Refinements to Hedgefundie's excellent approach

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MotoTrojan
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Re: Refinements to Hedgefundie's excellent approach

Post by MotoTrojan » Tue Jul 09, 2019 12:57 pm

siamond wrote:
Tue Jul 09, 2019 12:32 pm
Hydromod wrote:
Mon Jul 08, 2019 11:41 pm
MotoTrojan wrote:
Mon Jul 08, 2019 11:24 pm
Would you mind going a bit deeper into how these were constructed? Simply 3x the monthly return is not an accurate representation; you also need to factor in borrowing costs. A quick test would be to compare them with the actual funds since inception.
You need to ask Siamond for the details of the approach. The math is described in the thread on creating simulated leveraged ETFs. But Siamond implemented it in a slick way, all you need to change is the leverage level in one place and this gets propagated throughout, including accounting for borrowing costs. He used this clever approach for each ETF, and checked against a 2x inverse ETF with good results. I just changed the number and copied the results.
Yes, this is just using the very exact same formulas we've been using for 'bull' leveraged funds. See here for a reminder. I ran a test against the S&P 2x inverse index and against an actual 'bear' fund of the same nature, and this worked well (I hinted at it here, but I didn't provide a lot of details at the time - I could easily reconstruct such test if needs be).

For full disclosure, the numbers used by Hydromod in his 'dual momentum' test were fully based on the 'magic formula' (the one derived from intra-month volatility). I could run the daily actuals for the past couple of decades, but we know that the 'magic formula' works extremely well, so no point making our life complicated. I provided an easy way to do so by simply tweaking a couple of cells in the monthly simulation model. Send me a PM for more details if interested.
Sweet. Super impressive back-test. Bit cute for me but I would be curious other's thoughts (including hedgefundie).

robertmcd
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Re: Refinements to Hedgefundie's excellent approach

Post by robertmcd » Tue Jul 09, 2019 1:59 pm

HEDGEFUNDIE wrote:
Sat Jul 06, 2019 4:17 pm
MoneyMarathon wrote:
Sat Jul 06, 2019 3:30 pm
MotoTrojan wrote:
Sat Jul 06, 2019 9:14 am
MoneyMarathon wrote:
Sat Jul 06, 2019 2:52 am
Suppose someone starts this right now, and over the next year, the Fed decides that employment looks good and raises rates to 3.5% from their current levels. Around the same time, stock market investors get nervous, then full-out panic after a war breaks out somewhere, and stocks dip 40% in a few months. These things happen in the same year.

What happens when both duration risk and equity risk get pummeled at the same time? How bad is the outcome?
You think rates would hold steady? Flight to safety.
I'm asking about one of the worst case scenarios for this strategy.

Yes, I think a worst case scenario is possible and that people have lost huge fortunes betting on correlations being as expected.
And how much opportunity cost has been incurred by people preparing for the worst, only to see the world go on as usual?
The only risk this strategy faces is inflation IMO. Rising real rates will never happen long enough/large enough before the central banks will bring them back down just like Dec 18. We will not get inflation until the money printing experiment blows up. My best guess is it never will, and we will eventually have negative rates. It is the only way we avoid all out global collapse and kick the can a little longer. Heck we already have inflation due to the money printing but it doesn't show up in CPI/TIPS. Even if we get inflation of say 3%, real yields on sovereign bonds could just go more negative and you would still get increase in NAV on your long term bonds. A slow agonizing death of purchasing power vs. stock/bond returns for the next 30 yrs is what I see.

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Tue Jul 09, 2019 2:06 pm

It's really kind of a hack to see if there is something there with using TMV to supplement TMF.

Unfortunately Portfolio visualizer won't do risk parity with monthly data. It can't, because it needs daily volatility and this can't be determined from the monthly data.

The approach I cobbled together is not at all according to the dual momentum philosophy, which is trying to select just the best performing asset(s) and stay with those.

I'm basically forcing the model to give approximate weights using the dual momentum mechanisms. In practice I'd investigate using something like dual momentum to select the best two assets among UPRO, TMF, and TMV, then use risk parity to assign weights between the two winners.

The backtest had both TMF and TMV winning at various times during the 1955 to 1982 period. There were even times when both were selected at the same time. I was amazed to see that monthly returns for TMF and TMV had the same sign fairly often... sequence of returns!

Maybe in practice I'd use some long averaging period to select between TMF and TMV as the replacement asset.

There's some discussion regarding the dual momentum weighting periods. The original proponent argues a 12-month period, others suggest weighting 1, 3, and 6 months evenly. I think it depends on the assets; the shorter weights may be better for US/international selections, because these can be a few months out of phase.

The periods that seem to work well for this x3 leveraged model are 12 and 1 month. The weights that work well are roughly (sqrt(1)/(sqrt(12) + sqrt(1))) = 0.78 and (sqrt(12)/(sqrt(12) + sqrt(1))) = 0.22, which corresponds to correcting for the reduction in standard deviation with increasing number of values in the sample. Maybe a coincidence. Evenly weighting 1, 3, and 6 months doesn't do nearly so well.

MotoTrojan
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Re: Refinements to Hedgefundie's excellent approach

Post by MotoTrojan » Tue Jul 09, 2019 2:16 pm

Hydromod wrote:
Tue Jul 09, 2019 2:06 pm


The backtest had both TMF and TMV winning at various times during the 1955 to 1982 period. There were even times when both were selected at the same time. I was amazed to see that monthly returns for TMF and TMV had the same sign fairly often... sequence of returns!

Sorry, both TMF and TMV gained in value during the same month frequently?

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Re: Refinements to Hedgefundie's excellent approach

Post by MotoTrojan » Tue Jul 09, 2019 2:19 pm

Hydromod wrote:
Tue Jul 09, 2019 2:06 pm
It's really kind of a hack to see if there is something there with using TMV to supplement TMF.

Unfortunately Portfolio visualizer won't do risk parity with monthly data. It can't, because it needs daily volatility and this can't be determined from the monthly data.
Perhaps you don't have them (Siamond could share?) but I was thinking you could take the monthly returns and monthly approximated (magic formula) daily volatility and then use a tool like Matlab (which you mentioned using in previous work) to simulate risk parity based backtests.

