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 »

Start of December to start of June was down <10%, the last few weeks hammered it and it's now down ~25%. The overall slide began the middle of November, to date down ~30% from mid-November.

This period is where having the possibility of rotating into commodities and inverse funds made a big difference. That rotation wasn't really necessary for the last 40 years, with bonds doing their diversification and flight-to-safety jobs.
bgf
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Re: Refinements to Hedgefundie's excellent approach

Post by bgf »

Hydromod wrote: Sun Jun 19, 2022 7:36 am Start of December to start of June was down <10%, the last few weeks hammered it and it's now down ~25%. The overall slide began the middle of November, to date down ~30% from mid-November.

This period is where having the possibility of rotating into commodities and inverse funds made a big difference. That rotation wasn't really necessary for the last 40 years, with bonds doing their diversification and flight-to-safety jobs.
The only thing that has “saved” me is doing basically 1/2 HFEA with 25-25–50 of TMF UPRO IXUS. As stocks and bonds have dropped, every quarter I’ve shifted the 50 IXUS down by 5%. I’ll do the same again at the end of the month bringing it to 32.5-32.5-35.

If and when stocks and bonds rise again, I’ll shift back.
“TE OCCIDERE POSSUNT SED TE EDERE NON POSSUNT NEFAS EST"
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randyharris
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Re: Refinements to Hedgefundie's excellent approach

Post by randyharris »

Hydromod wrote: Sun Jun 19, 2022 7:36 am Start of December to start of June was down <10%, the last few weeks hammered it and it's now down ~25%. The overall slide began the middle of November, to date down ~30% from mid-November.

This period is where having the possibility of rotating into commodities and inverse funds made a big difference. That rotation wasn't really necessary for the last 40 years, with bonds doing their diversification and flight-to-safety jobs.
That is about half the drawdown of three highly leveraged strategies that I follow.
Kbg
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Re: Refinements to Hedgefundie's excellent approach

Post by Kbg »

If you don’t mind what are the other strategies?
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

Kbg wrote: Sun Jun 19, 2022 1:43 pm If you don’t mind what are the other strategies?
He has a link near the end of the hedgefundie thread with strategy and stats.
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randyharris
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Re: Refinements to Hedgefundie's excellent approach

Post by randyharris »

Kbg wrote: Sun Jun 19, 2022 1:43 pm If you don’t mind what are the other strategies?
https://dualmomentumsystems.com/resourc ... 220618.pdf
laurenthu
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Re: Refinements to Hedgefundie's excellent approach

Post by laurenthu »

Thanks Randy for taking the time to do this deck. This is really useful (and shows the superiority to the Max Pain, even if you chose to retire it from the main website). My guess is that Max Pain with some duration limiter switch like you implemented with the other strategies would have fared even better in this context and thus beat down the 2 other high flyers? I still see some merit in that strategy to be honest...
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randyharris
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Re: Refinements to Hedgefundie's excellent approach

Post by randyharris »

laurenthu wrote: Tue Jun 21, 2022 10:21 am Thanks Randy for taking the time to do this deck. This is really useful (and shows the superiority to the Max Pain, even if you chose to retire it from the main website). My guess is that Max Pain with some duration limiter switch like you implemented with the other strategies would have fared even better in this context and thus beat down the 2 other high flyers? I still see some merit in that strategy to be honest...
Here is what MAX PAIN looks like with Treasury Duration Limiter enabled, not great.

https://dualmomentumsystems.com/resourc ... imiter.pdf
yolointopants
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Re: Refinements to Hedgefundie's excellent approach

Post by yolointopants »

This entire thread has been absolutely fascinating. I appreciate all the links and Google Colab examples to play with. The irony of this being on the Bogleheads forum is not lost on me, so big thanks to all the theory and information here. Very eye opening.
digdug_08
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Re: Refinements to Hedgefundie's excellent approach

Post by digdug_08 »

This has been extremely fun/enlightening to read. I am interested in building a portfolio around GPMv, however I am unable to find a resource which can calculate the allocations & rebalancing schedule for the GPMv model. I've seen the GoogleDocs program and the excel spreadsheet, but see that these are just for testing.
I would gladly pay for access to a site or product that would show the allocations to the ETFs for this model. Is there somewhere that offers this?

EDIT: I found the monthly subscription page that shows the month-end performance and rebalance targets for each :happy .

I'm in my early 30s with a high tolerance to risk. I am considering a heavily-weighted portfolio towards Triad++, offset with GPMv. Somewhere around 70/30. This ratio is arbitrary, but I don't know a better way to arrive at the targeted split between the two :confused
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hiddenpower
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Re: Refinements to Hedgefundie's excellent approach

Post by hiddenpower »

no simpler wrote: Sat Jul 13, 2019 11:06 pm Put another way, if you actually use any kind of solver, and increase the number of parameters to solve for, you could easily get much, much better results than anything in this thread. But it would just be overfitting. Try tuning from 1955-1982. Ignore all data after. When you're all done, take the best strategy and run on 1982 on up. This would be a more accurate simulation of what performance would be like. There are of course more sophisticated ways of doing time series cross validation - you could use rolling windows. And it still wouldn't be a large enough series as others have mentioned. But it will at least give you intuition for what's going on.
How come this out of sample testing and overfitting doesn't apply to HFEA which seems to only be justified with a backtest?
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

hiddenpower wrote: Tue Jul 12, 2022 9:43 pm
no simpler wrote: Sat Jul 13, 2019 11:06 pm Put another way, if you actually use any kind of solver, and increase the number of parameters to solve for, you could easily get much, much better results than anything in this thread. But it would just be overfitting. Try tuning from 1955-1982. Ignore all data after. When you're all done, take the best strategy and run on 1982 on up. This would be a more accurate simulation of what performance would be like. There are of course more sophisticated ways of doing time series cross validation - you could use rolling windows. And it still wouldn't be a large enough series as others have mentioned. But it will at least give you intuition for what's going on.
How come this out of sample testing and overfitting doesn't apply to HFEA which seems to only be justified with a backtest?
You seem to be under the impression that the only support for using HFEA is from backtesting. I would say that backtesting is used to illustrate and support the ideas.

The point of HFEA is to lever up a somewhat optimal portfolio (in this case, composed of funds based on two indexes), which is supported by modern portfolio theory. That's qualitatively different from relying solely on backtesting to justify using a portfolio.

I would love to have corresponding daily data from 1955 to 1982 to test the approaches, but I agree with the point that using a fixed period to develop parameters and walking it forward for long periods of time will tend to give poor results.

You'll note that the backtesting approach that I prefer uses rolling windows and systematically differing starting points to reduce the impact of timing luck. Typically one can get a feel for approaches that offer a statistical edge that way. This approach makes it clear that timing luck around a few events can have a very large influence on results during backtesting. This approach can also give a little insight into rebalancing timing effects.

Another approach uses a variety of different assets to test the algorithms. Still not perfect, but it definitely builds intuition.

The statistics suggest that results can be improved by adjusting allocations dynamically based on recent volatility, taking advantage of the well-established phenomenon of volatility clustering. I think that finding is pretty well justified and has a good theoretical basis.

To a certain extent, the statistics suggest that momentum has been a thing but momentum's predictive capability is likely declining. That also seems reasonable based on the rise of algorithms.
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pezblanco
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Re: Refinements to Hedgefundie's excellent approach

Post by pezblanco »

A long time ago, in a land not so far away, I remember when the now revered Hedgefundie proposed his scheme. I was very interested in it and did some simple computer experiments to try to get an idea of what leveraging might bring about.

So the experiments just took past stock market prices (monthly data as I recall) and just took independent samples from that data to give Monte Carlo inputs for what future data would look like (simple and crude but whatever ... we're trying to get a rough general idea, right?). So, just using that, you find that leveraging a stock portfolio has an optimum of around 1.4 to 1.6 amount of leverage. When I say optimum, I mean the exponential growth rate of the portfolio is optimized at that point. So too much leverage actually gives a lower growth rate. This is well known and certainly not anything I discovered. I then tried modeling the HF scheme using bond prices and having a leveraged stock and bond portfolio. To my surprise, the HF scheme of 3 times leverage was quite close to the optimum exponential growth rate. I.e. at first glance it was not such a crazy scheme after all.

