Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

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jimbomahoney
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Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by jimbomahoney » Wed Feb 12, 2020 6:06 am

[Disclaimer - I have nothing to do with BreakingTheMarket, nor do I know who runs it - I'm just an average Joe with a nerdy streak]

Hi all,

I've been fascinated by, and roughly using, a Permanent Portfolio for my investing for some time.

Having read "How I Found Freedom in an Unfree World" as well as all of Taleb's books, I'm a "believer" in our inability to predict the future / appreciate tail-risk etc.

However, as a data and graph nerd, I've also always been fascinated with things like market timing, asset weighting etc.

I've previously written a few backtesting scripts that attempted to time the market (summary, as many of you will probably know already, is that it can't be done).

However, this guy has come up with a beautiful, mathematical method to decide what weight to assign each of the classic assets in the Permanent Portfolio.

EDIT - I appreciate that one needs to go hunting on that website to piece together what he's actually doing, so for general perusal, I recommend looking for the posts that are not "Portfolio on mm-dd-YY" and instead examine the ones with specific titles. This is as good a place to start as any. EDIT - I've also added links to posts of interest in some of my other responses - see my posts below.

Despite being a novice R coder, I've managed to piece together all the information in his posts and create a script that appears to work for the assets available to me, and priced in my currency.

I thought I would post here, as you may all be interested in his methods (I've only seen a couple of posts here mention his site before). I'd also be intrigued to hear others' thoughts.

The risk, as far as I can see it, for me is three-fold:

1) I only have 9 years of data to backtest.
2) I'm using index funds, rather than ETFs, which adds additional trading lag. [Removed ETF vs. index funds reference, as it's not relevant to the discussion]
3) My code might be wrong - since his methods are quite complex, I've had to make a number of simplifications in terms of cross-asset correlations and asset weights.

Having said that, my script seems to work, as including asset correlation in the weights improves the CAGR and Sharpe when compared with the method that simply weights assets based on their volatility (SD) / annual return.

Lastly, this thread is not about my code, which is almost certainly full of errors / look-ahead bias / too little data, but about BTM's theory of Geometric Rebalancing.
Last edited by jimbomahoney on Fri Feb 14, 2020 2:21 pm, edited 4 times in total.

dandinsac
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by dandinsac » Wed Feb 12, 2020 9:29 am

Thanks for sharing this site. I found it interesting as well.

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jimbomahoney
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by jimbomahoney » Wed Feb 12, 2020 2:04 pm

[Disclaimer - I know, both from experience and from theory, that backtesting is to be taken with a HUGE pinch of salt]

Some examples of the output of my script, which is my novice attempt to recreate what BreakingTheMarket has described on his blog:

Asset Weights over time, taking into account correlation (dotted lines for data are without correlation applied for comparison; horizontal dotted are average):

Image

Average for the period is ~20% Gold (Blue line), 45% Stocks (Green Line), 35% Bonds (Red Line), 0% Cash (Purple).

Returns:

Image

The key lines to concentrate on are:

1) Green line = stocks
2) Black line = Permanent Portfolio, rebalanced to maintain 25% in each asset.
3) Medium blue line ("Optimal Correlated Weights").

Stats:

Image

Annual Returns, including comparison with a 60/20/20 split : (UPDATED)

Image

Summary

This method appears to give stockmarket-like returns, but with almost PP-like volatility, and could therefore be leveraged. Correlation definitely helps, but was a complete nightmare to code!

Bonus graph

Just because I love graphs, as well as learning to code, this one is a test of ~15,000 random portfolios of various weights for each asset over the same period. I use it as a "sanity check". It's saying what would have been the best fixed ratio of assets to use over the period.

Image

Best Sharpe would have been 23% Bonds, 54% Stocks, 22% Gold, 1% Cash

"Optimal" (for me) would have been 15% Bonds, 58% Stocks, 27% Gold, 0% Cash.