I would be extremely interested and appreciative of a 1-month lookback risk parity of UPRO/TMF using this method, back to 1955.

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Tue Jul 09, 2019 3:00 pm

I will look into this further. The daily volatility for the raw index for each month is included with the spreadsheet, so I can extract that and use it for weighting. The magic formula uses the monthly return and month-averaged daily volatility to estimate the monthly return for the leveraged index, if I understand it correctly.

I'm pretty curious myself how this will work. It might be a couple of days before I have time to get to it though.

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Tue Jul 09, 2019 3:03 pm

MotoTrojan wrote:
Tue Jul 09, 2019 2:16 pm
Sorry, both TMF and TMV gained in value during the same month frequently?
At my quick glance it appeared to occur fairly often. I will double-check tonight to make sure I'm stating this correctly though.

MotoTrojan
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Re: Refinements to Hedgefundie's excellent approach

Post by MotoTrojan » Tue Jul 09, 2019 3:11 pm

Hydromod wrote:
Tue Jul 09, 2019 3:03 pm
MotoTrojan wrote:
Tue Jul 09, 2019 2:16 pm
Sorry, both TMF and TMV gained in value during the same month frequently?
At my quick glance it appeared to occur fairly often. I will double-check tonight to make sure I'm stating this correctly though.
Fascinating. Thanks for the above offer to take a look at the 1955-present period with risk-parity!

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siamond
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Re: Refinements to Hedgefundie's excellent approach

Post by siamond » Tue Jul 09, 2019 6:59 pm

Hydromod wrote:
Tue Jul 09, 2019 3:03 pm
MotoTrojan wrote:
Tue Jul 09, 2019 2:16 pm
Sorry, both TMF and TMV gained in value during the same month frequently?
At my quick glance it appeared to occur fairly often. I will double-check tonight to make sure I'm stating this correctly though.
Huh? This doesn't seem quite right? Sometimes, the monthly returns are really low and the borrowing costs are going in the same direction, which could explain what you've seen, but I am quite surprised you would have even noticed those rare situations. I took a quick look, comparing the +3x model with the -3x model, and I don't see anything like that happening 'frequently'. Am I missing something?

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Tue Jul 09, 2019 10:37 pm

siamond wrote:
Tue Jul 09, 2019 6:59 pm
Hydromod wrote:
Tue Jul 09, 2019 3:03 pm
MotoTrojan wrote:
Tue Jul 09, 2019 2:16 pm
Sorry, both TMF and TMV gained in value during the same month frequently?
At my quick glance it appeared to occur fairly often. I will double-check tonight to make sure I'm stating this correctly though.
Huh? This doesn't seem quite right? Sometimes, the monthly returns are really low and the borrowing costs are going in the same direction, which could explain what you've seen, but I am quite surprised you would have even noticed those rare situations. I took a quick look, comparing the +3x model with the -3x model, and I don't see anything like that happening 'frequently'. Am I missing something?
Yes, it seemed out of place. It's been bothering me all day so I went through the math to understand. It's actually pretty neat how the formulas fall into place.

And it turns out that in my rush I managed to cut and paste names to the wrong column in the spreadsheet I uploaded to portfolio visualizer at some point. The results I showed were with inverse x3 S&P 500 instead of inverse x3 LTT.

You might say that it was an "out of sample" test of the methodology...

The revised figures follow. I double-checked the file, cleared out all of the assets in portfolio visualizer, and reloaded them. All of the numbers look good now.

The dual-momentum case looks even better with the correct inputs.

Image

The relative strength model does better up until the last decade, then the prior model accelerates past.

Image

Sorry about the confusion and inadvertently casting shade on Siamond. It was all on my fumble fingers.

At least I understand the spreadsheet and its math better now. And there is some confirmation that the methodology is somewhat robust.

MotoTrojan
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Re: Refinements to Hedgefundie's excellent approach

Post by MotoTrojan » Tue Jul 09, 2019 11:14 pm

What color should we paint our G650’s?

HEDGEFUNDIE
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Re: Refinements to Hedgefundie's excellent approach

Post by HEDGEFUNDIE » Tue Jul 09, 2019 11:24 pm

Hydromod wrote:
Tue Jul 09, 2019 10:37 pm

The revised figures follow. I double-checked the file, cleared out all of the assets in portfolio visualizer, and reloaded them. All of the numbers look good now.

The dual-momentum case looks even better with the correct inputs.

Image

The relative strength model does better up until the last decade, then the prior model accelerates past.

Image

Sorry about the confusion and inadvertently casting shade on Siamond. It was all on my fumble fingers.

At least I understand the spreadsheet and its math better now. And there is some confirmation that the methodology is somewhat robust.
Please share the PV links for these two strategies using the actual funds over the ~10 years of their existence.

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siamond
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Re: Refinements to Hedgefundie's excellent approach

Post by siamond » Wed Jul 10, 2019 7:32 am

Hydromod wrote:
Tue Jul 09, 2019 10:37 pm
it turns out that in my rush I managed to cut and paste names to the wrong column in the spreadsheet I uploaded to portfolio visualizer at some point. The results I showed were with inverse x3 S&P 500 instead of inverse x3 LTT.
[...] Sorry about the confusion and inadvertently casting shade on Siamond. It was all on my fumble fingers.
Well... Ahem... There is a problem in the simulation spreadsheet too... I ran more tests using -2x and -3x LTT funds (I had only tested S&P 500 index/funds with negative leverage so far), and I couldn't understand the results. Coming back to the formula used to adjust the raw (leveraged) index returns, it became clear that it just can't be right for inverse ('bear') leveraged funds. Somehow the S&P 500 results worked ok, but I now think it was just luck, not design...

I'll be a bit in and out today. Give me a bit of time to figure it out... Sorry about that. :(

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Re: Refinements to Hedgefundie's excellent approach

Post by Time2Quit » Wed Jul 10, 2019 7:57 am

Very interesting. I am just replying so I can follow along and keep track of this thread.
"It is not the man who has too little, but the man who craves more, that is poor." --Seneca

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Wed Jul 10, 2019 8:53 am

HEDGEFUNDIE wrote:
Tue Jul 09, 2019 11:24 pm
Please share the PV links for these two strategies using the actual funds over the ~10 years of their existence.
Unfortunately PV isn't set up to do this. It only allows tickers to be selected. That's why I called it a bit of a hack.

