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

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breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

Uncorrelated wrote:
Wed Feb 19, 2020 3:37 pm
The academic approach is to use the arithmetic excess return, the return above the t-bill rate. This figure stays stable during periods of inflation/deflation.

I think the idea of calculating the arithmetic return based on anything less than the full sample is an extremely bad idea. There is a wide array of research that suggests that the monthly return of stocks has a correlation of zero with the return of the preceding month. Some academics claim it's impossible to create a better estimate than the average over the full sample.

What is the rationale for using gold, given that gold has a return and correlation with stocks/bonds that are statistically indistinguishable from zero. And that factors (for example, the value factor) have statistically significant positive return? How do you avoid survivorship bias with gold?

I don't think the graphs showing the rebalanced interval can be interpreted with any statistical confidence. The best resource I know about rebalancing is this page: https://www.aacalc.com/docs/when_to_rebalance. Don't forget transaction costs either, 0.5% per transaction seems to be a common figure.
jimbomahoney wrote:
Wed Feb 19, 2020 1:16 pm
Yes, I totally get that the arithmetic mean return is 7.6% (take the average of each year's returns).

I also totally get the geometric mean return is 3.1% (take the total period return and raise to one over the total period etc.)
His formula for calculating geometric from arithmetic assumes that the underlying distribution is normal and independently distributed. But if you are using a market timing algorithm, then chances are that you don't believe that returns are normal and independently distributed...
jimbomahoney wrote:
Wed Feb 19, 2020 11:30 am
6) No leverage, or possibly slightly small leverage using the remnants of a low-cost loan if I borrow to get the bathroom done or some such, or remortgage.
If your risk tolerance is so low you are unwilling to use 2-3x leverage, CAGR is unsuited as a performance metric.
Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.

mjb
Posts: 168
Joined: Sat Nov 30, 2013 11:43 am

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

breakingthemarkt wrote:
Fri Feb 21, 2020 5:31 pm
mjb wrote:
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.

Where did I ignore someone pointing out a perceived error in the math?

mjb
Posts: 168
Joined: Sat Nov 30, 2013 11:43 am

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

breakingthemarkt wrote:
Fri Feb 21, 2020 5:45 pm
Uncorrelated wrote:
Wed Feb 19, 2020 3:37 pm
The academic approach is to use the arithmetic excess return, the return above the t-bill rate. This figure stays stable during periods of inflation/deflation.

I think the idea of calculating the arithmetic return based on anything less than the full sample is an extremely bad idea. There is a wide array of research that suggests that the monthly return of stocks has a correlation of zero with the return of the preceding month. Some academics claim it's impossible to create a better estimate than the average over the full sample.

What is the rationale for using gold, given that gold has a return and correlation with stocks/bonds that are statistically indistinguishable from zero. And that factors (for example, the value factor) have statistically significant positive return? How do you avoid survivorship bias with gold?

I don't think the graphs showing the rebalanced interval can be interpreted with any statistical confidence. The best resource I know about rebalancing is this page: https://www.aacalc.com/docs/when_to_rebalance. Don't forget transaction costs either, 0.5% per transaction seems to be a common figure.
jimbomahoney wrote:
Wed Feb 19, 2020 1:16 pm
Yes, I totally get that the arithmetic mean return is 7.6% (take the average of each year's returns).

I also totally get the geometric mean return is 3.1% (take the total period return and raise to one over the total period etc.)
His formula for calculating geometric from arithmetic assumes that the underlying distribution is normal and independently distributed. But if you are using a market timing algorithm, then chances are that you don't believe that returns are normal and independently distributed...
jimbomahoney wrote:
Wed Feb 19, 2020 11:30 am
6) No leverage, or possibly slightly small leverage using the remnants of a low-cost loan if I borrow to get the bathroom done or some such, or remortgage.
If your risk tolerance is so low you are unwilling to use 2-3x leverage, CAGR is unsuited as a performance metric.
Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.
Actually in some cases your equation is off by more than 50%

Uncorrelated
Posts: 537
Joined: Sun Oct 13, 2019 3:16 pm

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

breakingthemarkt wrote:
Fri Feb 21, 2020 5:45 pm
Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.
I made no claims on whether the formula is a good or bad approximation of the geometric mean, I don't know. I said that CAGR is an unsuited performance metric.

