter difference only for the stats. The daily rebalance had essentially identical histories for the February and March stats, but not so much for the rest of the sequences. The monthly and quarterly definitely had better rebalancing returns with the March stats.

It looks like the end of the month/quarter stats show a bit higher asset volatility and the equities were less positively/more negatively correlated with the bonds and alternatives, which generates more favorable rebalances. I have no idea if that is a fluke or consistent over time.

I was surprised to see that the annual and multi-year rebalance stride tended to have increasingly large rebalance bonuses (presuming I'm doing it right). I haven't had a chance to delve further.

The tranch idea is a good one.

I tried plugging BTAL in. It doesn't seem to have enough volatility to balance 3x LETFs. I think it would be useful on a less-levered portfolio.

I tried plugging in some of the vix products. I didn't really get much promising, but I have not done enough testing to eliminate them.

Beyond that, I haven't looked at the other approaches. I've very recently started considering multi-strategy approaches with low correlation between the strategies, but haven't had a chance to code much up yet.
Football2408
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Football2408 »

Hydromod wrote: Sun Dec 10, 2023 8:17 pm
Football2408 wrote: Sun Dec 10, 2023 5:21 pm Just caught up on this post about your rebalancing analysis. Interesting. The “luck” of rebalancing quarterly in an HFEA posts has been talked about before. To me it seems that anything longer than monthly (or better 2x a month minimum) and there is going to be a decent amount of timing luck, depending on how volatile the asset and portfolios are. I have decided to do two different “tranches” and rebalance each on a monthly basis, so effectively rebalancing 50% of the portfolio every two weeks depending on momentum and vol.

have you added any other strategies to compliment your current construct? Looking at it, this type of strategy might go well with a tail hedge allocation (CAOS, CYA, TAIL). Or something that is essentially the inverse of momentum high vol (BTAL) or a value tilted buy and hold strategy. Or perhaps a combination sleeve of the above with other traditional alts and hedges(gold, long vix products, OTM puts).
I did a little bit of analysis after the last rebalancing post. I (i) aligned the sequence starting in 2007 with February 15 and with March 30, (ii) calculated the volatility and correlations based on the daily, weekly, monthly, etc. for these sequences, (iii) generated sets of normally distributed realizations obeying the stats, and (iv) calculated the rebalancing effect for each assuming no net returns for each asset. Half a quarter difference only for the stats. The daily rebalance had essentially identical histories for the February and March stats, but not so much for the rest of the sequences. The monthly and quarterly definitely had better rebalancing returns with the March stats.

It looks like the end of the month/quarter stats show a bit higher asset volatility and the equities were less positively/more negatively correlated with the bonds and alternatives, which generates more favorable rebalances. I have no idea if that is a fluke or consistent over time.

I was surprised to see that the annual and multi-year rebalance stride tended to have increasingly large rebalance bonuses (presuming I'm doing it right). I haven't had a chance to delve further.

The tranch idea is a good one.

I tried plugging BTAL in. It doesn't seem to have enough volatility to balance 3x LETFs. I think it would be useful on a less-levered portfolio.

I tried plugging in some of the vix products. I didn't really get much promising, but I have not done enough testing to eliminate them.

Beyond that, I haven't looked at the other approaches. I've very recently started considering multi-strategy approaches with low correlation between the strategies, but haven't had a chance to code much up yet.

Interesting. When you say end of the month / quarter being more favorable, how specific do you mean ? Rebalance on the very last day of the month? First day of next month? Within +- 2 days of last trading day of month?
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

My impression is that it more or less ramps linearly from turn to middle. So not much difference being a few days from the turn.

The two things that I've heard that would pace the market to the calendar are treasury auctions, which are in the middle of months, and activity around end-of-month/quarter balancing of accounts. So the treasury flurry is offset by a couple of weeks from the equity flurry.

Again, these effects may simply be coincidence.
Football2408
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Football2408 »

Hmm. I think with every two week rebalances, I suppose it won’t matter much.

I saw here or on Reddit that you now use two different crypto holdings. Do you cap these holdings at all? IE when crypto has had low volatility, these two holdings could combine to 25-35%. Would you cut them down to a lower more reasonable % of total? I think you somewhat do this for your low vol defensive holdings.
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

I just treat crypto like any other risk asset, their volatility is comparable to a 3x LETF. Right now they are combined at 13 percent of the portfolio.

I scale the risk budget according to momentum, but cap the scaling. Right now TQQQ, SOXL, NAIL, GBTC, and GDLC are high momentum, so their risk budget is capped and they all have the same risk allocation.