What I really want is for PV to allow the dual momentum algorithm to also consider portfolios and, even better, other strategies as possibilities that can be selected.

So it would be possible to use a portfolio such as the 40/60 UPRO/TMF as an asset and the 40/60 UPRO/TMV as another asset. Or use the result of an inverse-volatility calculation with UPRO and TMF as an asset and the result of a relative strength calculation as an asset.

I'd also like the option to weight the selected assets according to the expected gain. In other words, if I select 2 assets to hold (out of several possible assets), and one selected asset is predicted to have a relative gain of 2 and the other a relative gain of 1, the first should be weighted 2/3 and the second weighted 1/3. Currently they are simply weighted as 1/N.

This could be pretty slick.

What I actually did was create artificial tickers with different weight fractions for SPx3, LTTx3, and LTTxm3, corresponding to UPRO, TMV, and TMF. For example, ticker SP40LT60 is simply calculated as SPx3*0.4 + LTTx3*0.6. This only works properly when the rows in the spreadsheet correspond to the rebalancing period. So tickers provided with rebalancing by month or year are the only options that can be properly matched in PV.

I made several weights for each pair of assets, and forced the dual momentum algorithm to hold 3 or 4. Sometimes it doubles up on one asset. That kind of mashing together allows a bunch of discrete weight combinations. For example, with 0/100, 25/75, 50/50, 75/25, and 100/0 tickers and forcing the algorithm to hold two tickers, in effect the dual momentum approach can consider weight levels for UPRO by 1/8 between 0 and 1.

One can also create tickers in the worksheet that correspond to the inverse-volatility series or other weighting schemes, which would mimic what I want PV to do.

To reproduce this with real ticker data, you would need to do a similar process with externally creating tickers with UPRO etc. Sorry about that.

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Wed Jul 10, 2019 10:36 am

siamond wrote:
Wed Jul 10, 2019 7:32 am
Well... Ahem... There is a problem in the simulation spreadsheet too... I ran more tests using -2x and -3x LTT funds (I had only tested S&P 500 index/funds with negative leverage so far), and I couldn't understand the results. Coming back to the formula used to adjust the raw (leveraged) index returns, it became clear that it just can't be right for inverse ('bear') leveraged funds. Somehow the S&P 500 results worked ok, but I now think it was just luck, not design...

I'll be a bit in and out today. Give me a bit of time to figure it out... Sorry about that. :(
I think a reasonable formula for the leveraged returns should be

(1 + Y) = exp(N * xbr + (0.5 - N) xbr^2 + (1 - N) * sgr^2 / 2)

where Y is the leveraged return and N is the number of observations.

xbr is mean(r) * m
sgr is std(r) * m

r is the original series of daily returns
m is the leverage factor

You have std(r) in the spreadsheet but not mean(r).

You can get a decent estimate for mean(r) from (1 + X)^(1/N) - 1

where X is the unleveraged monthly return.

I did a quick test in MATLAB to see that it works with a random series.
This should work pretty well as long as the original standard deviation is small.

Leaving in the next term in the infinite series for a logarithm, corresponding to the sum of returns cubed, would give much better results when the original daily standard deviation is greater than 1 percent, but I don't think it can be easily expressed with mean and standard deviation.

Hope this helps.

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siamond
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Re: Refinements to Hedgefundie's excellent approach

Post by siamond » Wed Jul 10, 2019 11:22 am

Hydromod wrote:
Wed Jul 10, 2019 10:36 am
I think a reasonable formula for the leveraged returns should be

(1 + Y) = exp(N * xbr + (0.5 - N) xbr^2 + (1 - N) * sgr^2 / 2)
The issue (for inverse/bear leveraged funds) isn't the math derived from the index returns, that part works well, the issue is the borrowing cost side of the equation. The research literature we used for the initial modeling effort undoubtedly addressed this issue, I just need to dig a bit further. Sorry, I got fooled by the fact that the S&P 500 2x numbers seemed to work and didn't think any further, by lack of initial interest about inverse funds... My bad!

I have guests at home today, will not be able to look at it more closely until tonight.

Also, we should shift such modeling discussion to the appropriate thread.

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Re: Refinements to Hedgefundie's excellent approach

Post by rascott » Wed Jul 10, 2019 11:51 am

siamond wrote:
Tue Jul 09, 2019 12:32 pm
Hydromod wrote:
Mon Jul 08, 2019 11:41 pm
MotoTrojan wrote:
Mon Jul 08, 2019 11:24 pm
Would you mind going a bit deeper into how these were constructed? Simply 3x the monthly return is not an accurate representation; you also need to factor in borrowing costs. A quick test would be to compare them with the actual funds since inception.
You need to ask Siamond for the details of the approach. The math is described in the thread on creating simulated leveraged ETFs. But Siamond implemented it in a slick way, all you need to change is the leverage level in one place and this gets propagated throughout, including accounting for borrowing costs. He used this clever approach for each ETF, and checked against a 2x inverse ETF with good results. I just changed the number and copied the results.
Yes, this is just using the very exact same formulas we've been using for 'bull' leveraged funds. See here for a reminder. I ran a test against the S&P 2x inverse index and against an actual 'bear' fund of the same nature, and this worked well (I hinted at it here, but I didn't provide a lot of details at the time - I could easily reconstruct such test if needs be).

For full disclosure, the numbers used by Hydromod in his 'dual momentum' test were fully based on the 'magic formula' (the one derived from intra-month volatility). I could run the daily actuals for the past couple of decades, but we know that the 'magic formula' works extremely well, so no point making our life complicated. I provided an easy way to do so by simply tweaking a couple of cells in the monthly simulation model. Send me a PM for more details if interested.

Magic formula? Can you clarify for those of us that don't know what you are referring to?

Edit.... Sorry disregard. I realize now you were talking about your SIM data.