But, after some simulation, it turns out that the optimal growth rate versus the amount of leverage is a very broad flat curve. Three times leverage might be close to best but you only gain a couple of percent of portfolio growth versus not leveraging. And when you look at the spread of returns, there was a huge variance in what you should expect with leverage compared to not leveraging. The take away for me was that, there was going to be big shocks from time to time and those shocks would substantially take away from the portfolio growth from time to time. In other words, big draw downs are not a lamentable unforseen event, but rather a feature of the whole scheme. I concluded that for myself, even though there was a not insignificant amount to be gained (a couple of percent), it was not going to be worth the roller coaster ride ....

I realize that my experiments were crude but by doing what I did, I could manufacture a lot of data. Backtasting of course is more realistic perhaps, but that results in very little data and so you should have little confidence in it either. I think people look at the backtesting over periods of time and conclude huge returns are going to be possible. I strongly think this is an artifact of the backtesting itself. I.e. in my opinion, if this scheme doesn't deliver these huge returns with my simple model, then it's not going to deliver them in real life either.
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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

I don't disagree with your insights.

I assume that your backtesting was based on a straight fixed allocation, however.

I think that you would tilt the results towards a higher optimal leverage by biasing the allocations based on recent volatility. In effect, this tends to reduce the effective asset volatilities significantly without much affecting the long-term return. This will not preclude bad behavior, but it would have tended to give more consistent results.

In your approach, it might be interesting to investigate the returns with allocations set biased towards the realized volatilities. Maybe use the previous two months from each sample to estimate volatility, then use inverse volatility to estimate an asset allocation for the sample. I suspect that it will be tough to get volatility for data prior to the 1980s though.

I'll see if I can get some separate estimates for how adaptive allocation would have reduced effective volatility.
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Re: Refinements to Hedgefundie's excellent approach

Post by AlphaLess »

pezblanco wrote: Wed Jul 13, 2022 7:44 am A long time ago, in a land not so far away, I remember when the now revered Hedgefundie proposed his scheme. I was very interested in it and did some simple computer experiments to try to get an idea of what leveraging might bring about.

So the experiments just took past stock market prices (monthly data as I recall) and just took independent samples from that data to give Monte Carlo inputs for what future data would look like (simple and crude but whatever ... we're trying to get a rough general idea, right?). So, just using that, you find that leveraging a stock portfolio has an optimum of around 1.4 to 1.6 amount of leverage. When I say optimum, I mean the exponential growth rate of the portfolio is optimized at that point. So too much leverage actually gives a lower growth rate. This is well known and certainly not anything I discovered. I then tried modeling the HF scheme using bond prices and having a leveraged stock and bond portfolio. To my surprise, the HF scheme of 3 times leverage was quite close to the optimum exponential growth rate. I.e. at first glance it was not such a crazy scheme after all.

But, after some simulation, it turns out that the optimal growth rate versus the amount of leverage is a very broad flat curve. Three times leverage might be close to best but you only gain a couple of percent of portfolio growth versus not leveraging. And when you look at the spread of returns, there was a huge variance in what you should expect with leverage compared to not leveraging. The take away for me was that, there was going to be big shocks from time to time and those shocks would substantially take away from the portfolio growth from time to time. In other words, big draw downs are not a lamentable unforseen event, but rather a feature of the whole scheme. I concluded that for myself, even though there was a not insignificant amount to be gained (a couple of percent), it was not going to be worth the roller coaster ride ....

I realize that my experiments were crude but by doing what I did, I could manufacture a lot of data. Backtasting of course is more realistic perhaps, but that results in very little data and so you should have little confidence in it either. I think people look at the backtesting over periods of time and conclude huge returns are going to be possible. I strongly think this is an artifact of the backtesting itself. I.e. in my opinion, if this scheme doesn't deliver these huge returns with my simple model, then it's not going to deliver them in real life either.
1. % return vs leverage graph / curve being flat -> agreed.

So, what is leverage?
- borrow cash,
- invest in {stock + curve_treasuries}. When I say curve, it could be any point, e.g., 5-7Year, 7-10, 10-20, etc.

Why does it work? Simply because cash typically returns lower than most of the treasury curve points (except for inversions, which are rare, but even then cash may yield lower). And stocks produce higher returns than treasuries.

There is of course, the cost of leverage, and the costs of running the strategy, etc. 3x leverage funds are not cheap, as they may have some drag (due to trading, etc), and have built-in management fees.

2. correct way to reason about this is some penalized approached, whereby expected return (mean expected return) is compared vs the variance of the strategy.

ordinarily this is called the Sharpe of the strategy:

Sharpe = mean(daily_return) / stdev(daily_return) * sqrt(250) (to annualize, and sqrt(250) is 15.8).

You can penalize other ways as well. for example, you can put (stdev(daily_return)) ^ 1.2, to more severely penalize variance.

Once you make that curve/scatter (sharpe vs leverage) , you will see that IT IS NO LONGER FLAT.

Why does Sharpe matter?

Two answer:
- because,
- because.

Sharpe matters because that is a better notion of investor utility than return.
Simply put, if leverage were free, and Sharpe did not matter, you could leverage to infinity.
But then you would also lose 100% of your capital frequently.

Another reason Sharpe matters is that it allows you to compare two DIFFERENT investments apples-to-apples.

Say, I have two strategies portfolios:

A has annualized mean return of 10%, and stdev of 15%, i.e., Sharpe of 10/15 = 0.666
B has mean 15%, and stdev of 28%, i.e., Sharpe of 15/28 = 0.54

Most (uninformed / inexperienced) people would prefer B.

But it should be possible to lever-up A to match B's stdDev, and increase the return to higher than 15%.

In other words, {A + something} could become (for example):
- mean of 17.5%,
- stdev of 28%.

Since 17.5% >> 15%, and both have stdev of 27%, any rational investor would prefer {A + something} to B.

Now, the practical problem is finding that "something".

Heck, this entire strategy is based on that.

Instead of doing 60%S + 40%B, you do Lever-up(40%S + 60%B, N times), where N is 1.2, 1.3, 1.5, etc.

I personally thing levering up 3x is crazy.

There is no magic in this HedgeFundie strategy.

It is simple math.

But there is also some other simple math, which is understanding when the strategy works, and when it does not!

Lever{P, N times}, where N is for example 2, means:
- borrow cash,
- double your P.

So, levered strategy only makes if your portfolio is OUT-performing cash.

One: that does happen most of the time, but NOT always.
Two: if your portfolio P has a drawdown, then 2P has double the drawdown.

Three: the large part of the Lever_Up {Stock + Treasury} portfolio construction works because Cor(Stock,Treasury) has been negative (circa -20%) for a long, long time. Until, that is, that correlation broke down. In the last 6 months, that correlation is positive.

So, you are getting double-whammied.

What a coincidence that when this strategy became popularized, it hit a once-in-25, or once-in-50 year issue?

Well, it always is like this. When the MOST uninformed investors (such as bogleheads) get into a trade, the trade breaks down.
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pezblanco
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Re: Refinements to Hedgefundie's excellent approach

Post by pezblanco »

Hydromod wrote: Wed Jul 13, 2022 10:16 am
I assume that your backtesting was based on a straight fixed allocation, however.

I'll see if I can get some separate estimates for how adaptive allocation would have reduced effective volatility.
Yes, of course, I wasn't really doing a Monte Carlo from the data ... I was just assuming that future prices would be drawn independently from an empirical distribution of past prices. That allowed me to compute the exponential rate of growth exactly.

I suppose one could try to modify the empirical distributions to reflect what current volatility is and then you could again do as I did but that would be making another big set of assumptions.
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pezblanco
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Re: Refinements to Hedgefundie's excellent approach

Post by pezblanco »

AlphaLess wrote: Wed Jul 13, 2022 5:25 pm
pezblanco wrote: Wed Jul 13, 2022 7:44 am A long time ago, in a land not so far away, I remember when the now revered Hedgefundie proposed his scheme. I was very interested in it and did some simple computer experiments to try to get an idea of what leveraging might bring about.

So the experiments just took past stock market prices (monthly data as I recall) and just took independent samples from that data to give Monte Carlo inputs for what future data would look like (simple and crude but whatever ... we're trying to get a rough general idea, right?). So, just using that, you find that leveraging a stock portfolio has an optimum of around 1.4 to 1.6 amount of leverage. When I say optimum, I mean the exponential growth rate of the portfolio is optimized at that point. So too much leverage actually gives a lower growth rate. This is well known and certainly not anything I discovered. I then tried modeling the HF scheme using bond prices and having a leveraged stock and bond portfolio. To my surprise, the HF scheme of 3 times leverage was quite close to the optimum exponential growth rate. I.e. at first glance it was not such a crazy scheme after all.