I don't understand that you say that investment returns are i.i.d. and markets are efficient. If you truly believe those things, than it is impossible to improve upon a static allocation by market timing.

chi_capitalist
Posts: 3
Joined: Sat Feb 22, 2020 8:53 am

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

Wow Breakingthemarkets - super nice work and great blog

You have cracked and done a nice job of documenting something that has been a puzzle for me for a few years - how to manage higher risk portfolios than mean variance delivers, without doing something that is a total hack.

What I understand BTM to be saying:
1. Short run is well described by arithmetic returns, but long run is geometric, and you “eat” geometric - beyond the formulas, make sure you know which you are thinking about / estimating / using in any logic you apply to investing
2. BTM is using an objective of maximizing geometric mean of portfolio, and then Kelly betting the result. There are other ways to solve the allocation problem, but IF you have good inputs to the formulas, this is definitively the mathematically fastest way to grow a portfolio. There is some clever math from some academics that solves the geometric mean optimization - rather than just looking at the equation, I suggest clicking through to the referenced paper.[https://papers.ssrn.com/sol3/papers.cfm ... id=2927791] Very interesting. So of course it is all about the inputs…
3. For inputs, it appears BTM is using short run trailing vols and correlation and some simple carry measures like current yield, earnings / price, etc…
4. He discusses a range of leverage limits, rebalancing periods, etc…

As I just happen to have a quite robust backtesting and historical data framework built out, I thought I would try this, and finally set up an account and log in and let people know what I see. I don’t know how to post all the fancy graphs and stuff from R here, but I thought some of you might find an independent duplication of this effort interesting.

I am using as inputs the simplest I have available in my system:
- simple carry measures for long run expected returns - NOT any sort of momentum / trailing estimates (e.g. 20 year yields, 1 year yields, a 10 year CAPE adjusted for real growth during the 10 year window, gold matching inflation, etc…
- long run vols to back into rough long run arithmetic return expectations.
- short run correlation and vol estimation based on trailing recent history

Rough results are pretty good - for example:
- At 1.0 leverage, allowing up to 1x Kelly bet, monthly, with gold, long treasuries, cash, and US equities:
- Since 1986 where my daily data becomes limited:
- Sharpe is 0.84,
- Return above cash is ~7%, volatility ~8%
- Positive skew to annual returns, worst year is -6% vs cash in 1994
- Without leverage I can’t quite match the returns BTM shows, but directionally the same

And with leverage, and assuming some realistic costs of the leverage at retail, I see slightly over 1.0-1.1 Sharpe at ~15-18% volatility with Kelly betting. And similar positive skew and no substantial drawdowns other than in 1994. I get a little closer to BTM’s results if I assume very low leverage cost (e.g. if I were implementing with futures) - quite close but can’t quite match whatever BTM is doing.

Relative to MVO or a more static portfolio, very clear benefits are:
- Better at carrying higher risk when valuations and volatility suggest that is a good bet. MVO fails here terribly without much additional logic.
- Great at ramping down overall exposure in a logical and consistent way when spreads drop too narrow (e.g. 1999-2001) or when vol spikes (e.g. 2008)

A few downsides to manage or consider:
- The most spectacular results are at weekly or daily and with leverage. At this level this is a job, not a passive investment, turnover is high, and much of that turnover is likely both low value (due to tiny changes in estimates) and tough to get rid of. (Which tiny changes are important vs not?)
- Even at slower (monthly / quarterly) there is value, but no everyone has risk tolerance to carry 100% equity positions, so there may be some value for some people in blending this strategy at monthly/quarterly with something more static/strategic.

But overall pretty slick.

A couple comments for the BH folks commenting.