I used to limit allocations, but now I do an asset-by-asset scaling based on the ratio of recent to historical volatility that seems to take care of that issue pretty naturally. I discussed that not too long ago. I hate the idea of putting in limits, because each one is another fitting parameter to fuss over.
ag811987
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by ag811987 »

OP, this is awesome. I need to properly reread on my laptop or print out. I think you'd like the breaking the market blog.
Has some good information on dynamic rebalancing across stocks, bonds, and equities.

Vol and correlations are re-estimated each week based on recent data while LT returns expectations are more stable think CAPE and yield to maturity (although the actual methods are proprietary).
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

ag811987 wrote: Sat Dec 30, 2023 3:45 pm OP, this is awesome. I need to properly reread on my laptop or print out. I think you'd like the breaking the market blog.
Has some good information on dynamic rebalancing across stocks, bonds, and equities.

Vol and correlations are re-estimated each week based on recent data while LT returns expectations are more stable think CAPE and yield to maturity (although the actual methods are proprietary).
I've gone through the breaking the market site. It's very frustrating to me, because there is a lot of verbal explanation at the level of the absolute novice but it doesn't really get into the math enough to exactly get how to do the portfolio. I've listened to a couple of podcasts that helped a bit.
ag811987
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by ag811987 »

I think because he charges as an RIA and may have ambitions to one day go full time he doesn't want to give out the exact formulas. But he does share all the weights each week so you can presumably try and guess then replicate/fitbtue weights to determine parameters used
ag811987
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by ag811987 »

Finished reading and this has gotten very interesting. You've definitely evolved the methodology a long way from the original modifications to HFEA. What are your thoughts these days on the unemployment indicator? Your early analysis seemed to be very strong for it.

Are you just running matlab code, printing weights, and modifying your M1 pie every week? (Hitting the rebalance button daily)
- Do you have to generate a new CSV each week and then import that into matlab for the real world price data
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

ag811987 wrote: Sun Dec 31, 2023 1:06 am Finished reading and this has gotten very interesting. You've definitely evolved the methodology a long way from the original modifications to HFEA. What are your thoughts these days on the unemployment indicator? Your early analysis seemed to be very strong for it.

Are you just running matlab code, printing weights, and modifying your M1 pie every week? (Hitting the rebalance button daily)
- Do you have to generate a new CSV each week and then import that into matlab for the real world price data
I dropped the unemployment indicator during COVID, because COVID was a shock condition that was far outside prior experience. The unemployment indicator lags quite a bit, it's really best for slower-moving financial changes. I'm also a little more skeptical of the unemployment indicator now, because the values are adjusted at least once or twice after first publication. So backtesting numbers are different from the first available numbers that one would use for determining allocations.

I got even further from the HFEA approach based on the very poor performance in the spring of 2022. I'm happy enough with the updated momentum-based all-weather approach that I probably won't go back to HFEA or the unemployment indicator. With that said, HFEA should do okay going forward for some time, IMO, because TMF has some upside again.

I'll note that as of November the unemployment indicator is showing some signs of a slow upswing that historically was a harbinger of a recession shortly afterwards, for what that's worth.

From an operational perspective, most of the calculations are automated from ticker download through the weight calculations. I just push go on the matlab code; it obtains the ticker data from yahoo finance directly, calculates risk factors, updates weights, and dumps the weights to a sheet in an excel file as a type of permanent archive. I manually do a little formatting in the excel spreadsheet. I do use google sheets at the same time for some weekly downloads to update certain data that are only used for generating simulated tickers; this is not necessary for calculations, but I like to keep the database complete.

Once I have the new allocations, I manually update the allocations in M1.

As a practical matter, I only push rebalance when the allocation drifts a few percent (to minimize slippage), usually in M1's afternoon session. Maybe once or twice a week.

I track actual allocations and update my tracking spreadsheet whenever reallocating or rebalancing. This is basically a couple of cut and paste steps.

There isn't much difference in my effort level for an adaptive HFEA and my current approach. I don't really intend to post any weekly signals or supply code. Others have taken a whack at a python implementation.

I did come up with a google sheet some time back that could be used for the adaptive HFEA approach with two assets, and an excel sheet that solves the risk-balance minimum variance model for multiple assets. I don't like these because you only have price, not total returns, which screws things up with things like dividends and splits. The excel one was really clumsy, too.
konik
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

Hi Hydromod!

Have you see this article?
https://papers.ssrn.com/sol3/papers.cfm ... id=2328254

I feel their approach looks more or less similar to yours? What are your thoughts on this article? Im worried the time period they show in figures is rather short.
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

konik wrote: Thu Feb 01, 2024 12:46 pm Hi Hydromod!

Have you see this article?
https://papers.ssrn.com/sol3/papers.cfm ... id=2328254

I feel their approach looks more or less similar to yours? What are your thoughts on this article? Im worried the time period they show in figures is rather short.
I vaguely remember seeing that particular paper. I have poked around their website quite a bit (here) and recently picked up their book called Adaptive Asset Allocation, which fleshes that white paper out quite a bit. They have a podcast as well that has some insights based on guys chatting on Friday afternoons before going out for a drink.