But, after some simulation, it turns out that the optimal growth rate versus the amount of leverage is a very broad flat curve. Three times leverage might be close to best but you only gain a couple of percent of portfolio growth versus not leveraging. And when you look at the spread of returns, there was a huge variance in what you should expect with leverage compared to not leveraging. The take away for me was that, there was going to be big shocks from time to time and those shocks would substantially take away from the portfolio growth from time to time. In other words, big draw downs are not a lamentable unforseen event, but rather a feature of the whole scheme. I concluded that for myself, even though there was a not insignificant amount to be gained (a couple of percent), it was not going to be worth the roller coaster ride ....

I realize that my experiments were crude but by doing what I did, I could manufacture a lot of data. Backtasting of course is more realistic perhaps, but that results in very little data and so you should have little confidence in it either. I think people look at the backtesting over periods of time and conclude huge returns are going to be possible. I strongly think this is an artifact of the backtesting itself. I.e. in my opinion, if this scheme doesn't deliver these huge returns with my simple model, then it's not going to deliver them in real life either.
1. % return vs leverage graph / curve being flat -> agreed.

So, what is leverage?
- borrow cash,
- invest in {stock + curve_treasuries}. When I say curve, it could be any point, e.g., 5-7Year, 7-10, 10-20, etc.

Why does it work? Simply because cash typically returns lower than most of the treasury curve points (except for inversions, which are rare, but even then cash may yield lower). And stocks produce higher returns than treasuries.

There is of course, the cost of leverage, and the costs of running the strategy, etc. 3x leverage funds are not cheap, as they may have some drag (due to trading, etc), and have built-in management fees.

2. correct way to reason about this is some penalized approached, whereby expected return (mean expected return) is compared vs the variance of the strategy.

ordinarily this is called the Sharpe of the strategy:

Sharpe = mean(daily_return) / stdev(daily_return) * sqrt(250) (to annualize, and sqrt(250) is 15.8).

You can penalize other ways as well. for example, you can put (stdev(daily_return)) ^ 1.2, to more severely penalize variance.

Once you make that curve/scatter (sharpe vs leverage) , you will see that IT IS NO LONGER FLAT.

Why does Sharpe matter?

Two answer:
- because,
- because.

Sharpe matters because that is a better notion of investor utility than return.
Simply put, if leverage were free, and Sharpe did not matter, you could leverage to infinity.
But then you would also lose 100% of your capital frequently.

Another reason Sharpe matters is that it allows you to compare two DIFFERENT investments apples-to-apples.

Say, I have two strategies portfolios:

A has annualized mean return of 10%, and stdev of 15%, i.e., Sharpe of 10/15 = 0.666
B has mean 15%, and stdev of 28%, i.e., Sharpe of 15/28 = 0.54

Most (uninformed / inexperienced) people would prefer B.

But it should be possible to lever-up A to match B's stdDev, and increase the return to higher than 15%.

In other words, {A + something} could become (for example):
- mean of 17.5%,
- stdev of 28%.

Since 17.5% >> 15%, and both have stdev of 27%, any rational investor would prefer {A + something} to B.

Now, the practical problem is finding that "something".

Heck, this entire strategy is based on that.

Instead of doing 60%S + 40%B, you do Lever-up(40%S + 60%B, N times), where N is 1.2, 1.3, 1.5, etc.

I personally thing levering up 3x is crazy.

There is no magic in this HedgeFundie strategy.

It is simple math.

But there is also some other simple math, which is understanding when the strategy works, and when it does not!

Lever{P, N times}, where N is for example 2, means:
- borrow cash,
- double your P.

So, levered strategy only makes if your portfolio is OUT-performing cash.

One: that does happen most of the time, but NOT always.
Two: if your portfolio P has a drawdown, then 2P has double the drawdown.

Three: the large part of the Lever_Up {Stock + Treasury} portfolio construction works because Cor(Stock,Treasury) has been negative (circa -20%) for a long, long time. Until, that is, that correlation broke down. In the last 6 months, that correlation is positive.

So, you are getting double-whammied.

What a coincidence that when this strategy became popularized, it hit a once-in-25, or once-in-50 year issue?

Well, it always is like this. When the MOST uninformed investors (such as bogleheads) get into a trade, the trade breaks down.
Yes, Sharpe ratios are a variance based idea to try to get a handle on spread. I did try in my calculations to account for borrowing costs (otherwise leverage is free).

I think we're in substantial agreement ...

I recall Hedgefundie liked my spread calculations and graphs and included them on his original front page. He thought that they were testimonials to his methodology but I thought they were the reverse .... big warnings about the methodology.
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Re: Refinements to Hedgefundie's excellent approach

Post by AlphaLess »

pezblanco wrote: Wed Jul 13, 2022 6:03 pm
AlphaLess wrote: Wed Jul 13, 2022 5:25 pm What a coincidence that when this strategy became popularized, it hit a once-in-25, or once-in-50 year issue?

Well, it always is like this. When the MOST uninformed investors (such as bogleheads) get into a trade, the trade breaks down.
Yes, Sharpe ratios are a variance based idea to try to get a handle on spread. I did try in my calculations to account for borrowing costs (otherwise leverage is free).

I think we're in substantial agreement ...

I recall Hedgefundie liked my spread calculations and graphs and included them on his original front page. He thought that they were testimonials to his methodology but I thought they were the reverse .... big warnings about the methodology.
Agreed!

One key things that I want to emphasize is this.

A lot of effort went into "Backtesting" this data, which I view as a "hamster-in-a-wheel" type of effort.
Yea, sure, it is fun to:
- get data,
- clean it up,
- write a python script,
- plot pretty charts,
- speak cleverly.

But at a high level, if you don't understand WHY the trade works, all of that is useless.

A non-levered portfolio P1 of {60% S + 40% B} is:
- long stock,
- long bond (also known as long rates),
- and, in-so-far as the investor believes that the P1 has lower standard dev than equivalent dollar portfolio of either S or P, then implicitly, the investor is SHORT the correlation (which historically is negative).

So, those are the factors that the investor is long or short.

The levered portfolio P2 of {80% S + 120% B - 100% C} has other features, and thus, is harvesting, or is getting paid on all of those:
a. long(er) stock (1.25x),
b. even longer rates (3x),
c. long curve steep-ness (i.e., the trade is much entry deal when long-cash is at 5% vs at 1%, as opposed to at 3%-3%, or 2%-2%),
d. extremely short corr(S,B). Firstly, you have calibrated your weights to take optimal advantage of the correlation, which you have computed HISTORICALLY, and levered to that. Heck, even picking a random correlation, or assuming the correlation is zero, vs negative, would have provided better weights,

What the hamster-in-the-wheel simulation does not show is whether you are going to be hit with the drawdown from multiple sources at_the_same_time.

Let's recap the last 6 months:
- stocks went down (so you are down on factor a), 25%,
- interest rates went up (so you are down on factor b), 25% depending on which treasuries you are using,
- curve flattened (so you are down on factor c), to the tune of 2%, and that is a lot of DV01 risk,
- and correlation went positive, from around -20%, to 20%; so you are down on factor d and levered.

WHAT
A
SET
OF
COINCIDENCES?
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pezblanco
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Re: Refinements to Hedgefundie's excellent approach

Post by pezblanco »

AlphaLess wrote: Wed Jul 13, 2022 6:46 pm
Yea, sure, it is fun to:
- get data,
- clean it up,
- write a python script,
- plot pretty charts,
- speak cleverly.

But at a high level, if you don't understand WHY the trade works, all of that is useless.

WHAT
A
SET
OF
COINCIDENCES?
:D +100
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

pezblanco wrote: Wed Jul 13, 2022 5:59 pm Yes, of course, I wasn't really doing a Monte Carlo from the data ... I was just assuming that future prices would be drawn independently from an empirical distribution of past prices. That allowed me to compute the exponential rate of growth exactly.

I suppose one could try to modify the empirical distributions to reflect what current volatility is and then you could again do as I did but that would be making another big set of assumptions.
If I understand this correctly, the growth rate is r + f(mu - r) - (f sigma)^2 / 2, where r is the risk-free rate, mu is expected return, sigma is volatility, and f is the fraction of wealth to bet (i.e., leverage factor). The Kelly criterion gives the optimal growth rate of Sharpe/sigma, where Sharpe = (mu - r)/sigma. Typically it's advised that one bets half a Kelly.