1. This may work also with momentum or trailing returns as an estimator of returns, but I did not get the impression that that was the intent of BTM, and it definitely IS NOT necessary. That being said, SOMETHING has to estimate the returns. Saying “efficient market” does not get you these results unless you have a way to prioritize equities over other things, and equities more some times than others. Volatility and correlation alone don’t get you there.
2. I am seeing in the results very substantial value in simple value / carry estimates, including at quite short run. CAPE only predicts nominal returns at long run, but high/low spread of treasuries vs cash, of E/P vs cash, and E/P vs treasuries all are important and quite predictive in daily/weekly/monthly results.
3. The trick is in managing the fact that the input estimates are generally crap. So this algorithm on its own starts having trouble and generating really insane turnover if you run it with more than these 4 asset classes at a weekly level. This is where I am spending my time.
4. On the points re arithmetic vs geometric measures of a distribution, the carry estimates are clearly estimates of the GEOMETRIC distribution, as in the case that (e.g.) the bond delivers at maturity, that is in fact the return you get. And there is variance in the mean time. So the expected ARITHMETIC distribution is actually that carry plus 0.5 * the variance. I am embarrassed to say I have had this wrong and sometimes even backwards, despite quite a lot of fancy education in analytical finance.

Regards,

Chi_Capitalist.

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

mjb wrote:
Sat Feb 15, 2020 4:24 pm

All he is really doing is just a flavor of risk parity.
That's my take.

I'd rather listen to Dalio's opinions on this kind of tactic -- he's been doing risk parity for decades, with billions AUM.
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

breakingthemarkt wrote:
Fri Feb 21, 2020 5:42 pm

Risk Parity typically has portfolio weights of:
Stocks: 16%-30%
Bonds: 55%-70%
https://mebfaber.com/2015/05/28/chapter ... ortfolios/

Stocks: 50%
Bonds: 35%
https://breakingthemarket.com/geometric ... unlevered/

Kind of the exact opposite weighting wouldn’t you say? Have you ever seen a RP portfolio hold far more stocks than bonds?
RP ports do this for a good reason:

They're trying to match the *risk* (hence the name), and stocks carry more risk per unit of capital than bonds.

A portfolio that is 50% stocks / 35% bonds / 15% cash will get >90% of its risk decomposition from stocks.
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

chi_capitalist wrote:
Sat Feb 22, 2020 10:15 am
Wow Breakingthemarkets - super nice work and great blog

You have cracked and done a nice job of documenting something that has been a puzzle for me for a few years - how to manage higher risk portfolios than mean variance delivers, without doing something that is a total hack.

What I understand BTM to be saying:
1. Short run is well described by arithmetic returns, but long run is geometric, and you “eat” geometric - beyond the formulas, make sure you know which you are thinking about / estimating / using in any logic you apply to investing
JP Morgan gives their 10 year forecasts in both arithmetic and geometric values so you can plug it into whatever model you want to use accordingly.
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

chi_capitalist
Posts: 3
Joined: Sat Feb 22, 2020 8:53 am

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

JP Morgan gives their 10 year forecasts in both arithmetic and geometric values so you can plug it into whatever model you want to use accordingly.
Not sure I know how to quote correctly - just learning the forum tools.

Yes I know there are lots of sources for estimates, and they are interesting to look at.

I tend to use fewer simpler estimates for only very broad asset classes, and prefer to have mine built in a way that I know they are from consistent data sources and are in all my backtests in a way that is completely consistent with what I am doing in live trading, so I am building all my own from FRED data, shiller data, FF data, etc... Trying to be very systematic to ensure that at minimum I am not doing something that did not work like I might expect historically, and so that I am not "reinventing" to fit some narrative every week/month based on what I've seen in the news, or what I recent made/lost money on.

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

mjb wrote:
Fri Feb 21, 2020 8:25 pm
breakingthemarkt wrote:
Fri Feb 21, 2020 5:31 pm
mjb wrote:
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.

Where did I ignore someone pointing out a perceived error in the math?
Example?

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

mjb wrote:
Fri Feb 21, 2020 8:26 pm
breakingthemarkt wrote:
Fri Feb 21, 2020 5:45 pm
Uncorrelated wrote:
Wed Feb 19, 2020 3:37 pm
The academic approach is to use the arithmetic excess return, the return above the t-bill rate. This figure stays stable during periods of inflation/deflation.

I think the idea of calculating the arithmetic return based on anything less than the full sample is an extremely bad idea. There is a wide array of research that suggests that the monthly return of stocks has a correlation of zero with the return of the preceding month. Some academics claim it's impossible to create a better estimate than the average over the full sample.

What is the rationale for using gold, given that gold has a return and correlation with stocks/bonds that are statistically indistinguishable from zero. And that factors (for example, the value factor) have statistically significant positive return? How do you avoid survivorship bias with gold?