I will say that very little of what I'm doing is novel, I'm doing stuff that was pretty well understood ten years ago, I'm just applying it to LETFs. It's quite possible that the paper fed into my approach.

For the paper itself, that period was favorable for their approach. I suspect that results would have been just as good going back further in time, I'm hoping to test that out soon with some datasets to the 1920s or at least early 1960s. The last few years have been a good stress test, I've certainly made some adjustments to become more diversified.
konik
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

How do you make backtests? Are there any available tools for that? And do you have a reasonable estimation for trade costs?
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

konik wrote: Fri Feb 02, 2024 1:24 am How do you make backtests? Are there any available tools for that? And do you have a reasonable estimation for trade costs?
I wrote my own Matlab code to do backtesting, because I have been trying to learn about various approaches that are not necessarily available in any free software that I'm aware of. You can read about it a little in my first thread here. At one time I had thoughts of making it available, but it's a bit messy and would be hard for others to follow.

The point of the backtesting is to see if a strategy would have shown promise in previous decades. My suspicion is that some historical strategies were adopted in part to minimize trading costs, and some effective modern strategies may have been overwhelmed by trading costs. I'm trying to get simulated historical daily equity LETF sequences to the 1920s and treasury LETF sequences to the 1960s as "out of sample" data.

I've been using the recent bid-ask spread for trade costs. That underestimates past trading costs, since historical spreads were larger and there were added brokerage fees. Also, often there were delays inherent in trading that smeared out trades over days for retail investors. I'm trying to get a handle on the bid-ask behavior, but haven't implemented anything yet. I also simulate trades using randomly sampled prices during the day to add "fuzz" when trading multiple securities. I don't intend to account for the multi-day trading.
konik
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

I got very interested in the topic, so I have a lot of questions now:

1) How do you define the universe of assets? If you break stocks geographically, then by sectors, naturally you can go down to individual shares? How do you decide where to stop? It should be at least related to trade costs or smth else?

2) As I understand momentum, if you look back 12 months it gives you "forecast" for the next 12 months. If you rebalance every month, does it mean you should break your portfolio in 12 pieces and actually update one of pieces every 12 months?

3) Same goes for volatility and correlations. Am I right feeling that look-back period should be somehow synchronised to rebalancing?

4) You employ somewhat arbitrary "risk budget allocation" technique to control the overall risk-return profile. Did you try simple volatility targeting for the whole portfolio and either leverage or partially go cash to meet the goal volatility?
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

konik wrote: Fri Feb 02, 2024 10:14 am I got very interested in the topic, so I have a lot of questions now:

1) How do you define the universe of assets? If you break stocks geographically, then by sectors, naturally you can go down to individual shares? How do you decide where to stop? It should be at least related to trade costs or smth else?

I don't really want to have granularity below index funds, but certainly you could do that. I don't have enough invested to make that attractive and they get volatile.

I started out with just UPRO and TMF, then added TQQQ and later TYD. 2022 got me to broaden out. It is run in a separate Roth account; I can only access leverage in that account, so I have to handle it as a single portfolio.

The approach is designed to accommodate 3x index LETFs. So the universe is primarily 3x equity LETFs, I like to have the AUM above say $30M at a minimum. That cuts it down to around 15 available 3x LETFs, plus a few 2x that are volatile or plug holes. I don't use UPRO, it usually has a low allocation. Then there are the 3x treasuries, plus a few alternative assets to serve as ballast when the others are falling.


2) As I understand momentum, if you look back 12 months it gives you "forecast" for the next 12 months. If you rebalance every month, does it mean you should break your portfolio in 12 pieces and actually update one of pieces every 12 months?

I use the average of 1, 4, 10, and 12 month momentum. I just keep moving the window each time I update (weekly or monthly). There are times when an asset pops in and out each update for a few cycles, and times when an asset stays in for a year or more.

You could certainly update fractionally, I think that's what some folks do. It may cut trading costs and cut down on the asset appearance/disappearance, but may be too slow on crashes. At some point I may test this idea, it's on the list.


3) Same goes for volatility and correlations. Am I right feeling that look-back period should be somehow synchronised to rebalancing?


Yes, look-back is related to rebalancing frequency.

I like to use 3 months for correlations to get enough data and 2 months for volatility. It's a tradeoff between having enough data for decent estimates and updating frequently enough to capture changes. These seem to work reasonably well for both the weekly and monthly updating, because forward estimates tend to be predictive for a few months.

I haven't really looked at whether a longer lookback makes a difference with less frequent rebalancing.