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Wed Jul 10, 2019 12:10 pm

siamond wrote:
Wed Jul 10, 2019 11:22 am
The issue (for inverse/bear leveraged funds) isn't the math derived from the index returns, that part works well, the issue is the borrowing cost side of the equation. The research literature we used for the initial modeling effort undoubtedly addressed this issue, I just need to dig a bit further. Sorry, I got fooled by the fact that the S&P 500 2x numbers seemed to work and didn't think any further, by lack of initial interest about inverse funds... My bad!
Just to clarify that the impact on the dual momentum modeling results I presented is likely pretty small with respect to which assets are selected each time step, because the fluctuations are much larger than the magnitude of the LIBOR cost.

Misrepresenting LIBOR will systematically affect the long-term trend, though, which would affect the CAGR numbers.

The monthly values used are: (i) portfolio 2: LTT x3, (ii) portfolio 3: LTT x-3, and (iii) portfolio 1: LTT itself, for reference.

Image

PluckyDucky
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Re: Refinements to Hedgefundie's excellent approach

Post by PluckyDucky » Wed Jul 10, 2019 12:14 pm

So from 55-82 you were in inverse TMF instead of TMF?

So much for rising rates being a problem!

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Re: Refinements to Hedgefundie's excellent approach

Post by HEDGEFUNDIE » Wed Jul 10, 2019 12:17 pm

Hydromod wrote:
Wed Jul 10, 2019 8:53 am
HEDGEFUNDIE wrote:
Tue Jul 09, 2019 11:24 pm
Please share the PV links for these two strategies using the actual funds over the ~10 years of their existence.
Unfortunately PV isn't set up to do this. It only allows tickers to be selected. That's why I called it a bit of a hack.

What I really want is for PV to allow the dual momentum algorithm to also consider portfolios and, even better, other strategies as possibilities that can be selected.

So it would be possible to use a portfolio such as the 40/60 UPRO/TMF as an asset and the 40/60 UPRO/TMV as another asset. Or use the result of an inverse-volatility calculation with UPRO and TMF as an asset and the result of a relative strength calculation as an asset.

I'd also like the option to weight the selected assets according to the expected gain. In other words, if I select 2 assets to hold (out of several possible assets), and one selected asset is predicted to have a relative gain of 2 and the other a relative gain of 1, the first should be weighted 2/3 and the second weighted 1/3. Currently they are simply weighted as 1/N.

This could be pretty slick.

What I actually did was create artificial tickers with different weight fractions for SPx3, LTTx3, and LTTxm3, corresponding to UPRO, TMV, and TMF. For example, ticker SP40LT60 is simply calculated as SPx3*0.4 + LTTx3*0.6. This only works properly when the rows in the spreadsheet correspond to the rebalancing period. So tickers provided with rebalancing by month or year are the only options that can be properly matched in PV.

I made several weights for each pair of assets, and forced the dual momentum algorithm to hold 3 or 4. Sometimes it doubles up on one asset. That kind of mashing together allows a bunch of discrete weight combinations. For example, with 0/100, 25/75, 50/50, 75/25, and 100/0 tickers and forcing the algorithm to hold two tickers, in effect the dual momentum approach can consider weight levels for UPRO by 1/8 between 0 and 1.

One can also create tickers in the worksheet that correspond to the inverse-volatility series or other weighting schemes, which would mimic what I want PV to do.

To reproduce this with real ticker data, you would need to do a similar process with externally creating tickers with UPRO etc. Sorry about that.
I guess what I am really asking is, what is the comparison between these two strategies and the original strategy, for 1982-present and 2009-present?

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Wed Jul 10, 2019 12:21 pm

PluckyDucky wrote:
Wed Jul 10, 2019 12:14 pm
So from 55-82 you were in inverse TMF instead of TMF?

So much for rising rates being a problem!
I wish I were able to have done that! The opportunity was only available recently though.

That's the big takeaway. I should have posted this image first.

But really a practical algorithm should go back and forth, depending on the environment. That's the trickier part.

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Wed Jul 10, 2019 1:01 pm

HEDGEFUNDIE wrote:
Wed Jul 10, 2019 12:17 pm
I guess what I am really asking is, what is the comparison between these two strategies and the original strategy, for 1982-present and 2009-present?
The figures below show the hacked together one for 1982-2019 and 2009-present. Unfortunately the monthly dataset ends in January.

Dual momentum model

Image

Image

Not so different overall. Not so sensitive to the 2000-2010 period, more sensitive to Black Monday.

Relative strength model

Image

Image

Quite similar. Again not so sensitive to the 2000-2010 period, more sensitive to Black Monday. The 2009-2019 comparison is a bit misleading because of start conditions.

The comparison line uses the monthly data as well.

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Hydromod
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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Thu Jul 11, 2019 12:34 am

MotoTrojan wrote:
Tue Jul 09, 2019 2:19 pm
Hydromod wrote:
Tue Jul 09, 2019 2:06 pm
It's really kind of a hack to see if there is something there with using TMV to supplement TMF.

Unfortunately Portfolio visualizer won't do risk parity with monthly data. It can't, because it needs daily volatility and this can't be determined from the monthly data.
Perhaps you don't have them (Siamond could share?) but I was thinking you could take the monthly returns and monthly approximated (magic formula) daily volatility and then use a tool like Matlab (which you mentioned using in previous work) to simulate risk parity based backtests.

I would be extremely interested and appreciative of a 1-month lookback risk parity of UPRO/TMF using this method, back to 1955.
I took a first cut tonight. I hacked together something quick and dirty, just to get a feel. It looks something like the corrected plots above, sailing through 1955 to present. I'm very encouraged. Although the early data are missing any indication about volatility for treasuries, so it's maybe a weaker test.

The dual momentum model does remarkably well with just the inverse volatility sequence as a ticker and TMV analog as a ticker, with TMF as the fallback.

I want to do a better job before presenting, though, and give Siamond a chance to come to peace with inverse leveraged treasuries. So it might be a while before I throw up another figure.