I don't think the graphs showing the rebalanced interval can be interpreted with any statistical confidence. The best resource I know about rebalancing is this page: https://www.aacalc.com/docs/when_to_rebalance. Don't forget transaction costs either, 0.5% per transaction seems to be a common figure.
jimbomahoney wrote:
Wed Feb 19, 2020 1:16 pm
Yes, I totally get that the arithmetic mean return is 7.6% (take the average of each year's returns).

I also totally get the geometric mean return is 3.1% (take the total period return and raise to one over the total period etc.)
His formula for calculating geometric from arithmetic assumes that the underlying distribution is normal and independently distributed. But if you are using a market timing algorithm, then chances are that you don't believe that returns are normal and independently distributed...
jimbomahoney wrote:
Wed Feb 19, 2020 11:30 am
6) No leverage, or possibly slightly small leverage using the remnants of a low-cost loan if I borrow to get the bathroom done or some such, or remortgage.
If your risk tolerance is so low you are unwilling to use 2-3x leverage, CAGR is unsuited as a performance metric.
Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.
Actually in some cases your equation is off by more than 50%
Ok. Please provide and example of one of those cases if you can? I really don't want to be off by 50%.
Last edited by breakingthemarkt on Sat Feb 22, 2020 12:46 pm, edited 1 time in total.

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

Uncorrelated wrote:
Sat Feb 22, 2020 3:43 am
breakingthemarkt wrote:
Fri Feb 21, 2020 5:45 pm
Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.
I made no claims on whether the formula is a good or bad approximation of the geometric mean, I don't know. I said that CAGR is an unsuited performance metric.

I don't understand that you say that investment returns are i.i.d. and markets are efficient. If you truly believe those things, than it is impossible to improve upon a static allocation by market timing.
It's Impossible to market time iid and efficient markets if they grow through addition. But that relationship does not hold when the process grows through multiplication.

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

chi_capitalist wrote:
Sat Feb 22, 2020 12:22 pm
JP Morgan gives their 10 year forecasts in both arithmetic and geometric values so you can plug it into whatever model you want to use accordingly.
Not sure I know how to quote correctly - just learning the forum tools.

Yes I know there are lots of sources for estimates, and they are interesting to look at.

I tend to use fewer simpler estimates for only very broad asset classes, and prefer to have mine built in a way that I know they are from consistent data sources and are in all my backtests in a way that is completely consistent with what I am doing in live trading, so I am building all my own from FRED data, shiller data, FF data, etc... Trying to be very systematic to ensure that at minimum I am not doing something that did not work like I might expect historically, and so that I am not "reinventing" to fit some narrative every week/month based on what I've seen in the news, or what I recent made/lost money on.
The forecasts from Vanguard, Blackrock, JP Morgan, etc, all use multiple sources and models, many of which are the same as you're using, but they're going to be better and more sophisticated than any individual investor.

I can be fun to try to DIY, but I decided long ago that it's going to be quicker for me to use what the specialist experts are already putting out.
Last edited by watchnerd on Sat Feb 22, 2020 12:42 pm, edited 1 time in total.
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

chi_capitalist wrote:
Sat Feb 22, 2020 10:15 am
Wow Breakingthemarkets - super nice work and great blog

You have cracked and done a nice job of documenting something that has been a puzzle for me for a few years - how to manage higher risk portfolios than mean variance delivers, without doing something that is a total hack.

What I understand BTM to be saying:
1. Short run is well described by arithmetic returns, but long run is geometric, and you “eat” geometric - beyond the formulas, make sure you know which you are thinking about / estimating / using in any logic you apply to investing
2. BTM is using an objective of maximizing geometric mean of portfolio, and then Kelly betting the result. There are other ways to solve the allocation problem, but IF you have good inputs to the formulas, this is definitively the mathematically fastest way to grow a portfolio. There is some clever math from some academics that solves the geometric mean optimization - rather than just looking at the equation, I suggest clicking through to the referenced paper.[https://papers.ssrn.com/sol3/papers.cfm ... id=2927791] Very interesting. So of course it is all about the inputs…
3. For inputs, it appears BTM is using short run trailing vols and correlation and some simple carry measures like current yield, earnings / price, etc…
4. He discusses a range of leverage limits, rebalancing periods, etc…

As I just happen to have a quite robust backtesting and historical data framework built out, I thought I would try this, and finally set up an account and log in and let people know what I see. I don’t know how to post all the fancy graphs and stuff from R here, but I thought some of you might find an independent duplication of this effort interesting.