4) You employ somewhat arbitrary "risk budget allocation" technique to control the overall risk-return profile. Did you try simple volatility targeting for the whole portfolio and either leverage or partially go cash to meet the goal volatility?


That's another way to do it that some folks like.

I've tried a little of that kind of thing a few years ago, but I don't remember details. I don't think it made too much difference either way. The risk budget allocation part is appealing to my personality, so I've just gone with it.

One approach might be to scale leverage according to volatility/variance aggressively when the trend is above the moving average while being defensive when the trend is below the moving average. I haven't tested this idea though.

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hillclimber
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by hillclimber »

Hello Hydromod. I heard about your strategy on Risk Parity Radio, and I am interested by it. I do have some questions, though.

Have you tried backtesting your strategy on unleveraged mutual funds? Obviously, you won't get as strong of a rebalancing bonus, but you can get a lot more data with some old sector funds like FSUTX, FDFAX, and FIDSX. They are old actively managed Fidelity funds, some of which go back to the 80's. That would help out with concerns about survivorship bias, since there have been some notable crashes of leveraged sector etfs.

Just going with the defaults for dual momentum strategies in portfoliovisualizer, the strategy outperforms the market by 6% a year, which seems too good to be true, but shows the sorts of results you can get with backtests and sector funds.

https://www.portfoliovisualizer.com/tac ... MatENa8jDH
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

hillclimber wrote: Sat Feb 03, 2024 3:36 am Hello Hydromod. I heard about your strategy on Risk Parity Radio, and I am interested by it. I do have some questions, though.

Have you tried backtesting your strategy on unleveraged mutual funds? Obviously, you won't get as strong of a rebalancing bonus, but you can get a lot more data with some old sector funds like FSUTX, FDFAX, and FIDSX. They are old actively managed Fidelity funds, some of which go back to the 80's. That would help out with concerns about survivorship bias, since there have been some notable crashes of leveraged sector etfs.

Just going with the defaults for dual momentum strategies in portfoliovisualizer, the strategy outperforms the market by 6% a year, which seems too good to be true, but shows the sorts of results you can get with backtests and sector funds.

https://www.portfoliovisualizer.com/tac ... MatENa8jDH
Thanks for mentioning these funds.

I do like using those old mutual funds to extend the record. I've used many of them to stitch older funds together with newer funds to develop a single simulated sequence, then use the leverage formula to make an approximate 2x and 3x fund. I've used alternatives for a couple of the ones you show. There were a couple that I haven't used that don't have corresponding 3x LETFs.

I'm working on making a longer set of simulated 2x and 3x LETFs with daily returns, to the 1920s and 1960s, based on Ken French's dataset and other sources. We'll see how that goes. That will provide a type of out of sample dataset.

Backtesting suggests that my strategy works better with LETFs than with unlevered assets once trading costs are accounted for. One wants frequent rebalancing for risk reduction and volatility harvesting, but also wants winners to keep going as long as possible. Frequent rebalancing seems to be accommodated pretty well with 3x funds because of the volatility harvesting and seems to overcome trading costs. The volatility harvesting part is 9 times less effective with 1x compared to 3x, which is why I think that volatility harvesting isn't effective enough to overcome trading costs for 1x. Instead, the rebalancing stride should be tuned to longer periods with 1x, such as protection for large crashes.

Taking out FCYIX and playing around a bit, most of the outperformance with the dual momentum comes in bursts (1999 and 2008), perhaps 10 percent of the time or less with particularly favorable conditions.

I like to use around 35 to 45% of the assets at a time, because (i) the asset with highest momentum tends not to be the best the next month and (ii) spreading among assets tends to reduce portfolio volatility. There are a few PV options for allocation weights that I don't understand (the geometric and linear increasing and decreasing), but the geometric decreasing seems to do pretty well with these sector funds.
Football2408
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Football2408 »

“ volatility harvesting part is 9 times less effective with 1x compared to 3x”

This is interesting. I remember awhile ago you posted a chart of 3x LETFs that had excess return CAGRs (higher than buy and hold) using your momentum strategy. This effect would be almost nothing in one time ETFs ? Assume you would still have vol reduction though / better Sharp than buy and hold.
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

Football2408 wrote: Sat Feb 03, 2024 9:59 am “ volatility harvesting part is 9 times less effective with 1x compared to 3x”

This is interesting. I remember awhile ago you posted a chart of 3x LETFs that had excess return CAGRs (higher than buy and hold) using your momentum strategy. This effect would be almost nothing in one time ETFs ? Assume you would still have vol reduction though / better Sharp than buy and hold.
I was alluding to the chart in this entry. That chart has nothing to do with momentum, it's just using a static covariance structure and daily rebalancing with zero mean return on the underlying assets.