Again, this thread is not about this code - I did this just to challenge myself to see if I could piece together what BTM is doing. It was a fun challenge, both given the nature of his somewhat cryptic / piecemeal snippets and given the nature of some of the mathematics involved. I'm neither an experienced coder, nor mathematician. There was a lot of this... :oops:
Last edited by jimbomahoney on Fri Feb 14, 2020 2:46 pm, edited 4 times in total.

MotoTrojan
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by MotoTrojan » Wed Feb 12, 2020 3:08 pm

Non of these assets have a lack of past data. Why are you not using other proxies to gather decades of results throughout various market cycles and conditions?

I don't quite understand why you feel an ETF is less safe than a Mutual Fund. An ETN is one thing, but I can't understand what makes an ETF a concern.

rascott
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by rascott » Wed Feb 12, 2020 3:46 pm

You realize that an ETF is a fund, right?.... it's right there in the name.

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jimbomahoney
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by jimbomahoney » Wed Feb 12, 2020 4:59 pm

rascott wrote:
Wed Feb 12, 2020 3:46 pm
You realize that an ETF is a fund, right?.... it's right there in the name.
You realize that this thread is about geometric rebalancing to minimise volataility, right? It's right there in the title.

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jimbomahoney
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by jimbomahoney » Wed Feb 12, 2020 5:00 pm

MotoTrojan wrote:
Wed Feb 12, 2020 3:08 pm
Non of these assets have a lack of past data. Why are you not using other proxies to gather decades of results throughout various market cycles and conditions?
Because BTM has already done that for me.

I want to make sure I'm recreating the theory to apply to assets that I want to trade / relevant to the currency with which I'm working.
MotoTrojan wrote:
Wed Feb 12, 2020 3:08 pm
I don't quite understand why you feel an ETF is less safe than a Mutual Fund. An ETN is one thing, but I can't understand what makes an ETF a concern.
I just have this weird paranoia about ETF vs. OEICs (what I meant when I said "fund"). I guess it's based on thing like this.

Anyway, ETF vs. OEIC vs. Fund vs. whatever is not relevant to the discussion at hand, so I won't go off-topic again.
Last edited by jimbomahoney on Wed Feb 12, 2020 5:03 pm, edited 1 time in total.

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willthrill81
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by willthrill81 » Wed Feb 12, 2020 5:01 pm

jimbomahoney wrote:
Wed Feb 12, 2020 4:59 pm
rascott wrote:
Wed Feb 12, 2020 3:46 pm
You realize that an ETF is a fund, right?.... it's right there in the name.
You realize that this thread is about geometric rebalancing to minimise volataility, right? It's right there in the title.
You didn't address the question. Mutual funds and exchange traded funds are both funds.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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jimbomahoney
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by jimbomahoney » Wed Feb 12, 2020 5:08 pm

Hmm, I suspect I should have known from other threads that this would get derailed into grammar / one-upmanship / holier than thou instead of staying on-topic.

I had hoped that the mathematics behind BTM's theory would appeal, combined with the PP, but I think the PP is frowned upon around here?

However, the method seems sound and is aimed at increasing CAGR and Sharpe, which I would have thought would have been the aim for most (all?) posters here.

Either way, could we pretty please stay on-topic with the discussion of BTM's theory, rather than my personal idiocy? :sharebeer
Last edited by jimbomahoney on Fri Feb 14, 2020 2:23 pm, edited 1 time in total.

rich126
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by rich126 » Wed Feb 12, 2020 5:28 pm

It seems like he is trading or rebalancing weekly. That seems excessive. In a taxable account it would be a mess. With all of the zero commissions around, at least that expense is gone.

How do the numbers look if you do something quarterly?

I started to go through his web site but haven't had time to go through it all. While I find the numbers interesting the frequent trading is definitely a concern. I also got the impression, maybe falsely, that he seemed to be rather full of himself. Rather that just document everything in a long post, he seemed to drag things out over months.