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Re: Refinements to Hedgefundie's excellent approach

Post by MotoTrojan » Thu Jul 11, 2019 9:36 pm

Hydromod wrote:
Thu Jul 11, 2019 12:34 am
MotoTrojan wrote:
Tue Jul 09, 2019 2:19 pm
Hydromod wrote:
Tue Jul 09, 2019 2:06 pm
It's really kind of a hack to see if there is something there with using TMV to supplement TMF.

Unfortunately Portfolio visualizer won't do risk parity with monthly data. It can't, because it needs daily volatility and this can't be determined from the monthly data.
Perhaps you don't have them (Siamond could share?) but I was thinking you could take the monthly returns and monthly approximated (magic formula) daily volatility and then use a tool like Matlab (which you mentioned using in previous work) to simulate risk parity based backtests.

I would be extremely interested and appreciative of a 1-month lookback risk parity of UPRO/TMF using this method, back to 1955.
I took a first cut tonight. I hacked together something quick and dirty, just to get a feel. It looks something like the corrected plots above, sailing through 1955 to present. I'm very encouraged. Although the early data are missing any indication about volatility for treasuries, so it's maybe a weaker test.

The dual momentum model does remarkably well with just the inverse volatility sequence as a ticker and TMV analog as a ticker, with TMF as the fallback.

I want to do a better job before presenting, though, and give Siamond a chance to come to peace with inverse leveraged treasuries. So it might be a while before I throw up another figure.
Excited to check it out!

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hdas
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Re: Refinements to Hedgefundie's excellent approach

Post by hdas » Thu Jul 11, 2019 11:21 pm

Hydromod wrote:
Fri Jul 05, 2019 10:59 pm
I've been backtesting aspects of Hedgefundie's approach with leveraged ETFs, and I thought it would be appropriate to start a new thread to keep the information more readily available. I'm expecting a few more posts as I go along, and the more the merrier!
While you seem capable and motivated, this whole exercise is worthless overfitting. In this field clean data to test hypothesis is priceless. Given the nature/granularity of the strategy there’s simple not enough data for you to find anything statistically significant. Cheers :greedy
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes

MotoTrojan
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Re: Refinements to Hedgefundie's excellent approach

Post by MotoTrojan » Thu Jul 11, 2019 11:38 pm

hdas wrote:
Thu Jul 11, 2019 11:21 pm
Hydromod wrote:
Fri Jul 05, 2019 10:59 pm
I've been backtesting aspects of Hedgefundie's approach with leveraged ETFs, and I thought it would be appropriate to start a new thread to keep the information more readily available. I'm expecting a few more posts as I go along, and the more the merrier!
While you seem capable and motivated, this whole exercise is worthless overfitting. In this field clean data to test hypothesis is priceless. Given the nature/granularity of the strategy there’s simple not enough data for you to find anything statistically significant. Cheers :greedy
Worthless? Really?

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Re: Refinements to Hedgefundie's excellent approach

Post by hdas » Fri Jul 12, 2019 9:10 am

MotoTrojan wrote:
Thu Jul 11, 2019 11:38 pm
hdas wrote:
Thu Jul 11, 2019 11:21 pm
Hydromod wrote:
Fri Jul 05, 2019 10:59 pm
I've been backtesting aspects of Hedgefundie's approach with leveraged ETFs, and I thought it would be appropriate to start a new thread to keep the information more readily available. I'm expecting a few more posts as I go along, and the more the merrier!
While you seem capable and motivated, this whole exercise is worthless overfitting. In this field clean data to test hypothesis is priceless. Given the nature/granularity of the strategy there’s simple not enough data for you to find anything statistically significant. Cheers :greedy
Worthless? Really?
For the purpose of prediction and making money. Yes, absolutely. It's a hard lesson to learn in conjunction with occam's razor, even for technical people. Physicist and fellow travelers that have done real science have a natural tendency to be good at formulating clean experiments which results have a better chance to replicate. Cheers :greedy
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes

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Re: Refinements to Hedgefundie's excellent approach

Post by MotoTrojan » Fri Jul 12, 2019 9:40 am

hdas wrote:
Fri Jul 12, 2019 9:10 am
MotoTrojan wrote:
Thu Jul 11, 2019 11:38 pm
hdas wrote:
Thu Jul 11, 2019 11:21 pm
Hydromod wrote:
Fri Jul 05, 2019 10:59 pm
I've been backtesting aspects of Hedgefundie's approach with leveraged ETFs, and I thought it would be appropriate to start a new thread to keep the information more readily available. I'm expecting a few more posts as I go along, and the more the merrier!
While you seem capable and motivated, this whole exercise is worthless overfitting. In this field clean data to test hypothesis is priceless. Given the nature/granularity of the strategy there’s simple not enough data for you to find anything statistically significant. Cheers :greedy
Worthless? Really?
For the purpose of prediction and making money. Yes, absolutely. It's a hard lesson to learn in conjunction with occam's razor, even for technical people. Physicist and fellow travelers that have done real science have a natural tendency to be good at formulating clean experiments which results have a better chance to replicate. Cheers :greedy
So for example saying the point of risk parity is to maintain equal volatility and rebalancing to that more frequently improves that more than using the longterm average volatility. Then seeing the 1-2% CAGR improvement that nets. That’s more sound?

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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Fri Jul 12, 2019 11:11 am

hdas wrote:
Thu Jul 11, 2019 11:21 pm
Hydromod wrote:
Fri Jul 05, 2019 10:59 pm
I've been backtesting aspects of Hedgefundie's approach with leveraged ETFs, and I thought it would be appropriate to start a new thread to keep the information more readily available. I'm expecting a few more posts as I go along, and the more the merrier!
While you seem capable and motivated, this whole exercise is worthless overfitting. In this field clean data to test hypothesis is priceless. Given the nature/granularity of the strategy there’s simple not enough data for you to find anything statistically significant. Cheers :greedy
I appreciate your candor. On the face of it, I suspect that you are over-generalizing the intent of this little thread.

I'm not exactly sure what you are referring to as the whole exercise in this case. Could you be a little more specific? Is it Hedgefundie's initial premise? The idea of validating the premise? Testing the limits of the approach?

I can agree that we will only be able to see what will happen in the future once the future has become the past. Regardless of how much data there exists currently.