It isolates the rebalancing bonus by assuming the assets have zero mean return. This is not the same as saying that the 1x has zero mean return and the 2x and 3x assets are simply multiples of the 1x (that would also introduce additional volatility drag). So the chart is a bit rosy for returns, but does show that one can counteract volatility drag to some extent.

You can see that the bonus for 1x was a little better than 1 percent CAGR, which would get eaten up by trading costs. The 3x version was better than 10 percent CAGR, which should outpace trading costs.
konik
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

So after all you think daily rebalancing is the way to go, even with trading and tax costs, thanks to 3x funds?
Football2408
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Football2408 »

Image

https://ibb.co/VVwbbck


Was referring to this post. But yea that makes sense too. The frequent weekly or bi weekly or monthly style means trading costs need to be worth it.
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

konik wrote: Sat Feb 03, 2024 11:46 am So after all you think daily rebalancing is the way to go, even with trading and tax costs, thanks to 3x funds?
I'm really waffling a bit. It depends on your ultimate objective, how much weight the momentum part is playing, and how much effort you want to invest. But certainly the 3x part makes frequent rebalancing more palatable.

With a fixed allocation, it seems like there is a bit of a smile with respect to returns. There's a drop in returns from daily to weekly to monthly, then a rise to quarterly, but portfolio volatility and the effects of timing luck both increase monotonically as the rebalancing duration increases. I think band approaches would probably be a good compromise.

With adaptive approaches holding a fixed set of assets but adjusting allocations based purely on volatility or variance, portfolio volatility is damped at the cost of reducing overall returns. At least with HFEA, there was a similar smile except that it seemed like time of month/quarter for rebalancing also influenced the smile.

The momentum approach is trying to blend the smoothness of volatility-based allocation with some boost from using higher-returning assets. The asset switching does cause noticeably larger portfolio volatility but seems to give better returns (maybe not better risk adjusted returns, though). The jury is still out on best frequency, but I would wait at least a week before recalculating allocations (or split the portfolio and stagger recalculations).
 
I wouldn't argue with anybody using daily through quarterly rebalancing for 3x, but I personally lean towards weekly to monthly to balance the tradeoff between risk control and returns. If I had a reliable automated tool for daily rebalancing, I'd certainly consider that as an option.
konik
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

I made a small literature review on momnetum today, mainly based on Ilmanen book "Investing amid low expected returns" and the bibliography there. Some points:
- the best simple metric is to hold the best asset from 12 prior months for 1 month.
- even better is to equally combine 1, 3 and 12 months lookback window
- making mean variance is better than equal weight

Note, that in literature they usually speak about long-short portfolios, where u should be short the losers. Can we do that with -3x funds?

I was also surprised to find out commodities spot price actually exhibit negative momentum, only their futures have positive ones.

There should be even better scheme to forecast returns by taking into account value, but it seems like it's trickier to find a good measuring stick for all assets.

One last question: are you sure we can easily extrapolate momentum of assets to momentum of 3x assets. It looks reasonable, but I'm not sure it's 100% correct.
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Hydromod
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

konik wrote: Sat Feb 03, 2024 2:40 pm I made a small literature review on momnetum today, mainly based on Ilmanen book "Investing amid low expected returns" and the bibliography there. Some points:
- the best simple metric is to hold the best asset from 12 prior months for 1 month.
- even better is to equally combine 1, 3 and 12 months lookback window
- making mean variance is better than equal weight

Note, that in literature they usually speak about long-short portfolios, where u should be short the losers. Can we do that with -3x funds?


I have tried using long-short with 3x and -3x. I just had no luck with that, the only one I use is TYO. Even including SH as a -1x doesn't seem to help. The problem is that most assets tend to go up and the periods where shorting works tend to be hard to capture with momentum. At least at my level of sophistication.


I was also surprised to find out commodities spot price actually exhibit negative momentum, only their futures have positive ones.


I think of commodities as a short-term store of value when all of the 3x assets are crashing. Most of the time I don't have commodities in the portfolio, they only pop in 15 to 20 percent of the time and usually for fairly short periods of time. Same with YCS.


There should be even better scheme to forecast returns by taking into account value, but it seems like it's trickier to find a good measuring stick for all assets.

One last question: are you sure we can easily extrapolate momentum of assets to momentum of 3x assets. It looks reasonable, but I'm not sure it's 100% correct.


I just do momentum of the 3x assets directly. It seems to work pretty well. Note that individual stocks may have greater volatility than most of the 3x assets, so if momentum works for individual stocks it should for 3x LETFs as well.

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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

I'm based in Europe right now and don't have access to 3x ETFs (only some 2x). Im using IB, so I have rather good margin terms and can easily use it. How do you think with 3x margin would there be a significant difference from using 3x LETFs directly? The benefit could be using some factor funds, which do not exist in leverage form, but may provide some extra diversification.