Unlike most here, I'm not a big indexer and think it is the only way to succeed, and honestly, going forward I think those returns will be poor although I hope I'm wrong.

Uncorrelated
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by Uncorrelated » Wed Feb 12, 2020 5:54 pm

The problem with this analysis is that it only looks at an extremely short time period, and it is considered impossible to accurately estimate the parameters involved. Your analysis boils down to a mean variance analysis, which is a very valid analysis (I use it often), but is very much garbage-in-garbage out and without an out-of-sample analysis, there is no way of knowing how much you overfitted.

To give some indication to how difficult it is to estimate the correlations between different assets, the paper Gold Returns by Robert J. Barro investigates the correlation and return of gold over a long time period. In the period 1975-2011, neither the returns nor the correlation of gold vs stocks or bonds is statistically significantly different from zero (at the 95% confidence threshold). There is also the argument that gold is a big case or recency bias, there are very good arguments for using silver and a bunch of other precious metals and commodities to diversify, but that hasn't really panned out lately. I would consider picking gold over a commodities index a sin comparable to picking amazon over total stock market.

So in summary, this analysis is only as useful as the underlying assumptions. I believe that there is no reasonable set of assumptions that result in the inclusion of gold in a portfolio, so.. there is that.

Also, there is no particular reason why optimizing for max sharpe ratio or max CAGR is useful. Your goal should be to maximize your personal utility (or risk aversion) over the probability distribution of outcomes. For very specific cases that rarely occur in practice, this coincidences with maximizing the CAGR. Your chart marks the optimal portfolio for your specific assumptions, but there is no way of knowing which one is optimal without knowing your individual risk tolerance. Depending on your risk tolerance the optimal portfolio might be further to the right or left.

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jimbomahoney
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by jimbomahoney » Thu Feb 13, 2020 3:11 am

rich126 wrote:
Wed Feb 12, 2020 5:28 pm
It seems like he is trading or rebalancing weekly. That seems excessive. In a taxable account it would be a mess. With all of the zero commissions around, at least that expense is gone.

How do the numbers look if you do something quarterly?
He's posted about that here.

He's suggested, maybe on that page or elsewhere on the site, that due to the high frequency of trades, the portfolio should be ~300k.
Uncorrelated wrote:
Wed Feb 12, 2020 5:54 pm
The problem with this analysis is that it only looks at an extremely short time period, and it is considered impossible to accurately estimate the parameters involved. Your analysis boils down to a mean variance analysis, which is a very valid analysis (I use it often), but is very much garbage-in-garbage out and without an out-of-sample analysis, there is no way of knowing how much you overfitted.
Thanks, that's a valid concern too. Although the data I'm using is short, and I absolutely agree with needing as much data as possible (during my backtesting / momentum / market-timing days, I thought I had found a "magic" frequency that worked beautifully for one market, but when I tested it on another market over a long period of time, Buy n Hold would have been better! I'm now very sceptical of anyone suggesting that their X day / Y day moving average method works because they invariably run it over the past 20 years, which of course was two massive bull and bear markets).

BTM has tested over much longer time periods. He also addresses, somewhat, the GIGO issue.
Uncorrelated wrote:
Wed Feb 12, 2020 5:54 pm
Also, there is no particular reason why optimizing for max sharpe ratio or max CAGR is useful. Your goal should be to maximize your personal utility (or risk aversion) over the probability distribution of outcomes. For very specific cases that rarely occur in practice, this coincidences with maximizing the CAGR. Your chart marks the optimal portfolio for your specific assumptions, but there is no way of knowing which one is optimal without knowing your individual risk tolerance. Depending on your risk tolerance the optimal portfolio might be further to the right or left.
Agreed. Again, that's just my personal "bonus graph" for fun. The "Optimal" point is just what I consider optimal for me, plus it was fun trying to code the detection of that top left corner.