We are working with a fair amount of uncertainty. That's the nature of the beast. That's the nature of my business, too; try predicting the effects of climate on water resources and energy demands over the next few generations if you want uncertainty. But if you are able to mitigate uncertainty to some measure, you may have to adapt less after the fact.

I agree that the data are sparser than we would like. But in fact I'm enjoying having so much data to work with here!

I would assert that there is enough data to (i) identify conditions where no approach is likely to work, or (ii) identify areas where the approach needs to be adjusted before it can work, or (iii) identify refinements to an approach that works under certain conditions. This is useful information, even the negative results. That's what the thread is about.

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Re: Refinements to Hedgefundie's excellent approach

Post by PluckyDucky » Fri Jul 12, 2019 12:58 pm

If we were going to switch from UPRO/TMF to UPRO/TMV, how would we know what to look for? There's been talk of the Fed changing it's goals in 1982, so how do we know if we go back to pre-1982 world?

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Re: Refinements to Hedgefundie's excellent approach

Post by MoneyMarathon » Fri Jul 12, 2019 3:10 pm

Hydromod wrote:
Fri Jul 12, 2019 11:11 am
I'm not exactly sure what you are referring to as the whole exercise in this case. Could you be a little more specific?
It's the market timing part.

Back in the great stock market doldrums of 2015-2016 (remember those?), I was a little worried about a stock market pullback. So I did some backtests and found some great heuristics that avoided big stock pullbacks and added to results numbers over the decades going back to the 1930s. They had perfect accuracy (in the backtest). Naturally of course they also predicted that someone should sell during the pullback in early 2016.

If someone did that, they'd lose out on some of the strongest growth in recent memory, at least until the signal said to get back in. In effect a perfect backtested strategy ended up telling you to sell low and buy high. The remorse is real!

There are several challenges:

(1) There aren't enough recessions in history, in terms of the number of such events. Not enough data, overfitting.
(2) If you have more than one hypothesis to test, in-sample, statistical significance is further strained. Too much power (flexibility) in the model, overfitting.
(3) Not enough future recessions to live through, reliably, in order to yield greater returns (if you ever judge one wrong, that is, and chances are that you might).
(4) Behavioral errors. Sticking with a strategy for a multi-decade period is hard enough when there's a bear market. It's even harder when you had a timing "plan" for a bear market and it blew up in your face.

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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Fri Jul 12, 2019 4:51 pm

There's no question that timing the market can't be done consistently, and even strategies that look good from backtesting must fail regularly. I suspect that this will only become harder in the future, because there are so many folks using advanced techniques that the market may become even more chaotic.

But I'm not asking whether you can time the market. I'm really asking whether you can do better overall with leveraged portfolios than buy and hold with unleveraged portfolios, and if there are things that you can do to improve your chances.

I think it may be a little bit different animal with the 3x leveraging going on. I think you may be able to afford to be conservative in your strategies, get out early and miss the biggest bounces, and still come out ahead overall. Sooner or later there will be misses, no question.

It's important to know when the strategies are unlikely to be successful overall, so you can get out entirely when those conditions arise. I'm working over some thoughts on this.

I'm curious about these kinds of questions, that's why I'm looking at this. I know there's no guarantees.

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Re: Refinements to Hedgefundie's excellent approach

Post by joan_01 » Fri Jul 12, 2019 10:48 pm

the strong negative correlation between stocks and bonds since 2000 has been a huge benefit for risk parity strategies

looking further back in time, stock/bonds actually been positively correlated more of the time

Image

this would make a 3x risk parity strategy much riskier than it's been over the past two decades. sort of similar to what happened in q4 2018 when stocks fell and bonds didn't really provide a big offset

graph source: "Dennis Rodman and the Art of Portfolio Optimization" from Artemis Capital

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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Sat Jul 13, 2019 1:17 am

I have a couple of plots from 1955 to present to share, now that Siamond has verified that the leverage model appears to be appropriate for representing inverse leverage. There's still some residual tracking error that is causing uncertainty, on the order of 0.5 bp/day. In these plots, I assume an ER of 1 percent above and beyond the LIBOR costs. These are all based on monthly aggregated statistics, and assume monthly rebalancing.

The first plot shows several portfolios.
  • Portfolio 1 is the inverse-volatility weighted UPRO/TMF analog.
  • Portfolio 2 is the inverse-volatility weighted UPRO/TMV analog.
  • Portfolio 3 is the TMV should be TMF. Dang. analog.
The benchmark is the 40/60 UPRO/TMF analog.

Image

Notice that there are several periods of interest: (i) 1955-1967, (ii) 1967-1983, (iii) 1983-2000, (iv) 2000-2010, and (v) 2010-present.

The 1967 and 2010 breakpoints correspond to the switches in correlation in joan_01's figure. The 1983 breakpoint corresponds to the switch in Fed policy.

So we see that
  • prior to the 1967 breakpoint, the inverse-volatility and 40/60 track closely,
  • between 1967 and 1983, the inverse-volatility tracks below the 40/60,
  • between 1983 and 2010, the inverse-volatility and 40/60 track closely in parallel,
  • after the 2010 breakpoint, the inverse-volatility tracks closely above the 40/60 (by surviving 2010 better).
While TMF tracks down, UPRO/TMV performs better, and while TMF tracks up, UPRO/TMF performs better. These trends are amplified or muted, depending on the correlation between UPRO and TMF/TMV.

As an interesting comparison, the next figure shows a simple dual momentum model switching between the inverse-volatility UPRO/TMF model and TMV, with TMF left as the cash option. The model uses two timing periods, 1 month (20 percent weight) and 12 months (80 percent weight), to decide on which option to select.

Image

This combination pretty much mimics the previous dual momentum model, except that the inverse-volatility model is the only option providing UPRO exposure. Note that the previous model did not have the 1% ER included.

The next figure adds the option of selecting UPRO/TMF, UPRO/TMV, or TMV, with TMF left as the cash option. It performs very slightly better.

Image

The dual momentum model is fairly sensitive to assumptions, which is a big drawback. In particular, the overall results rapidly deteriorate with changes in the method for assigning the winning model (changing volatility periods or weights). I would be suspicious that these factors are robust.