Alternatively there are some ETPs, which are not ETFs, like WisdomTree or Leverage Shares products. I'm a bit scared to use them. Also there are some 5x products provided. Have you tested something like that?
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

Also I have been reading on volatility clustering. What type of formula do you use to calculate volatility of assets?

More importantly, how do you calculate asset correlations? I would be thankful if you could provide links to literature on this topic.
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

konik wrote: Sun Feb 04, 2024 9:37 am Also I have been reading on volatility clustering. What type of formula do you use to calculate volatility of assets?

More importantly, how do you calculate asset correlations? I would be thankful if you could provide links to literature on this topic.
I pull in the daily total return data to matlab. There are standard routines that calculate standard deviation (that's volatility) and the correlation coefficient between two vectors. You can get the same information from portfolio visualizer, although I don't know if the data is completely up to date. Or save the return data to Excel and use its routines. You can download historical data from yahoo finance; the adjusted close accounts for dividends and splits.

I calculate the standard deviation using 42 daily returns (2 months) correlation coefficient between each pair of assets using 63 daily returns (3 months). I don't think that the asset allocation approach is very sensitive to the precise lookback period.

I have never used margin and really don't know the ins and outs. I understand that some margin terms can be more favorable if the portfolio as a whole is considered than the independent assets. I think that it would be possible to get a fairly stable portfolio that I would be comfortable levering more than 3 times, but I haven't done any cost analysis of that type of thing.

I've not really looked into ETPs at more than a quick surface level, since they aren't really a thing in the US. ETPs are a general class that includes ETFs, ETNs, and ETCs (commodities) as a subset. The knock that I've heard on ETNs and ETCs is that they have greater counterparty risk. I don't know how easy it is to tell how much an individual ETP behaves like an ETF. I think that the concern is greatest during market stress periods, when you might want to reduce leverage anyway.

You might want to check costs on these, and make sure that market share is large enough to provide trading liquidity.

I think that the 5x products are probably too volatile for any extended hold, except maybe for the 5x 7-10 year treasury bond. You might get away with some 5x equity during bull markets, but definitely get out when volatility rises.

Sorry I can't be of more help.
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

Thanks for the replies!

About volatility, what I meant is whether you take into account any type of exponential or hyperbolic weighting of day volatilities, when calculating 1-2 month volatility?

About correlations, I wonder whether you can use past correlations as future predictors at all. From what I read it is at best very weak. Maybe you have any sources to support prediction power?
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

I just do plain old standard deviation with no weighting.

Correlations certainly do change over time. I'm worried about predicting daily correlations over the next rebalance period (a week to a month) using the previous 3 months, which is a pretty short lookahead. You can see that moving correlations remain quite similar over that duration (check rolling 60-day correlation).

The minimum variance algorithm actually uses covariances. The covariance of two assets is the correlation multiplied by the volatility of each asset. I think that the change in correlation is usually small compared to the change in volatility, so the allocations coming out of the minimum variance algorithm are much more sensitive to volatilities than to errors in correlations.

In any case, I think that the effect of errors in volatility and correlation will tend to wash out with ongoing frequent updates.
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

konik wrote: Sun Feb 04, 2024 9:12 am Also there are some 5x products provided. Have you tested something like that?
It occurred to me that a rule of thumb for rebalancing frequency seems to scale with asset variance, which is proportional to the square of leverage.

So if a portfolio with 1x leverage is rebalanced annually, using 5x products should be rebalanced 25 times more frequently or about biweekly.
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by comeinvest »

Hydromod wrote: Sun Feb 04, 2024 6:59 pm
konik wrote: Sun Feb 04, 2024 9:12 am Also there are some 5x products provided. Have you tested something like that?
It occurred to me that a rule of thumb for rebalancing frequency seems to scale with asset variance, which is proportional to the square of leverage.

So if a portfolio with 1x leverage is rebalanced annually, using 5x products should be rebalanced 25 times more frequently or about biweekly.
That is something I have been trying to find the answer for a long time. Do you have a link or reference where this formula is explained or tested?
What I gathered from backtests and discussions in this forum is that the rebalancing frequency for unleveraged stocks/bonds portfolios doesn't matter in the long run (except for adjusting the asset allocation risk buckets, but not for a rebalancing bonus or to avoid volatility decay); HFEA style portfolios (ca. 165% equities / 135% long-term treasuries, or similar) using 3x LETFs need to be rebalanced more frequently to avoid or counter-act volatility decay from the daily rebalancing of the LETFs; HFEA style portfolios using futures, margin, or options for leverage (for example mHFEA) need to be rebalanced less often to avoid volatility decay than those using 3x LETFs. But I was not sure about the last one, and how to quantify it. I know this thread is not HFEA but HOA; but rebalancing paradigms are possibly similar. Could you shed a little more light on the formula, and possibly clarify how it might apply to HFEA, if you have any insight? How would the internal rebalancing frequency of the components (e.g. daily rebalanced LETFs vs unbalanced futures/margin/options vs. monthly internally rebalanced products) affect the portfolio level rebalancing frequency between the components needed to avoid volatility decay (or create an overall rebalancing bonus)? Your contributions to this forum a much appreciated!