I am using as inputs the simplest I have available in my system:
- simple carry measures for long run expected returns - NOT any sort of momentum / trailing estimates (e.g. 20 year yields, 1 year yields, a 10 year CAPE adjusted for real growth during the 10 year window, gold matching inflation, etc…
- long run vols to back into rough long run arithmetic return expectations.
- short run correlation and vol estimation based on trailing recent history

Rough results are pretty good - for example:
- At 1.0 leverage, allowing up to 1x Kelly bet, monthly, with gold, long treasuries, cash, and US equities:
- Since 1986 where my daily data becomes limited:
- Sharpe is 0.84,
- Return above cash is ~7%, volatility ~8%
- Positive skew to annual returns, worst year is -6% vs cash in 1994
- Without leverage I can’t quite match the returns BTM shows, but directionally the same

And with leverage, and assuming some realistic costs of the leverage at retail, I see slightly over 1.0-1.1 Sharpe at ~15-18% volatility with Kelly betting. And similar positive skew and no substantial drawdowns other than in 1994. I get a little closer to BTM’s results if I assume very low leverage cost (e.g. if I were implementing with futures) - quite close but can’t quite match whatever BTM is doing.

Relative to MVO or a more static portfolio, very clear benefits are:
- Better at carrying higher risk when valuations and volatility suggest that is a good bet. MVO fails here terribly without much additional logic.
- Great at ramping down overall exposure in a logical and consistent way when spreads drop too narrow (e.g. 1999-2001) or when vol spikes (e.g. 2008)

A few downsides to manage or consider:
- The most spectacular results are at weekly or daily and with leverage. At this level this is a job, not a passive investment, turnover is high, and much of that turnover is likely both low value (due to tiny changes in estimates) and tough to get rid of. (Which tiny changes are important vs not?)
- Even at slower (monthly / quarterly) there is value, but no everyone has risk tolerance to carry 100% equity positions, so there may be some value for some people in blending this strategy at monthly/quarterly with something more static/strategic.

But overall pretty slick.

A couple comments for the BH folks commenting.

1. This may work also with momentum or trailing returns as an estimator of returns, but I did not get the impression that that was the intent of BTM, and it definitely IS NOT necessary. That being said, SOMETHING has to estimate the returns. Saying “efficient market” does not get you these results unless you have a way to prioritize equities over other things, and equities more some times than others. Volatility and correlation alone don’t get you there.
2. I am seeing in the results very substantial value in simple value / carry estimates, including at quite short run. CAPE only predicts nominal returns at long run, but high/low spread of treasuries vs cash, of E/P vs cash, and E/P vs treasuries all are important and quite predictive in daily/weekly/monthly results.
3. The trick is in managing the fact that the input estimates are generally crap. So this algorithm on its own starts having trouble and generating really insane turnover if you run it with more than these 4 asset classes at a weekly level. This is where I am spending my time.
4. On the points re arithmetic vs geometric measures of a distribution, the carry estimates are clearly estimates of the GEOMETRIC distribution, as in the case that (e.g.) the bond delivers at maturity, that is in fact the return you get. And there is variance in the mean time. So the expected ARITHMETIC distribution is actually that carry plus 0.5 * the variance. I am embarrassed to say I have had this wrong and sometimes even backwards, despite quite a lot of fancy education in analytical finance.

Regards,

Chi_Capitalist.
Nice summary. You've got a good grasp on what I'm doing.

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

watchnerd wrote:
Sat Feb 22, 2020 11:27 am
breakingthemarkt wrote:
Fri Feb 21, 2020 5:42 pm

Risk Parity typically has portfolio weights of:
Stocks: 16%-30%
Bonds: 55%-70%
https://mebfaber.com/2015/05/28/chapter ... ortfolios/

Stocks: 50%
Bonds: 35%
https://breakingthemarket.com/geometric ... unlevered/

Kind of the exact opposite weighting wouldn’t you say? Have you ever seen a RP portfolio hold far more stocks than bonds?
RP ports do this for a good reason:

They're trying to match the *risk* (hence the name), and stocks carry more risk per unit of capital than bonds.