Based on these plots, I think that the best case is to use UPRO with either TMF or TMV, depending on which is trending up.

The optimal selection has both UPRO and its mate (TMF or TMV) both trending up, correlated or not. It's possible to get performance with a negative-trending mate to UPRO, as long as it is anti-correlated, but an upward trend with positive correlation is better than a downward trend with negative correlation. If both mates are relatively flat, the negatively correlated one should be used.

I hope this clarified some issues.

I still think that it is not completely resolved how to robustly switch between UPRO/TMF and UPRO/TMV. The problem is that the oscillations in return from month to month tend to be large relative to the trend, so there is only a small signal for picking the right combination.
Last edited by Hydromod on Wed Jul 17, 2019 1:41 pm, edited 1 time in total.

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Re: Refinements to Hedgefundie's excellent approach

Post by hdas » Sat Jul 13, 2019 10:46 am

Hydromod wrote:
Fri Jul 12, 2019 11:11 am
I'm not exactly sure what you are referring to as the whole exercise in this case. Could you be a little more specific? Is it Hedgefundie's initial premise? The idea of validating the premise? Testing the limits of the approach?
Finding timing rules that work well "in sample"
Hydromod wrote:
Fri Jul 12, 2019 11:11 am
That's the nature of my business, too; try predicting the effects of climate on water resources and energy demands over the next few generations if you want uncertainty. But if you are able to mitigate uncertainty to some measure, you may have to adapt less after the fact.
Very different domains, specially once you introduce betting. Nobody in this business that has a scientific bent and some integrity works with this range of data, you go to the higher frequencies, that's where the quant methods can offer robust results. The problem then is that you start swimming with the sharks.
Hydromod wrote:
Fri Jul 12, 2019 11:11 am
I agree that the data are sparser than we would like. But in fact I'm enjoying having so much data to work with here!
The only data that is abundant in this forum (and of a decent quality), is related to sentiment of participants.
Hydromod wrote:
Fri Jul 12, 2019 11:11 am
I would assert that there is enough data to (i) identify conditions where no approach is likely to work, or (ii) identify areas where the approach needs to be adjusted before it can work, or (iii) identify refinements to an approach that works under certain conditions. This is useful information, even the negative results. That's what the thread is about.
This is the gist of the problem, your approach is descriptive of the past, not predictive. You seem capable enough to research on your own the best practices on the field. Good Luck.
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes

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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Sat Jul 13, 2019 11:32 am

Thanks for your comments. I think we're pretty much on the same page then.

I am suspicious of methods that try to abruptly swap out one fund for another. That's what I would call market timing, and I agree that it is dreadfully hard to get robust strategies with the existing data for backtesting. But looking at the outcomes of methods that do this kind of swapping can give some insight that leads to identifying the underlying behavior that is triggering the swaps. The dual momentum case I showed is an example of this.

I do think that there is benefit to gradually adjusting weights over time to keep trends, volatilities, and correlations in a favorable configuration. That just incrementally keeps the odds more favorable as the market flips around. I think that blending information from several time scales, ranging from perhaps a couple of years to the most recent weeks, will end up improving the overall odds a bit.

I agree that the very short-term behavior is most suitable for rooting out information. That's already come out from the early analyses, and I acknowledge that squeezing an extra few percent from very frequent rebalancing is likely something that very few individuals should be trying to do over decade-long intervals. It may be that the benefit is mainly from more targeted rebalancing under certain short-term conditions (e.g., during downturns) that improves the odds, though, in which case perhaps it becomes more actionable for motivated folks.

It'll be fun to try and figure it out with folks.

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Re: Refinements to Hedgefundie's excellent approach

Post by Kbg » Sat Jul 13, 2019 8:58 pm

Take a look at not doing all or nothing on a signal. Use several momentum or moving average lookbacks and then the percent invested in an asset is cumulative of each separate signal. For example, one could use 3 through 12 month measurements and that means 10% to each month.

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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Sat Jul 13, 2019 9:52 pm

That is right along the lines I'm thinking. I am getting convinced that the daily and monthly noise is so large that it's very hard to find a signal large enough to justify large rapid changes in strategy.

Getting a better feel for the data and seeing what limits there are for extrapolating from the data is high on my list.

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Re: Refinements to Hedgefundie's excellent approach

Post by no simpler » Sat Jul 13, 2019 10:01 pm

you need to use time split cross validation if you start tuning weights to improve performance. As others mentioned, there isn't enough data to have representative holdout windows. This stuff is better left for folks with experience in time series forecasting.

A redflag should be if your sharpe starts getting too high. Very unlikely you just stumbled on a strategy that no hedge fund figured out.

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Re: Refinements to Hedgefundie's excellent approach

Post by Kbg » Sat Jul 13, 2019 10:58 pm

Don’t tune. Momentum works, but what works best is in constant motion and we don’t what that is going forward. Diversification is good in signals as well as assets.

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Re: Refinements to Hedgefundie's excellent approach

Post by no simpler » 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.

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Re: Refinements to Hedgefundie's excellent approach

Post by PluckyDucky » Tue Jul 16, 2019 1:14 pm

Hydromod, for your timing model, are you looking at the LETF or the underlying unleveraged ETF (or index) to determine your buy/sell signal?

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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Tue Jul 16, 2019 4:23 pm

PluckyDucky wrote:
Tue Jul 16, 2019 1:14 pm
Hydromod, for your timing model, are you looking at the LETF or the underlying unleveraged ETF (or index) to determine your buy/sell signal?
At this point, I wouldn't say that I have a timing model per se, unless you are referring to the idea of using adaptive inverse-volatility weights based on the most recent time period. I use the LETF index for that purpose.

The dual momentum model I posted results from is indeed a timing model. It's from portfolio visualizer, and the model uses LETF values.

I would tend to favor using the LETF index in any strategy, to account for volatility decay.

Personally I am coming to favor the idea of gradual and incremental adjustments over months to years to adjust the portfolio composition, and perhaps more rapid adjustments to adjust for changes in volatility. I don't think I'm brave enough to switch things drastically in response to market signals.