PV gives US stock market Sharpe = 0.42 and sigma = 0.16 since 1972, for f = 2.6 or half Kelly of 1.3. Since 1982, large cap has f = 3.7 and half Kelly of 1.8.

So would you say this is comparable to you finding that levering the S&P by 1.4 to 1.6 had the maximum exponential growth, even though leverage up to 3 works okay? I think I've seen numbers for the S&P that are fairly consistent with these values.

If that's the case, then HFEA allocations should be around your optimal value for equities (3 * 0.55 = 1.65), accounting for rebalancing. Presumably levering treasuries should have a similar value.

I'll also say that my adaptive allocation portfolios with the risk-budget minimum variance approach tend to have ex post portfolio Sharpe/sigma > 2, at least since the late 80s/early 90s. That would suggest the portfolio is at about a half Kelly. Those portfolios have enough volatility that I don't want to go more aggressive.

I've calculated values >5 for some of the less aggressive versions, which would suggest that the portfolio itself could be leveraged further for improved returns. See the discussion here, for example.

With that said, the near future is probably not the time to be pushing any leverage limits.
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Re: Refinements to Hedgefundie's excellent approach

Post by pezblanco »

Hi Hydromod,

I'm not really doing this stuff anymore but back when I thought Bogleheads was a worthwhile place to discuss intellectual ideas (I no longer think so ... I find it to be so over-moderated that most interesting discussion is stifled, so I rarely bother anymore.)

These are the two contributions that I made that I think are relevant to the HF idea:

Maximizing Portfolio Growth Rate - Kelly Criterion - Empirical Market Data
viewtopic.php?f=10&t=237430


Leveraging Stock/Bond Portfolios and the Kelly Criterion
viewtopic.php?p=4385767&hilit=kelly#p4385767

Most of the graphs are now dead ... sorry about that.

The growth rate formulas you quote are from a different set of assumptions (basically an Ito process (a diffusion model of stock returns) ... I wasn't doing anything like that. I explain my approach in the first URL. I thought it was interesting that such a model as that and my own gave such similar conclusions. It sort of indicated to me that this is the way this thing works.
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Re: Refinements to Hedgefundie's excellent approach

Post by AlphaLess »

Hydromod wrote: Wed Jul 13, 2022 8:34 pm
pezblanco wrote: Wed Jul 13, 2022 5:59 pm Yes, of course, I wasn't really doing a Monte Carlo from the data ... I was just assuming that future prices would be drawn independently from an empirical distribution of past prices. That allowed me to compute the exponential rate of growth exactly.

I suppose one could try to modify the empirical distributions to reflect what current volatility is and then you could again do as I did but that would be making another big set of assumptions.
If I understand this correctly, the growth rate is r + f(mu - r) - (f sigma)^2 / 2, where r is the risk-free rate, mu is expected return, sigma is volatility, and f is the fraction of wealth to bet (i.e., leverage factor). The Kelly criterion gives the optimal growth rate of Sharpe/sigma, where Sharpe = (mu - r)/sigma. Typically it's advised that one bets half a Kelly.

PV gives US stock market Sharpe = 0.42 and sigma = 0.16 since 1972, for f = 2.6 or half Kelly of 1.3. Since 1982, large cap has f = 3.7 and half Kelly of 1.8.

So would you say this is comparable to you finding that levering the S&P by 1.4 to 1.6 had the maximum exponential growth, even though leverage up to 3 works okay? I think I've seen numbers for the S&P that are fairly consistent with these values.

If that's the case, then HFEA allocations should be around your optimal value for equities (3 * 0.55 = 1.65), accounting for rebalancing. Presumably levering treasuries should have a similar value.

I'll also say that my adaptive allocation portfolios with the risk-budget minimum variance approach tend to have ex post portfolio Sharpe/sigma > 2, at least since the late 80s/early 90s. That would suggest the portfolio is at about a half Kelly. Those portfolios have enough volatility that I don't want to go more aggressive.

I've calculated values >5 for some of the less aggressive versions, which would suggest that the portfolio itself could be leveraged further for improved returns. See the discussion here, for example.

With that said, the near future is probably not the time to be pushing any leverage limits.
Solid post. Are you able to re-do you math, by also incorporating the stock-bond (non-demeaned) correlation.

Two possible correlation inputs:
a. use the past 6-month correlation for the next 6 months (reasonable, and possible),
b. if I were to tell you the future 6 months correlation, use that (impossible, but much more accurate ex-post fact).

By un-demeaned, i mean cov(stock,bond) / sqrt (var(s) * var(b)).

The problem with de-meaned correlation is that both assets could be going own (or up), and yet, correlation could show negative.

I have a good metric for whether the correlation is good or not.
Simply take a dot product, divide by lagged std dev, and cumsum it.

For stock/bond, that metric is up very consistently the las 20 years (and then breaks down in the last 6-7 months).
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

AlphaLess wrote: Thu Jul 14, 2022 1:46 pm Solid post. Are you able to re-do you math, by also incorporating the stock-bond (non-demeaned) correlation.

Two possible correlation inputs:
a. use the past 6-month correlation for the next 6 months (reasonable, and possible),
b. if I were to tell you the future 6 months correlation, use that (impossible, but much more accurate ex-post fact).

By un-demeaned, i mean cov(stock,bond) / sqrt (var(s) * var(b)).

The problem with de-meaned correlation is that both assets could be going own (or up), and yet, correlation could show negative.

I have a good metric for whether the correlation is good or not.
Simply take a dot product, divide by lagged std dev, and cumsum it.

For stock/bond, that metric is up very consistently the las 20 years (and then breaks down in the last 6-7 months).
The risk-budget minimum variance approach uses the variance/covariance matrix, not the correlations, to calculate portfolio allocations. I use a 3-month lookback for the matrix, although the results suggest that it's not particularly sensitive to lookback within a range of several months.

I think that your suggestion would be implemented in my scheme by using a moving matrix centered on the prediction period instead of estimated from the recent history.

It's always a bit nerve wracking making sure that backtests don't use information that isn't already available, because that can misleadingly improve results by large margins. I've gotten excited several times when using future information that turns out to not be predictable, so I'm a bit reluctant to intentionally modify my code to do so.

If I understand correctly, that's what you are suggesting. If not, please clarify.
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

pezblanco wrote: Wed Jul 13, 2022 9:27 pm Hi Hydromod,

I'm not really doing this stuff anymore but back when I thought Bogleheads was a worthwhile place to discuss intellectual ideas (I no longer think so ... I find it to be so over-moderated that most interesting discussion is stifled, so I rarely bother anymore.)

These are the two contributions that I made that I think are relevant to the HF idea:

Maximizing Portfolio Growth Rate - Kelly Criterion - Empirical Market Data
viewtopic.php?f=10&t=237430


Leveraging Stock/Bond Portfolios and the Kelly Criterion
viewtopic.php?p=4385767&hilit=kelly#p4385767

Most of the graphs are now dead ... sorry about that.

The growth rate formulas you quote are from a different set of assumptions (basically an Ito process (a diffusion model of stock returns) ... I wasn't doing anything like that. I explain my approach in the first URL. I thought it was interesting that such a model as that and my own gave such similar conclusions. It sort of indicated to me that this is the way this thing works.
I remember the posts from before. Actually, it makes some sense that using actual returns would give more conservative leverage than is implied with the growth rate formulas I cited. I think that they basically assume a normal distribution, while the observed return distributions are much more fat tailed. That may explain why biasing towards the half Kelly is reasonable for the cited formulas.
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Re: Refinements to Hedgefundie's excellent approach

Post by AlphaLess »

Hydromod wrote: Fri Jul 15, 2022 7:20 am
AlphaLess wrote: Thu Jul 14, 2022 1:46 pm Solid post. Are you able to re-do you math, by also incorporating the stock-bond (non-demeaned) correlation.

Two possible correlation inputs:
a. use the past 6-month correlation for the next 6 months (reasonable, and possible),
b. if I were to tell you the future 6 months correlation, use that (impossible, but much more accurate ex-post fact).

By un-demeaned, i mean cov(stock,bond) / sqrt (var(s) * var(b)).