A portfolio that is 50% stocks / 35% bonds / 15% cash will get >90% of its risk decomposition from stocks.
I was trying to show I'm not doing risk parity. No risk parity fund would have the weights my portfolio does.

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

breakingthemarkt wrote:
Sat Feb 22, 2020 12:40 pm

Nice summary. You've got a good grasp on what I'm doing.
It's one thing to play mad scientist with numbers, but it's a whole different animal to put significant portions one's investment portfolio into play.

I'm curious how much of your portfolio AA and/or net worth you're dedicating to this method?
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

Uncorrelated
Posts: 537
Joined: Sun Oct 13, 2019 3:16 pm

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

breakingthemarkt wrote:
Sat Feb 22, 2020 12:31 pm
Uncorrelated wrote:
Sat Feb 22, 2020 3:43 am
breakingthemarkt wrote:
Fri Feb 21, 2020 5:45 pm
Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.
I made no claims on whether the formula is a good or bad approximation of the geometric mean, I don't know. I said that CAGR is an unsuited performance metric.

I don't understand that you say that investment returns are i.i.d. and markets are efficient. If you truly believe those things, than it is impossible to improve upon a static allocation by market timing.
It's Impossible to market time iid and efficient markets if they grow through addition. But that relationship does not hold when the process grows through multiplication.
Sometimes I come across something that really doesn't make any sense. This is one of those cases.

In order to time the markets, there must be some elements that are predictable, meaning that the probability distribution of future returns on time A differs from time B. If returns are i.i.d., the best possible allocation is static.

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

watchnerd wrote:
Sat Feb 22, 2020 12:44 pm
breakingthemarkt wrote:
Sat Feb 22, 2020 12:40 pm

Nice summary. You've got a good grasp on what I'm doing.
It's one thing to play mad scientist with numbers, but it's a whole different animal to put significant portions one's investment portfolio into play.

I'm curious how much of your portfolio AA and/or net worth you're dedicating to this method?
It's the only way I invest in the stock/bond market.

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

Uncorrelated wrote:
Sat Feb 22, 2020 1:11 pm

Sometimes I come across something that really doesn't make any sense. This is one of those cases.

In order to time the markets, there must be some elements that are predictable, meaning that the probability distribution of future returns on time A differs from time B. If returns are i.i.d., the best possible allocation is static.
+1
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watchnerd
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Location: Seattle, WA, USA

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

breakingthemarkt wrote:
Sat Feb 22, 2020 1:16 pm

It's the only way I invest in the stock/bond market.
Kudos to putting it into real practice.

For me, personally, we use the public markets in stocks/bonds to get the 'dumb money', i.e. market beta, as cheaply and simply as possible.

I don't waste neurons trying to seek alpha in public markets, preferring to pursue that in private markets, which are less efficient.
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

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

Uncorrelated wrote:
Sat Feb 22, 2020 1:11 pm
breakingthemarkt wrote:
Sat Feb 22, 2020 12:31 pm
Uncorrelated wrote:
Sat Feb 22, 2020 3:43 am
breakingthemarkt wrote:
Fri Feb 21, 2020 5:45 pm
Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.
I made no claims on whether the formula is a good or bad approximation of the geometric mean, I don't know. I said that CAGR is an unsuited performance metric.

I don't understand that you say that investment returns are i.i.d. and markets are efficient. If you truly believe those things, than it is impossible to improve upon a static allocation by market timing.
It's Impossible to market time iid and efficient markets if they grow through addition. But that relationship does not hold when the process grows through multiplication.
Sometimes I come across something that really doesn't make any sense. This is one of those cases.

In order to time the markets, there must be some elements that are predictable, meaning that the probability distribution of future returns on time A differs from time B. If returns are i.i.d., the best possible allocation is static.
I do think volatility is related to recent volatiltiy. I don't think that contraversial. Maybe that's technically not iid. But I don't think the direction of volatility is predictable. I don't think I can predict returns either, just a estimate a very simple average, and that average has nothing to do with prior returns. If tomorrow is up or down, who knows.

The best possible allocation is static if return, vol and correlation are static, but you must continually rebalance to that allocation because it's always moving away from the optimal allocation.