P.S. I know in another thread you examined the effect of the rebalancing frequency on leveraged portfolios, HFEA portfolios if I remember right, and you showed that monthly, quarterly, and annual result in similar long-term performance, except that the shorter rebalancing frequencies have more consistent results (when the rebalancing day within the period is changed) as the "rebalancing luck" is more spread out. Is that still true in your opinion, and would you say that more frequent rebalancing is mostly relevant to implementations using LETFs?
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

comeinvest wrote: Sun Feb 04, 2024 9:15 pm That is something I have been trying to find the answer for a long time. Do you have a link or reference where this formula is explained or tested?
What I gathered from backtests and discussions in this forum is that the rebalancing frequency for unleveraged stocks/bonds portfolios doesn't matter in the long run (except for adjusting the asset allocation risk buckets, but not for a rebalancing bonus or to avoid volatility decay); HFEA style portfolios (ca. 165% equities / 135% long-term treasuries, or similar) using 3x LETFs need to be rebalanced more frequently to avoid or counter-act volatility decay from the daily rebalancing of the LETFs; HFEA style portfolios using futures, margin, or options for leverage (for example mHFEA) need to be rebalanced less often to avoid volatility decay than those using 3x LETFs. But I was not sure about the last one, and how to quantify it. I know this thread is not HFEA but HOA; but rebalancing paradigms are possibly similar. Could you shed a little more light on the formula, and possibly clarify how it might apply to HFEA, if you have any insight? How would the internal rebalancing frequency of the components (e.g. daily rebalanced LETFs vs unbalanced futures/margin/options vs. monthly internally rebalanced products) affect the portfolio level rebalancing frequency between the components needed to avoid volatility decay (or create an overall rebalancing bonus)? Your contributions to this forum a much appreciated!

P.S. I know in another thread you examined the effect of the rebalancing frequency on leveraged portfolios, HFEA portfolios if I remember right, and you showed that monthly, quarterly, and annual result in similar long-term performance, except that the shorter rebalancing frequencies have more consistent results (when the rebalancing day within the period is changed) as the "rebalancing luck" is more spread out. Is that still true in your opinion, and would you say that more frequent rebalancing is mostly relevant to implementations using LETFs?
I'm basing the rule of thumb on the rebalancing bonus, it's not a formal all-encompassing thing.

The chart in the earlier entry (here) shows that the rebalancing bonus is proportional to the square of leverage. Bill Bernstein gives a formula for the rebalancing bonus of (1/2) sum_i sum_j ((var_i + var_j)/2 - covar_i,j) here.

The logic follows the idea that rebalancing is intended to bring assets back to within bands. The average time until the bands are exceeded is proportional to the variance, and variance is proportional to the square of the leverage.

Of course, there is a tension between returns and risk management. One tends to increase returns by concentrating risk into the best-performing assets (letting winners run). I suspect that performance is better in trending markets with less frequent rebalancing (letting winners run) and better in sideways markets with more frequent rebalancing (rebalancing bonus). This is something that has been niggling at me for a while, but I haven't tried to take an active look yet (other than backtesting with different strides). I've sort of thought that the tradeoff is a personality and circumstances thing; letting winners run is more for the risk tolerant and frequent rebalancing is more for the risk averse.

In terms of avoiding volatility decay with futures, I did a little backtest with a simulated daily S&P 500 from around 1928. I generated simulated 2x and 3x LETFs with a 1% ER. I also generated simulated 21-day 2x and 3x futures returns with the same borrowing rate (an optimistic assumption) but no ER. I started off separate sequences on 21 consecutive days.

Just for grins, I did the same for quarterly (63-day sequences, starting on 63 consecutive days).

Image
Image

The left panel in the figure shows the cumulative futures return divided by the cumulative LETF return (blue is 2x, red is 3x). The right panel gives the frequency of single-period drawdown (i.e., during the 21 days of the futures) for each 21-day period (this is a measure of ruin).

There are several periods: (i) leadup to Great Depression crash, (ii) Great Depression crash, (iii) 1930s, (iv) post-WW II to 1987, and (v) 1987 to present. The odd-numbered periods show futures performing better, the even-numbered periods show LETFs performing better.

The 2x leverage has relatively muted outperformances, aside from the dispersion from timing luck around the Great Depression.