The problem with de-meaned correlation is that both assets could be going own (or up), and yet, correlation could show negative.

I have a good metric for whether the correlation is good or not.
Simply take a dot product, divide by lagged std dev, and cumsum it.

For stock/bond, that metric is up very consistently the las 20 years (and then breaks down in the last 6-7 months).
The risk-budget minimum variance approach uses the variance/covariance matrix, not the correlations, to calculate portfolio allocations. I use a 3-month lookback for the matrix, although the results suggest that it's not particularly sensitive to lookback within a range of several months.

...
If I understand correctly, that's what you are suggesting. If not, please clarify.
One scheme I suggested is exactly what you are doing: that is, for every X month period, take the covariance from the previous X months.

Another thought I had making is this:
- what if stock / bond covariance is set to ZERO?
- how would that change the leverage.

A: it ought to reduce the leverage.
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

I was a little surprised when I started comparing asset statistics with the time-weighted performance. I'm glad I was pushed into the comparison.

For the tests, I use an asset set of TQQQ, SOXL, UMMD, URTY, FAS, WAT, RETL, NAIL, CURE, UTSL, EDC, EURL, DRN, BIG, ERX, UGL, DBC, TMF, TYD, and FIGTX. I also tried adding SPXU and TMV (3x inverse S&P and LTT). So 20 to 22 assets, ranging from very volatile to near-cash. The lookback period is set by ERX, with inception date of 11/6/2008. I'm particularly interested in the period from 2014 to present, because that has been very challenging for momentum approaches.

I set up a rule set where by default the asset is dropped if the momentum isn't in the top 75% of all assets. To reduce drag, I further required UGL and TYD to be in the top 40%, EDC and DBC to be in the top 25%, and SPXU, TMV, and FIGTX to be in the top 15%. These values are a bit arbitrary.

I also artificially skewed TYD for the minimization algorithm by making the effective volatility 2.5 times larger (basically making it act like the duration was 2.5 times longer). In effect, this is maintaining a similar allocation for TMF and TYD, but TYD sacrifices some of the flight to safety.

For the test, I only accept assets that have positive momentum when the allocations are calculated. Asset momentum is based on a short and a long lookback (1 and 10 months, respectively). The calculated momentum is a volatility-weighted average, so that the short lookback is favored in volatile periods and the long lookback is favored in calm periods.

I also set up a scheme that scales the asset risk budget according to the difference between momentum and a threshold value, so high-momentum assets are assigned a larger risk budget.

The net effect of all of these little tweaks is that the asset allocation is constantly shifting, but usually not dramatically at any one time. To further reduce frequent dramatic shifts that might have tax implications, the test calculates the target allocation every 20 trading days, but I allow more frequent rebalancing (e.g., every day, once a week).

This is the framework that I'm using going forward with my own LETF portfolio for now. There may still be adjustments for the taxable account.

With all that as a preamble, the backtests have suggested CAGRs above risk-free between the low 30s and mid 40s over this period, steadily declining from the post-recovery period peak (2009 and 2010), and drawdowns generally <40%.

I was expecting that the combination of approaches would have produced outperformance due to reduced allocation-weighted volatilities. Roughly 2/3 of the assets show a reduction. Usually it's just a 5 or 10% reduction. Allocation-weighted volatility is calculated as std(w * v) / mean (w), where w is the vector of allocations and v is the vector of daily returns. The calculation only uses days with w > 0.

What's more interesting is that the effective CAGR is usually larger than the asset CAGR during the period. To calculate the effective CAGR, I calculate the allocation-weighted cumulative return [prod(1 + w*v), where w is the allocation and v is the daily return], then solve for the effective daily return that gives the same allocation-weighted cumulative return.

The interesting thing is that the effective CAGR tends to be substantially larger than the asset CAGR (e.g., TQQQ return is 66% vs. 52%, SOXL return is 97% vs. 46%, UGL is 18% vs. 3%). Even EDC and ERX had positive effective returns despite negative asset returns. These numbers are for daily rebalancing and allocation resets every 20 days. The numbers drop if the rebalancing duration increases (reducing volatility harvesting) or if the frequency of allocation resets increases. I don't quite understand the links between allocation frequency affects and return.

I attribute that largely to the momentum part of the algorithm, which (i) drops the assets if they are doing poorly and (ii) boosts the allocation when they are trending strongly. The minimum variance part also does its part in dropping overall volatility.

I was particularly interested in the effect of adding SPXU and TMV. SPXU seemed to be quite effective (39% vs. -44%, active about 8% of the time). TMV is the one asset I tested that had worse effective CAGR than asset CAGR (-54% vs. -22%, active about 5% of the time). At least so far, any recent benefit from TMV has been far outweighed by timing issues during other periods, which dropped portfolio CAGR for the period by ~10% (e.g., 44% to 40%).

My conclusion is that enabling FIGTX as a backup during declines of both stocks and bonds seemed to be more effective overall than being aggressive with TMV. Assets do poorly before being dropped, so they require periods of performance to overcome timing lags. TMV hasn't had extended periods of performance. The opposite would have been true in the 70s, where TMV would have been very valuable.

As a note, the momentum signals very recently switched to a broad bull signal across equities and bonds, dropping the inverse LETFs and commodities/gold. We'll see if that holds up.

Just an update with some observations about where the performance seems to be coming from.
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

A little coda.

I have been doing some on/off tests to see which assets benefit from the momentum ideas.

In general, this works better with streaky assets, where the streaks are long.

Assets that haven't been suited during their available history include SLV, AGQ, and GDLC (1x & 2x silver, crypto).

It is a bit unfair to directly evaluate GDLC, because it is too new to have experienced the big run-up, but since 5/2018 the scheme tended to emphasize the downsides more than the upsides. Limiting GLDC to the top 25% of assets (instead of top 75%) did capture substantial return over this period.

Under the hypothesis that the BTC-USD (bitcoin) and ETH-USD (ethereum) exchange rates were ETFs, the approach would have captured quite a substantial return for both BTC-USD (since 2015) and ETH-USD (since 2018).

I strongly suspect that TMV and TYO would have been very suitable prior to the early 1980s, but have not been since. Maybe these assets need a long momentum duration to switch between the 3x and -3x versions, so the -3x versions would have been selected during the 1970s and largely precluded after the early 1980s.

Assets with moderate or poor overall returns can benefit from restricting the inclusion criteria when there is reason to think that there will be periods of substantial performance. I restrict the following to contribute only when they are in a higher bracket than the default top 75%: DBC (top 25%), REMX (top 40%), EDC (top 25%), EURL (top 50%), DRN (top 50%), SPXU (top 15%), TYD (top 40%), and SHY (top 15%).

These examples suggest that streaky assets be allowed in the active set most of the time, but tighter constraints might be placed for assets that (i) have relatively small average returns, (ii) are volatile without significant trends, or (iii) are highly defensive (e.g., store-of-value assets like cash).
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Re: Refinements to Hedgefundie's excellent approach

Post by adaptive_allocation »

Has anyone thought to use the US Dollar Index (DXY) as a form of hedging during rising interest rate periods? It looks like it’s one of the few asset classes doing well this year.

Here’s one example: https://www.portfoliovisualizer.com/tes ... odWeight=0. I’ve done backtests for UUP using Yahoo Finance’s DX-Y.NYB data and it’s held up quite well since the mid 1980s. Anyone else interested in this strategy?
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

UUP is not one that I have thought about. I'll have to play a bit.

But if you are doing asset allocation, I think you get more robust results using a larger asset universe including some risky assets with modest correlations, then selecting a significant subset, such as 30 to 60%.

Example
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Re: Refinements to Hedgefundie's excellent approach

Post by jarjarM »

Hydromod wrote: Thu Jul 28, 2022 8:06 pm UUP is not one that I have thought about. I'll have to play a bit.

But if you are doing asset allocation, I think you get more robust results using a larger asset universe including some risky assets with modest correlations, then selecting a significant subset, such as 30 to 60%.

Example
I think the original white paper on adaptive allocation suggest the same as well. They started with 10 asset class and holds 5 based on prior 126 days (6months) return. allocate smartly
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Re: Refinements to Hedgefundie's excellent approach

Post by adaptive_allocation »

To what extent are we just picking asset classes at random and hoping for the best? Sure, adding more assets can potentially give you more data to work with, but there’s the problem of overfitting. There’s bound to be assets that perform incredibly well in the backtesting, and stop working tomorrow.