In a perfect scenario, we'd all shoot for infinite returns and infinite Sharpe Ratios though! :D

dandinsac
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by dandinsac » Thu Feb 13, 2020 9:39 am

Great work! After reading the BTM I’m impressed you were able to create this. The BTM weekly rebalance was much more dynamic than I expected.

For an individual investor, one would have to have a tax advantaged account with low trading fees, the willingness to spend time analyzing and rebalancing, and the discipline to stay with it. It’s probably not practical for more than just a few dedicated folks.
jimbomahoney wrote:
Wed Feb 12, 2020 2:04 pm
Just because I love graphs, as well as learning to code, this one is a test of ~15,000 random portfolios of various weights for each asset over the same
Best Sharpe would have been 23% Bonds, 54% Stocks, 22% Gold, 1% Cash

"Optimal" (for me) would have been 15% Bonds, 58% Stocks, 27% Gold, 0% Cash.
EDITED, this question was already answered above: For the equal split, did you periodically rebalance the portfolio as well, or was it static over the study period?

Your post got me thinking on how I manage my investments. I can’t really move the funds around weekly due to trading restrictions. But, I do have recurring investments that I could direct to specific areas. Right now, those investments are directed to the investment(s) that is “under” my target valuation(s). My approach seems lacking as I don’t ever reevaluate the targets themselves. The BTM blog shows that the asset allocation target vary a lot. And compared with the fixed 25% approach, BTM did much better.

Can the BTM methodology be applied to do a better job of directing recurring investments and doing monthly rebalancing? Or is simply rebalancing enough?
Last edited by dandinsac on Thu Feb 13, 2020 12:34 pm, edited 1 time in total.

snailderby
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by snailderby » Thu Feb 13, 2020 9:53 am

1. This is fascinating. Thanks for sharing.

2. Does he address the best way to leverage this portfolio, if someone wanted to do that?

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jimbomahoney
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by jimbomahoney » Fri Feb 14, 2020 11:46 am

snailderby wrote:
Thu Feb 13, 2020 9:53 am
1. This is fascinating. Thanks for sharing.

2. Does he address the best way to leverage this portfolio, if someone wanted to do that?
Glad you like it too! I'm loving it! I finally have a mathematical way to assign asset weights!

Re: Leverage - yes, the technical details are in this post and this post.

It's also discussed here and here.

I managed to code (in R) an approximation of both the correlation and leverage methods. Again, this was seriously challenging but seriously fun!

I've added an annual returns bar chart to an earlier post showing the various assets, an equal split (rebalanced) and a 60/20/20 (Stocks/Bonds/Gold), again rebalanced as well as the BTM, BTM (correlation) and leveraged versions. Again, that's for the assets I'm choosing to use (Long UK Gilts, World Stock Market and Gold in GBP).

klaus14
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by klaus14 » Fri Feb 14, 2020 9:56 pm

can someone explain how their system works?
it looks like every friday, they look at weekly std and correlations of assets.
then they determine allocations to optimize what? expected (mean) geometric return?
so they use historical return expectations?
15% VFMF, 15% NTSX | 10% ISCF, 5% EFAV | 5% FNDE, 5% EMGF, 5% VEGBX, 5% LEMB | 15% EDV, 5% CD (5y), 5% I/EE Bonds | 10% GLDM

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jimbomahoney
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by jimbomahoney » Sat Feb 15, 2020 8:29 am

klaus14 wrote:
Fri Feb 14, 2020 9:56 pm
can someone explain how their system works?
it looks like every friday, they look at weekly std and correlations of assets.
then they determine allocations to optimize what? expected (mean) geometric return?
so they use historical return expectations?
I've provided plenty of links in each of my posts to the more relevant entries on his blog.

e.g. Check the "GIGO" link from my previous post.