Vol and correlation are not static however. Therefore I'm not trying to time the market. I'm just following the optimal allocation for that moment, with no idea or call on whats going up or down. It is a passive strategy in that sense. Timing the market would be anything different than the optimal strategy.

chi_capitalist
Posts: 3
Joined: Sat Feb 22, 2020 8:53 am

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

Uncorrelated wrote:
Sat Feb 22, 2020 1:11 pm
Sometimes I come across something that really doesn't make any sense. This is one of those cases.

In order to time the markets, there must be some elements that are predictable, meaning that the probability distribution of future returns on time A differs from time B. If returns are i.i.d., the best possible allocation is static.
Well, two things in reaction to the "doesn't make any sense." I agree it "doesn't make any sense for most people to execute" - but completely disagree it "doesn't make any sense"- in terms of logic or correctness of the math or in whether or not you can know the things you need to know for this to work.

1. If your expectations are static, then the right portfolio is static. Yes. However, you do have a choice re how to construct that static portfolio, and building it to explicitly plan for rebalancing returns, and to explicitly build it to grow as fast as possible, or to have a specific risk, or to maximize sharpe ratio, or whatever, is clearly a thing folks talk about here. There is a bunch of good thinking here that I think is interesting and useful even if you don't apply it as BTM does. Certainly between the geometric mean / maximum rebalanced growth ideas and the kelly betting ideas, there is some good raw material to incorporate in the next argument about 100% stocks vs. 70/30 or whatever.

2. There is quite a lot that is predictable in the financial markets, especially if you think about that in the useful sense of "this predicts a different random distribution of outcomes than that does". Some of these things are slow enough moving to impact people that are "near static BH", and some require faster actions to respond to - to each their own. But saying (as many do here) that things are not AT ALL predictable is just ignoring a ton of evidence.

Examples:
• Volatility clusters and is quite predictable (in a statistical sense) for at least 30 days
• Bond yields predict bond returns, even at quite long time periods
• CAPE does a sort of kind of OK job on equities over the long term
• If you compare E/P vs real rates you will see that that spread predicts VERY different relative stock/bond returns even at 1 month time horizon
• It at least appears there are asset class level momentum effects that everyone likes to talk about, but I personally draw the line there, as the idea of selling when things get cheap is something I just can't get my head around
There is more... but I assume you get my point.

My point is - I think everything BTM has discussed makes perfect sense, none of it requires making anything but the most aggregate/slow moving predictions, and all the data I can find backs BTM up 100%. However, the argument is a bit academic as I would say there are very few people who should be executing a monthly version of this strategy for all the behavioral reasons everyone discusses here, and REALLY few who should be leveraging this in a significant way and running it daily/weekly.

To each their own

Cheers

chi_capitalist

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

chi_capitalist wrote:
Sat Feb 22, 2020 2:29 pm

2. There is quite a lot that is predictable in the financial markets, especially if you think about that in the useful sense of "this predicts a different random distribution of outcomes than that does". Some of these things are slow enough moving to impact people that are "near static BH", and some require faster actions to respond to - to each their own. But saying (as many do here) that things are not AT ALL predictable is just ignoring a ton of evidence.

Examples:
• Volatility clusters and is quite predictable (in a statistical sense) for at least 30 days
• Bond yields predict bond returns, even at quite long time periods
• CAPE does a sort of kind of OK job on equities over the long term
• If you compare E/P vs real rates you will see that that spread predicts VERY different relative stock/bond returns even at 1 month time horizon
• It at least appears there are asset class level momentum effects that everyone likes to talk about, but I personally draw the line there, as the idea of selling when things get cheap is something I just can't get my head around
There is more... but I assume you get my point.

My point is - I think everything BTM has discussed makes perfect sense, none of it requires making anything but the most aggregate/slow moving predictions, and all the data I can find backs BTM up 100%. However, the argument is a bit academic as I would say there are very few people who should be executing a monthly version of this strategy for all the behavioral reasons everyone discusses here, and REALLY few who should be leveraging this in a significant way and running it daily/weekly.

To each their own

Cheers

chi_capitalist
Here's the thing, though....

You're basically seeking alpha in public markets, and by doing so, you're entering an arena full of some world class players, with access to capital that you don't have, more smart people thinking about things than an individual investor by themselves, and, in some cases, enough firepower to move substantial portions of the market in major ways (e.g. JP Morgan's recent affects on the repo market).