I might be more interested in a general theory regarding why assets move the way they do, where the risk/potential drawdowns come from, and how AA can help us. Something like an all-weather portfolio, for example. The other issue is getting the data for backtesting - the longer we can backtest it the better we can understand how it performs in good and bad periods.
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Re: Refinements to Hedgefundie's excellent approach

Post by typical.investor »

adaptive_allocation wrote: Thu Jul 28, 2022 3:17 pm Has anyone thought to use the US Dollar Index (DXY) as a form of hedging during rising interest rate periods? It looks like it’s one of the few asset classes doing well this year.

Here’s one example: https://www.portfoliovisualizer.com/tes ... odWeight=0. I’ve done backtests for UUP using Yahoo Finance’s DX-Y.NYB data and it’s held up quite well since the mid 1980s. Anyone else interested in this strategy?
This year, yeah the USD is up with inflation.
In '80-'82, inflation fell 8% and the USD was up 20%
The late '70s saw USD depreciation with high inflation. I don't understand it well enough to predict if what we are seeing currently will continue to hold. Do you?

https://www.newyorkfed.org/medialibrary ... ticle4.pdf
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Re: Refinements to Hedgefundie's excellent approach

Post by adaptive_allocation »

typical.investor wrote: Thu Jul 28, 2022 8:29 pm
Has anyone thought to use the US Dollar Index (DXY) as a form of hedging during rising interest rate periods? It looks like it’s one of the few asset classes doing well this year.

Here’s one example: https://www.portfoliovisualizer.com/tes ... odWeight=0. I’ve done backtests for UUP using Yahoo Finance’s DX-Y.NYB data and it’s held up quite well since the mid 1980s. Anyone else interested in this strategy?
This year, yeah the USD is up with inflation.
In '80-'82, inflation fell 8% and the USD was up 20%
The late '70s saw USD depreciation with high inflation. I don't understand it well enough to predict if what we are seeing currently will continue to hold. Do you?

https://www.newyorkfed.org/medialibrary ... ticle4.pdf
I am not sure I can untangle the effects of inflation with changes in the USD, yet it looks like the correlation between rising interest rates and the USD changed from negative to positive sometime in the 1980s. This article talks about it in more detail: https://www.kansascityfed.org/documents ... hip%3F.pdf.
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

jarjarM wrote: Thu Jul 28, 2022 8:20 pm
Hydromod wrote: Thu Jul 28, 2022 8:06 pm UUP is not one that I have thought about. I'll have to play a bit.

But if you are doing asset allocation, I think you get more robust results using a larger asset universe including some risky assets with modest correlations, then selecting a significant subset, such as 30 to 60%.

Example
I think the original white paper on adaptive allocation suggest the same as well. They started with 10 asset class and holds 5 based on prior 126 days (6months) return. allocate smartly
Now I remember that article. I switch it up a little by doing a risk budget version of minimum variance to emphasize equities and assets with greater momentum, but hold a higher percentage of the assets as well. And go for market sectors rather than very broad index funds.
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Re: Refinements to Hedgefundie's excellent approach

Post by adaptive_allocation »

Hydromod, I’m a little confused on what you’re doing. I am reading your posts in this thread to no avail. You have a lot of good thoughts and strategies. Which is your latest strategy? The best one so far (in terms of risk-adjusted returns)? It’d be easier if we could keep track of them somehow. Will we have a Hydromod excellent adventure? As in - what strategy so far has been shown superior to HFEA?
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Re: Refinements to Hedgefundie's excellent approach

Post by hiddenpower »

adaptive_allocation wrote: Thu Jul 28, 2022 11:59 pm Hydromod, I’m a little confused on what you’re doing. I am reading your posts in this thread to no avail. You have a lot of good thoughts and strategies. Which is your latest strategy? The best one so far (in terms of risk-adjusted returns)? It’d be easier if we could keep track of them somehow. Will we have a Hydromod excellent adventure? As in - what strategy so far has been shown superior to HFEA?
Wondering the exact same. I'm interested in potentially applying this and digging deeper but it's not super clear from the thread (backtests / conviction, and methodology). Is the codelab sufficient to follow say on a monthly basis?
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Re: Refinements to Hedgefundie's excellent approach

Post by cos »

Not to suggest that anyone is doing this, but it probably isn't the wisest idea to adopt a strategy solely based on the fact that someone else is doing it.

Invest only in that which you understand.
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

adaptive_allocation wrote: Thu Jul 28, 2022 11:59 pm Hydromod, I’m a little confused on what you’re doing. I am reading your posts in this thread to no avail. You have a lot of good thoughts and strategies. Which is your latest strategy? The best one so far (in terms of risk-adjusted returns)? It’d be easier if we could keep track of them somehow. Will we have a Hydromod excellent adventure? As in - what strategy so far has been shown superior to HFEA?
Yeah, this thread is really more about documenting my thoughts as I learned about investing. Figuring out the ingredients to a sound strategy that suits my personal preferences and tolerances, and hoping that folks can use some of the information.

At this point in my life, my goal is a strategy that has reasonably good odds of consistently delivering good returns going forward over a rolling three-year period or so (say at least 20% CAGR). I prefer LETFs, they are flexible enough to design adaptive strategies around, but they are so volatile that I am convinced that some sort of active management is needed to meet my goals. I'm also convinced that market sectors are cyclical and one of my big concerns is the behavior of treasuries prior to the 1980s, so I think that there may be some advantage in rotating assets through the portfolio.

I like a family of strategies that would have been quite successful at meeting those goals. All of the strategies rely on at least some adaptive allocation to reduce risk. The particular flavor is dependent on how often the investor is willing to trade and how actively the investor is willing to switch assets. In my case, I'm looking at three separate portfolios: (i) 403b, no LETFs available; (ii) Roth; and (iii) taxable. The Roth and taxable are much smaller, so that I can take some risk in those portfolios without much affecting my financial goals. I consider these as completely separate portfolios, because I can't exchange money between these accounts, therefore I manage them as independent portfolios.

The Roth and taxable accounts differ in the tax implications of trading, so it is useful to track different strategies to handle the different tax status. In particular, there is no tax barrier to daily trading and heavy turnover in the Roth, but there is in the taxable. Heavy trading in taxable also imposes a share tracking management cost.

These different requirements have led me to consider strategies trading between daily and annually. I've since rejected strategies trading more than quarterly, really more than every six weeks or so.

These different requirements have led me to consider strategies trading with very few assets and dozens of assets.

The few things that I use to guide strategy selection include
  • Volatility tends to cluster, which gives a statistical predictability regarding future volatility
  • Expected returns appear to be relatively independent of volatility
  • Daily fluctuations in volatile assets can be harvested by rebalancing to somewhat mitigate volatility drag
  • Some statistical predictability in future asset trends has been historically observed
  • Predictability in trend is much weaker than predictability in volatility, and appears to be getting weaker
  • Portfolio volatility tends to decrease with increasing numbers of assets (maybe by the square of N?)
The first two observations imply that simply adjusting allocations based on recent volatility can reduce portfolio volatility without much affecting long-term returns. This will get the biggest bang for the buck.

The third observation implies that daily rebalancing will give an independent boost to returns. This may or may not be useful.

The fourth observation implies that trend-following approaches may be more robust for screening out the worst from many assets, rather than selecting the few best assets. It also implies that trend-following approaches increase portfolio volatility due to hit-or-miss asset switching and timing luck.

The last observation implies that strategies with few assets should use broad index funds, while strategies allowing many assets should go for disparate sectors.

I use a risk-budget minimum variance strategy as the core of the asset allocation approach. I find this approach does a nice job of minimizing portfolio volatility while allowing different assets to have different allocations to the overall portfolio risk budget. I use the risk budget allocations to adaptively tune the portfolio allocations towards preferred assets and away from deprecated assets.

Some explicitly include trend estimates in the minimum variance solver; I prefer to bias the risk budget towards favored assets instead.

All of my recommendations are more work than the standard quarterly rebalanced 55/45 UPRO/TMF. The active allocation requires more frequent rebalancing than quarterly.

I would recommend at the simple extreme
  • UPRO/TMF or UPRO/TQQQ/TMF or UPRO/TQQQ/TMF/TYD, adaptively adjusted every six weeks (good for taxable)
  • same selection, adaptively adjusted daily or weekly (more active, better in Roth)
My default is to assign 3x the risk to the equities than to treasuries, with (i) the equity risk budget evenly spread between UPRO and TQQQ and (ii) the treasury risk budget allocated 2.5x larger to TMF than TYD to control for duration.