klaus14
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by klaus14 » Sat Feb 15, 2020 2:04 pm

jimbomahoney wrote:
Sat Feb 15, 2020 8:29 am
klaus14 wrote:
Fri Feb 14, 2020 9:56 pm
can someone explain how their system works?
it looks like every friday, they look at weekly std and correlations of assets.
then they determine allocations to optimize what? expected (mean) geometric return?
so they use historical return expectations?
I've provided plenty of links in each of my posts to the more relevant entries on his blog.

e.g. Check the "GIGO" link from my previous post.
i checked those links but still didn't get the algorithm. Have you managed to produce the numbers he posts?
Can you share your code?
it shouldn't be that complicated. inputs seem to be daily returns of 3 assets. and maybe return expectations.
15% VFMF, 15% NTSX | 10% ISCF, 5% EFAV | 5% FNDE, 5% EMGF, 5% VEGBX, 5% LEMB | 15% EDV, 5% CD (5y), 5% I/EE Bonds | 10% GLDM

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Ethelred
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by Ethelred » Sat Feb 15, 2020 2:47 pm

It's an interesting blog, but I am sceptical to some extent. I'm not sure all of his assumptions are reasonable, and I don't think economists do concentrate on arithmetic averages of growth rate instead of compound to the extent he claims. That said, the CAGR and maximum drawdown he claims from back testing are consistent and very impressive.

I too was unable to find the actual algorithm he used, but the inputs seem to be current returns, current volatility (standard deviation?) and current correlation between each asset. Not sure if current means daily or a shorter period than that.

mjb
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by mjb » Sat Feb 15, 2020 4:24 pm

I read his blog. He has some good points about geometric mean and effects of rebalancing.

However, he has some math errors that really skew his results and he ignores anyone that points them out. Mainly his conversion from arithmetic to geometric.

Additionally, several of his assumptions aren't fully true and he is using a short time horizon.

All he is really doing is just a flavor of risk parity.

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jimbomahoney
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Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Post by jimbomahoney » Sun Feb 16, 2020 8:15 am

klaus14 wrote:
Sat Feb 15, 2020 2:04 pm
i checked those links but still didn't get the algorithm. Have you managed to produce the numbers he posts?
Can you share your code?
it shouldn't be that complicated. inputs seem to be daily returns of 3 assets. and maybe return expectations.
No, he doesn't give the algorithm, just the explanation from which I attempted to code it.

Yes, I get very similar returns when I backtest using the same assets as him (SPY, TLT, GLD in USD). Sometimes I get better returns, sometimes worse.

I can't match his volatility numbers though - for example, over the period 2005 - 2019, he reports about a 7% annual SD, whereas I can only achieve about 9%. I think this is almost certainly because:

1) I don't know what period he's using to get trailing annual returns. I'm guessing 2-3 years.
2) I'm not correcting for the correlations as well as him. I've had to cut corners to get it into code.

No, I'm not going to share my code because if "it shouldn't be that complicated", then anyone could code it, right? :wink:

But seriously, I don't want to share the code because:

a) It's ugly because I'm a novice (I started teaching myself R about 6 months ago).
b) It's probably wrong, although it seems to approximate his results, which is reassuring.
c) Probably most importantly, it isn't in a structure suitable to provide to someone else and they simply be able to run it. It has some dependencies, hard-coded directories and personal details. I can't be bothered to simplify it so that others can use it.
Ethelred wrote:
Sat Feb 15, 2020 2:47 pm
I too was unable to find the actual algorithm he used, but the inputs seem to be current returns, current volatility (standard deviation?) and current correlation between each asset. Not sure if current means daily or a shorter period than that.
Yes, for inputs I'm using:

1) Trailing annual returns (2 - 3 years probably) to estimate "current" returns. Shorter leads to more extreme asset allocation swings. Longer leads to more lag in asset allocation.
2) "Current" volatility, which is between 20 and 50 days (I use 38, as I found for my dataset, that worked best, but I don't think it makes much difference beyond about 30 days).
3) "Current" correlation - I use the same period as volatility.

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