The 3x leverage has more exaggerated outperformances in both directions, with timing luck dramatically affecting overall outcomes.

So it seems to me that in the modern era (since 1990), the futures approach generally has been a winner for 2x leverage with occasional hiccups at crashes. For 3x, futures generally did better than LETFs for periods of up to a decade, punctuated by large changes dependent on timing luck around crashes; those crashes have an outsided effect on ultimate outcome.

I can't say what drove the change from the postwar period to 1990 (LETF outperformance) to 1990-present (mostly futures outperformance). Maybe something to do with interest rates?

I would say that getting out of futures before a big crash would be prudent. You just need to know when that crash will occur, of course.
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

comeinvest wrote: Sun Feb 04, 2024 9:15 pm
Hydromod wrote: Sun Feb 04, 2024 6:59 pm
konik wrote: Sun Feb 04, 2024 9:12 am Also there are some 5x products provided. Have you tested something like that?
It occurred to me that a rule of thumb for rebalancing frequency seems to scale with asset variance, which is proportional to the square of leverage.

So if a portfolio with 1x leverage is rebalanced annually, using 5x products should be rebalanced 25 times more frequently or about biweekly.
That is something I have been trying to find the answer for a long time. Do you have a link or reference where this formula is explained or tested?
What I gathered from backtests and discussions in this forum is that the rebalancing frequency for unleveraged stocks/bonds portfolios doesn't matter in the long run (except for adjusting the asset allocation risk buckets, but not for a rebalancing bonus or to avoid volatility decay); HFEA style portfolios (ca. 165% equities / 135% long-term treasuries, or similar) using 3x LETFs need to be rebalanced more frequently to avoid or counter-act volatility decay from the daily rebalancing of the LETFs; HFEA style portfolios using futures, margin, or options for leverage (for example mHFEA) need to be rebalanced less often to avoid volatility decay than those using 3x LETFs. But I was not sure about the last one, and how to quantify it. I know this thread is not HFEA but HOA; but rebalancing paradigms are possibly similar. Could you shed a little more light on the formula, and possibly clarify how it might apply to HFEA, if you have any insight? How would the internal rebalancing frequency of the components (e.g. daily rebalanced LETFs vs unbalanced futures/margin/options vs. monthly internally rebalanced products) affect the portfolio level rebalancing frequency between the components needed to avoid volatility decay (or create an overall rebalancing bonus)? Your contributions to this forum a much appreciated!

P.S. I know in another thread you examined the effect of the rebalancing frequency on leveraged portfolios, HFEA portfolios if I remember right, and you showed that monthly, quarterly, and annual result in similar long-term performance, except that the shorter rebalancing frequencies have more consistent results (when the rebalancing day within the period is changed) as the "rebalancing luck" is more spread out. Is that still true in your opinion, and would you say that more frequent rebalancing is mostly relevant to implementations using LETFs?
Some real life rebalance bonus estimation can be found in commodity futures basket:
https://www.tandfonline.com/doi/pdf/10. ... j.v74.n2.4
https://summerhavenim.com/wp-content/up ... o-2018.pdf
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

How often do you recalculate weights based on past volatility? Every week? Every month, same moment you choose new assets?
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

In taxable, I'm pretty much just updating and rebalancing monthly.

In Roth, I do the updating and rebalancing weekly. Backtesting suggests that rebalancing more frequently just was reacting to noise.

If I had a larger account and automation, I would probably do something like updating 1/5 of the portfolio daily. I had tried doing daily rebalancing for a short while (holding the allocation fixed), but it got old very fast. I couldn't tell whether the benefit outweighed the slippage.
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by konik »

I think this all is sound and reasonably evidence-based. What I don't understand is how this strategy agrees with "you can't brat the market" and SPIVA reports, supporting this claim? The strategy is built upon persistent efficient market anomalies, but why don't others use it for better than market returns?
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Re: Hydromod's Okay Adventure: Leverage, Momentum, and Risk Management

Post by Hydromod »

I don't think that the strategy would beat the market if the strategy was limited to 1x funds; trading costs would be too large.

The fairer comparison would be to something like a 60/40 portfolio.

The key thing is that the strategy is not limited to 1x funds; it takes advantage of leverage to boost returns during good times. The leverage is what allows it to outperform the market. On average, the strategy averages ~1.65x the market, but in backtests the effective equity allocation drops to 0.6x during high volatility periods.

I don't think that I'm really proposing anything that fund managers haven't seen and won't use. It's just that the constraints for DIY are different than for fund managers, who generally have to track and even outperform some index on short-term horizons (trailing 1-, 3-, and 5-year records).

And it seems to me that many DIY investors are at the stage where they are trying to build the portfolio as rapidly as possible rather than building steadily. It's a different mindset.
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