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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Tue Jul 16, 2019 9:00 pm

Just for clarification. In the dual momentum model, the choice is between two inverse-volatility portfolios, not the LETFs directly. Both portfolios have the same UPRO weight. I think this helps with determining momentum, because the portfolio volatility is less than the individual ETF volatilities.

Also note that the dual momentum model usually switches TMF and TMV, keeping UPRO, or swaps UPRO in and out. The inverse-volatility portfolios continually adjust the relative weighting as well. So it's really more an adaptive model than a pure timing model. The timing part mainly gets the more favorable bonds.

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Re: Refinements to Hedgefundie's excellent approach

Post by PluckyDucky » Wed Jul 17, 2019 9:05 am

Can you explain more on the mechanics of how it works?

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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Wed Jul 17, 2019 9:46 am

PluckyDucky wrote:
Wed Jul 17, 2019 9:05 am
Can you explain more on the mechanics of how it works?
The model implementation requires some external preprocessing outside of portfolio visualizer.

PV works with actual tickers or imported tickers. I use imported tickers to represent specific portfolio combinations that I want PV to select among.

First I created inverse-volatility portfolios based on UPRO & TMF, and UPRO & TMV (actually using simulated monthly versions). I made these in an Excel worksheet.

The portfolio return for each month is the weighted return for the two components. For example, the upro/tmf return is

uprotmf_return = w * upro_return + (1 - w) * tmf_return
w = sd_tmf / (sd_upro + sd_tmf)

I just use the previous month's volatility for the inverse-volatility weights.

I imported these two portfolio returns into PV as tickers. You might call them UPROTMFSIM and UPROTMVSIM. I also imported simulated TMF and TMV as tickers.

I give the PV dual momentum model these simulated tickers as options to work with, and only allow the model to select one of the four tickers.

So basically the dual momentum model is selecting between UPROTMFSIM, UPROTMVSIM, TMFSIM, and TMVSIM, for the best expected positive gain each month; if none of them are positive, then it defaults to TMFSIM as the "cash" option.

In the earlier dual momentum model, I did something similar but considered portfolios with several fixed weights between UPROSIM and TMFSIM. In this case I required that the dual momentum model select three or four portfolios at the same time to get a poor man's inverse volatility model.

Is this what you are looking for? Or is it more the theory?

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Re: Refinements to Hedgefundie's excellent approach

Post by PluckyDucky » Wed Jul 17, 2019 12:25 pm

That's what I was looking for. Why did you use the dual momentum model?

Is there a reason you look at indicators on the LETF instead of the underlying ETF? Is one way better than the other?

It seems like the excellent adventure has been hashed out for the basic leveraged balanced portfolio idea and people are discussing timing now to try to enhance it. If there were a simple way to switch TMF and TMV and even UPRO and SPXU, that would be cool.

M1Finance where I set mine up isn't made for timing changes as far as I know, but it is pretty easy to redo the pies and rebalance.

For example, the 200 day sma timing method is common.

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Re: Refinements to Hedgefundie's excellent approach

Post by MotoTrojan » Wed Jul 17, 2019 12:38 pm

PluckyDucky wrote:
Wed Jul 17, 2019 12:25 pm
That's what I was looking for. Why did you use the dual momentum model?

Is there a reason you look at indicators on the LETF instead of the underlying ETF? Is one way better than the other?

It seems like the excellent adventure has been hashed out for the basic leveraged balanced portfolio idea and people are discussing timing now to try to enhance it. If there were a simple way to switch TMF and TMV and even UPRO and SPXU, that would be cool.

M1Finance where I set mine up isn't made for timing changes as far as I know, but it is pretty easy to redo the pies and rebalance.

For example, the 200 day sma timing method is common.
Those sorts of changes are a lot more hand-wavey IMHO. TMV and SPXU both have expected negative returns, not something I want to play with. Dynamic allocation/volatility though shows some promise and still maintains a positive expected return.

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Re: Refinements to Hedgefundie's excellent approach

Post by Hydromod » Wed Jul 17, 2019 1:34 pm

MotoTrojan wrote:
Wed Jul 17, 2019 12:38 pm
Those sorts of changes are a lot more hand-wavey IMHO. TMV and SPXU both have expected negative returns, not something I want to play with. Dynamic allocation/volatility though shows some promise and still maintains a positive expected return.
It's pretty clear that one should want to use the funds that have expected positive returns.

It's also true that TMV and SPXU have expected negative returns under current conditions (1982 to present). But the question is what happens if conditions change?

I'm trying to be prepared for conditions returning to 1955 to 1982, for example.
Hydromod wrote:
Sat Jul 13, 2019 1:17 am
  • Portfolio 1 is the inverse-volatility weighted UPRO/TMF analog.
  • Portfolio 2 is the inverse-volatility weighted UPRO/TMV analog.
  • Portfolio 3 is the TMV should be TMF. Dang. analog.
The benchmark is the 40/60 UPRO/TMF analog.

Image

Notice that there are several periods of interest: (i) 1955-1967, (ii) 1967-1983, (iii) 1983-2000, (iv) 2000-2010, and (v) 2010-present.

The 1967 and 2010 breakpoints correspond to the switches in correlation in joan_01's figure. The 1983 breakpoint corresponds to the switch in Fed policy.

So we see that
  • prior to the 1967 breakpoint, the inverse-volatility and 40/60 track closely,
  • between 1967 and 1983, the inverse-volatility tracks below the 40/60,
  • between 1983 and 2010, the inverse-volatility and 40/60 track closely in parallel,
  • after the 2010 breakpoint, the inverse-volatility tracks closely above the 40/60 (by surviving 2010 better).
While TMF tracks down, UPRO/TMV performs better, and while TMF tracks up, UPRO/TMF performs better. These trends are amplified or muted, depending on the correlation between UPRO and TMF/TMV.
If I allow monthly switching between (optimized) UPRO/TMF, (optimized) UPRO/TMV, TMF, and TMV, I get a CAGR of 20.83% from 1956 to 1982.

Without allowing TMV, I get a CAGR of -0.47%.

You simply do better with TMV than TMF prior to 1982.

That there's the point of considering TMV. Having the strategy in my back pocket if needed.

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