I'm currently running a more complex approach in Roth that uses 16 to 20 assets, mostly 3x and volatile 2x equity sector LETFs, with TMF, TYD, and DBC allowed. I discard the bottom 25 percent of assets based on the average of 1- and 10-month momentum and toss out assets with negative momentum. I require that TYD and DBC are in the top 40 and 25 percent of assets for inclusion, because they are just for defense. I adaptively increase the risk budget towards higher-momentum assets. I typically rebalance weekly at the moment, but I'm tempted to automate daily rebalancing. I'm waffling between weekly and monthly calculations for the asset allocation.

The cited numbers are rules of thumb. I don't think the approach is very sensitive to these parameters.

I find that including TMV, SPXU, UGL, REMX, and UUP did not improve longer-duration backtests, although that says nothing about conditions going forward. Hedging to mitigate crashes has its costs. I'm still working out how to work in TMV appropriately to mitigate pre-1980s conditions.

I was running the UPRO/TQQQ/TMF/TYD flavor with six-week rebalance in taxable for a while, became convinced of merits of the more complex approach and switched, and very well may go back. Once again I caused a market inflection point, and the original portfolio would have been better off. However, I accepted the likelihood that the complex approach would lag on early recovery and decided to hedge a further decline.

That's where I'm at. A spectrum of alternatives better suited to my situation. Hope it helps.
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Re: Refinements to Hedgefundie's excellent approach

Post by hiddenpower »

cos wrote: Fri Jul 29, 2022 9:27 am Not to suggest that anyone is doing this, but it probably isn't the wisest idea to adopt a strategy solely based on the fact that someone else is doing it.

Invest only in that which you understand.
+1. I think it would just be nice to have an easier one-pager to understand. It would also make it more open to scrutiny and iteration. HFEA's opening thread was simple to digest and go off of for example. I realize this is a more complex strat though.
adaptive_allocation
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Re: Refinements to Hedgefundie's excellent approach

Post by adaptive_allocation »

Thanks for the summary Hydromod. It makes sense to me now why you are trying this approach, and I appreciate the effort.
hiddenpower wrote: Fri Jul 29, 2022 9:30 am
cos wrote: Fri Jul 29, 2022 9:27 am Not to suggest that anyone is doing this, but it probably isn't the wisest idea to adopt a strategy solely based on the fact that someone else is doing it.

Invest only in that which you understand.
+1. I think it would just be nice to have an easier one-pager to understand. It would also make it more open to scrutiny and iteration. HFEA's opening thread was simple to digest and go off of for example. I realize this is a more complex strat though.
I agree with this as well. It would be great if there's one predominant strategy everyone can evaluate and improve. It also requires people to have similar investing goals. For my case, I've been allocating a small portion of my investments into HFEA as a "lottery ticket". But the recent downturns in both UPRO and TMF have raised the question - are there "better lottery tickets" out there? (i.e. one with similar returns but lower drawdowns, risk, and volatility). I also wouldn't invest something that hasn't been backtested/vetted for at least a few decades, since I plan to follow the strategy for a similar amount of time.
bigblue1ca
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Re: Refinements to Hedgefundie's excellent approach

Post by bigblue1ca »

Hydromod wrote: Fri Jul 29, 2022 9:28 am That's where I'm at. A spectrum of alternatives better suited to my situation. Hope it helps.
Yes, very much. Thanks!
digdug_08
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Re: Refinements to Hedgefundie's excellent approach

Post by digdug_08 »

Is there a way to simulate portfolio performance in a taxable account with monthly rebalancing?
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

Thought experiment. A contention is that adding an asset with negative returns is always detrimental to the portfolio.

Simple example, based on a risk-budget minimum variance version of a golden butterfly for the last 15 years. To reduce timing luck dispersion, allocations are recalculated weekly and rebalancing is daily. However, trades are executed randomly between the highs and lows for the day. Trades also incur slippage.

Risk assignment: 4 times greater for the equity class than the gold class and the bond class. To roughly balance duration effects within the bond class, TMF has 2.5 times larger risk budget than TYD.

Two cases, both with UPRO/URTY/UTSL/TMF/TYD (all 3x LETFs). Case 1 (golden butterfly) uses UGL (2x gold), Case 2 (energy butterfly) uses ERX (2x energy).

Over this period, UGL has a CAGR of 8.4%, ERX has a CAGR of -16.2%.

Three runs with different random daily trade samplings:

Golden butterfly
CAGR 28%, 29%, 31%
volatility 22%, 22%, 24%
Sharpe 1.37, 1.41, 1.44

Energy butterfly
CAGR 26%, 25%, 27%
volatility 25%, 25%, 25%
Sharpe 1.20, 1.28, 1.24

The energy butterfly does perform a bit poorer overall with the replacement of UGL with ERX, but it's not a dramatic falloff even with the high overall drag from ERX. Why is this?

The risk budget for UGL ended up having UGL occupy 21% of the average allocation, while ERX occupied 11% of the average allocation. Replacing UGL with ERX resulted in UPRO, URTY, and UTSL slightly dropping their average allocations and TMF and TYD increasing their average allocations.

I recently started calculating the allocation-weighted CAGR for each asset. This is the equivalent daily return that would have yielded the same total return with the same time-varying allocations.

The very interesting thing to me is that the allocation-weighted CAGR is larger than the underlying CAGR for every asset, even though all assets are always invested. For example, for UPRO the asset CAGR is calculated as 23.3% while the allocation-weighted CAGR is 38%. Each asset had essentially the same increase for the golden butterfly and energy butterfly portfolios (different increases for different assets, of course).

The following lists change from asset CAGR to allocation-weighted CAGR for each asset. The equities had the same change in both the golden and energy butterfly portfolios

ERX: -16.2 to 13.0 (net 29.2)
URTY: 14.8 to 36.3 (net 21.5) both
UTSL: 27.9 to 47.3 (net 19.4) both
UPRO: 23.3 to 38.1 (net 14.8) both
TMF: 7.7 to 16.7 (net 9.0) energy, and to 17.9 (net 10.2) golden
TYD: 9.6 to 15.1 (net 5.5) energy, and to 17.3 (net 7.7) golden
UGL: 8.4 to 11.6 (net 3.2)

I don't have a definitive answer for why these assets experienced better returns in the portfolio than the underlying.

My strong suspicion is that these apparent increases in CAGR are basically returns generated from rebalancing. I don't think that the risk-budget approach should strongly change the CAGR simply by timing effects based on volatility.

As an aside, I find that the same type of increase seems to occur with various combinations of assets, as long as they are always invested. However, using the momentum approach to adaptively select assets loses this behavior for some assets and enhances the effect for others. In particular, FAS, UTSL, and to some extent CURE and TQQQ tend to have lower allocation-weighted CAGRs when momentum selections are used.

It may be worthwhile reserving momentum screening selection to the more volatile equities and the defensive assets, while always retaining a core group of lower-volatility assets.

Ah, the intricacies of portfolio construction!
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

digdug_08 wrote: Sun Jul 31, 2022 10:22 am Is there a way to simulate portfolio performance in a taxable account with monthly rebalancing?
I've put in a module to calculate tax consequences based on the M1 approach (sell short-term losers first, short-term gainers last). I find that some of these approaches with large turnovers can have a huge tax hit, but something that just keeps the same assets with different weights tends to settle down to something like an ER of 1 to 3 percent on average after the first year or two (although this can be quite variable year to year). One isn't often selling huge amounts each year, and selecting shares can help a lot to reduce it to losers and minimal long-term gainers.

That all takes work, though, unless you use M1 or something similar.
adaptive_allocation
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Re: Refinements to Hedgefundie's excellent approach

Post by adaptive_allocation »

Hi Hydromod, do you mind exploring UUP paired with gold? In my backtests, adding both seems to help more than just adding each alone.
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

adaptive_allocation wrote: Sun Jul 31, 2022 2:39 pm Hi Hydromod, do you mind exploring UUP paired with gold? In my backtests, adding both seems to help more than just adding each alone.
Huh. I did a back test from 2008 to present with 15 assets (no gold) with and without UUP. This was with momentum on. First I set it to only include UUP in the asset set if its momentum was one of the top 2 assets. It was only allocated <3% of the time, but the CAGR increased 4 percent and the portfolio volatility dropped from 36.4% to 35.5%.

UUP got selected 2008/2009, briefly 2015, end of 2018, 2020, and 2022. So trouble spots.

I get some random noise in the results because I throw in trading luck, but this was persistent for a couple of tries.

Color me surprised.

I ran the same test with UUP included if it was one of the top 4 assets. It was allocated about 6.6% of the time. The CAGR dropped by 0.7 percent but volatility dropped to 34.2%, so Sharpe went from 1.28 to 1.31.

Over this same period UGL modestly drags down returns and Sharpe (average allocation 8%) and the combination of UGL and UUP was even a little worse.

Overall I'm not a fan of UGL, although there are limited times when it does seem to help a bit.

UUP looks like one of those things that may really help on those few occasions when nothing else will quite do.
digdug_08
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Re: Refinements to Hedgefundie's excellent approach

Post by digdug_08 »

Hydromod wrote: Sun Jul 31, 2022 1:23 pm
digdug_08 wrote: Sun Jul 31, 2022 10:22 am Is there a way to simulate portfolio performance in a taxable account with monthly rebalancing?
I've put in a module to calculate tax consequences based on the M1 approach (sell short-term losers first, short-term gainers last). I find that some of these approaches with large turnovers can have a huge tax hit, but something that just keeps the same assets with different weights tends to settle down to something like an ER of 1 to 3 percent on average after the first year or two (although this can be quite variable year to year). One isn't often selling huge amounts each year, and selecting shares can help a lot to reduce it to losers and minimal long-term gainers.

That all takes work, though, unless you use M1 or something similar.
Thank you for the prompt reply! This is what I've been scratching my head about for a while. The AAA Portfolios with 2/3x LETFs in Portfolio Visualizer as very attractive, and "managing" that portfolio is fun for me as I like to do that sort of thing. However, since I am doing this in my taxable account, I'm really not sure how much of an edge I am getting after getting hit with the highest capital gains tax bracket. Because of my income, I cannot contribute to a Roth IRA. I tried doing a "Backdoor Roth IRA" with M1 Finance a few years ago, however according to my CPA they didn't do the conversion correctly so I ended up getting hit with taxes on that account, which scared me away from trying to do the backdoor all together.

After that experience, aside from my 401(k) and my kids 529 Plans, I'm left with fiddling with money in my taxable accounts. I am debating on just going back to the 3-fund portfolio (FZROX, FZILX, FXNAX), though I do like the involvement of rebalancing and playing with a portfolio with LEFTs.
adaptive_allocation
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Re: Refinements to Hedgefundie's excellent approach

Post by adaptive_allocation »

Hydromod wrote: Sun Jul 31, 2022 9:13 pm
Hi Hydromod, do you mind exploring UUP paired with gold? In my backtests, adding both seems to help more than just adding each alone.

Huh. I did a back test from 2008 to present with 15 assets (no gold) with and without UUP. This was with momentum on. First I set it to only include UUP in the asset set if its momentum was one of the top 2 assets. It was only allocated <3% of the time, but the CAGR increased 4 percent and the portfolio volatility dropped from 36.4% to 35.5%.

UUP got selected 2008/2009, briefly 2015, end of 2018, 2020, and 2022. So trouble spots.

I get some random noise in the results because I throw in trading luck, but this was persistent for a couple of tries.

Color me surprised.

I ran the same test with UUP included if it was one of the top 4 assets. It was allocated about 6.6% of the time. The CAGR dropped by 0.7 percent but volatility dropped to 34.2%, so Sharpe went from 1.28 to 1.31.

Over this same period UGL modestly drags down returns and Sharpe (average allocation 8%) and the combination of UGL and UUP was even a little worse.

Overall I'm not a fan of UGL, although there are limited times when it does seem to help a bit.

UUP looks like one of those things that may really help on those few occasions when nothing else will quite do.
That’s good to hear - thanks for exploring. I stick with deleveraged gold, I think UGL’s volatility is too high to use properly. By the way, an Adaptive Allocation backtest going back to Dec 1986 of UUP (backtest with DXY), VFINX, VUSTX, and ^GOLD gets me a Sharpe ratio of 0.68, CAGR of 8.46% and max drawdown of -9.18%. I’m really interested to see if anyone has better returns over similar periods of time with other assets.
Topic Author
Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod »

I ran across a short-term trading strategy that a redditor published recently. The core of the idea was to have a boring and sedate portfolio (equal weight SPY/XLP/SHY), but to use mean reversion ideas to temporarily deviate to leveraged funds when the market is sufficiently oversold (SPXL or TECL) or overbought (UVXY) using a 10-day relative strength index (RSI) for signals.

The strategy was developed using the composer site, which makes its money by providing automated trading using algorithms that the user can develop with their tool set.

The composer site calculated that the strategy would return >85% annual returns from January 2016 to present, using daily checks for the conditionals. The site doesn't provide a log scale for the strategy performance, so it is extremely difficult to understand where performance is coming from, but the strategy has very noticeable stair steps with up to 50% portfolio gain in a few days.

I found this a bit unbelievable, so I did a very simple test case of UUP unless the 10-day RSI for QQQ was >79%. The RSI is basically (sum of gainers) / (sum of gainers + sum of |losers|), where the gainers and losers are daily returns. I used VIXY when the trigger was on.

I could not reproduce the site values, or even the daily allocations provided by the site, using independent calculations. Comparing the allocations provided by the site with my independent RSI values, it seemed that the site was missing a substantial fraction of the days that I calculated as exceeding the trigger value. Even with the reported allocations, I calculated much smaller portfolio returns. I sent an email notifying them of the issue, but as of now I'd be very cautious about relying on algorithms developed with the site.

Nevertheless, I tried to explore the idea a bit. I was interested in how this would perhaps overlay my other strategies. As a test, I used a 10-year sequence ending 8/5/2022.

Some observations:
  • The sweet spot for the RSI is around 10 to 12 days look back, and an RSI threshold of 90 to 75%. The higher threshold seems to have had more consistent returns year to year.
  • The results were more consistent with RSI based on SPY/UPRO than with QQQ/TQQQ, although the NASDAQ-based signal arguably has given a stronger response in the last few years.
  • The procedure seems to need enough repetitions to generate a fair number of repetitions per year, but not so many that the signal is entirely lost. The threshold criterion triggering an event seems to work best with something like 7 to 11 events per year, so a longer RSI lookback tends to have a lower trigger threshold.
  • It appears to be very important to get out in quickly once the trigger appears and get out quickly once the trigger disappears. Waiting a single extra day on either end drops the returns very substantially.
  • It appears unrealistic to expect much greater than 6 to 8 percent CAGR using VIXY, especially considering trading costs of liquidation and repurchase. Returns may be better with UVXY, which is 1.5x leveraged.
  • There is an opportunity cost with using VIXY/UVXY instead of the base portfolio. Equities tend to have some positive returns on average during the trigger period, but it looks like the approach layers on top of the equities pretty well. Treasuries tend to have better returns than equities during the trigger period, and the trigger strategy only weakly outperforms. Interestingly, treasuries continue to pick up gains for an extra couple of days after the trigger shuts off.
I don't know that I'd make a bet on this if I was using a base 3x LETF strategy, given that treasuries will be a good-sized chunk of the portfolio and have tended to give a similar response over the same interval (albeit less strongly). If half of the portfolio is equities, then the benefit would be roughly halved at the cost of substantial disruption every five or six weeks. It might be worthwhile for a big boost to a 1x approach, if one were inclined that way.

If I was doing the strategy, I'd be tempted to use a 10-day SPY RSI trigger of 90%, kick into UVXY to start, trade from UVXY into TMF the day after the trigger stops to milk a slower response, and finally trade back into the base portfolio after another two days. I have not checked that this works, I'm just spitballing from what the results seem to indicate.

As a final note, I wouldn't be surprised if there was some benefit to rebalancing the portfolio based on RSI signals. Perhaps the same trigger would be useful for the overbought rebalance signal, and using a trigger of RSI < 30 or so might be useful for the oversold rebalance signal. I have not checked, it's just a hunch.

This stuff is a bit out of the norm, but I find it interesting nevertheless.
perplexed
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Re: Refinements to Hedgefundie's excellent approach

Post by perplexed »

Is there a way I can replicate your data? Your analysis has been always very insightful and data driven, and I read your posts with a lot of interest.
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