You can spend a lot of time trying to play in that arena, but you're not likely to better at creating alpha than the pros....and the ways the pros are creating alpha may mess up your back-testing based model. And it's bordering on hubris, frankly, to imagine that you've engineered a way to beat the market that hasn't been examined or tried before, by people with more money and collective intelligence.

Personally, I don't think that's a very winning game for the individual investor to play.

Instead, the individual investor can play where they can't -- private markets and other arenas where the trade-offs in liquidity and information create inefficiencies that are more exploitable at the individual level.
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

mjb
Posts: 168
Joined: Sat Nov 30, 2013 11:43 am

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

breakingthemarkt wrote:
Sat Feb 22, 2020 12:26 pm
mjb wrote:
Fri Feb 21, 2020 8:25 pm
breakingthemarkt wrote:
Fri Feb 21, 2020 5:31 pm
mjb wrote:
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.

Where did I ignore someone pointing out a perceived error in the math?
Example?
Sure, since this has gotten petty, first example of equation issues being called out and ignored is the first comment here https://breakingthemarket.com/the-most- ... -universe/

I'm not going to take the time to refind and link more.

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

watchnerd wrote:
Sat Feb 22, 2020 2:48 pm
chi_capitalist wrote:
Sat Feb 22, 2020 2:29 pm

2. There is quite a lot that is predictable in the financial markets, especially if you think about that in the useful sense of "this predicts a different random distribution of outcomes than that does". Some of these things are slow enough moving to impact people that are "near static BH", and some require faster actions to respond to - to each their own. But saying (as many do here) that things are not AT ALL predictable is just ignoring a ton of evidence.

Examples:
• Volatility clusters and is quite predictable (in a statistical sense) for at least 30 days
• Bond yields predict bond returns, even at quite long time periods
• CAPE does a sort of kind of OK job on equities over the long term
• If you compare E/P vs real rates you will see that that spread predicts VERY different relative stock/bond returns even at 1 month time horizon
• It at least appears there are asset class level momentum effects that everyone likes to talk about, but I personally draw the line there, as the idea of selling when things get cheap is something I just can't get my head around
There is more... but I assume you get my point.

My point is - I think everything BTM has discussed makes perfect sense, none of it requires making anything but the most aggregate/slow moving predictions, and all the data I can find backs BTM up 100%. However, the argument is a bit academic as I would say there are very few people who should be executing a monthly version of this strategy for all the behavioral reasons everyone discusses here, and REALLY few who should be leveraging this in a significant way and running it daily/weekly.

To each their own

Cheers

chi_capitalist
Here's the thing, though....

You're basically seeking alpha in public markets, and by doing so, you're entering an arena full of some world class players, with access to capital that you don't have, more smart people thinking about things than an individual investor by themselves, and, in some cases, enough firepower to move substantial portions of the market in major ways (e.g. JP Morgan's recent affects on the repo market).

You can spend a lot of time trying to play in that arena, but you're not likely to better at creating alpha than the pros....and the ways the pros are creating alpha may mess up your back-testing based model. And it's bordering on hubris, frankly, to imagine that you've engineered a way to beat the market that hasn't been examined or tried before, by people with more money and collective intelligence.

Personally, I don't think that's a very winning game for the individual investor to play.

Instead, the individual investor can play where they can't -- private markets and other arenas where the trade-offs in liquidity and information create inefficiencies that are more exploitable at the individual level.
I'm intrigued though you think most of these players are creating alpha. I thought it was pretty well known they don't on average. Of all sites, I would have put this one near the top of understanding that.

Of course your not likely to find a way to beat the pros. But that doesn't mean you can't. And it doesn't mean the average investor can't learn why my strategy works and apply those principles to thier own investing strategies.

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

mjb wrote:
Sat Feb 22, 2020 3:13 pm
breakingthemarkt wrote:
Sat Feb 22, 2020 12:26 pm
mjb wrote:
Fri Feb 21, 2020 8:25 pm
breakingthemarkt wrote:
Fri Feb 21, 2020 5:31 pm
mjb wrote:
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.

Where did I ignore someone pointing out a perceived error in the math?
Example?
Sure, since this has gotten petty, first example of equation issues being called out and ignored is the first comment here https://breakingthemarket.com/the-most- ... -universe/

I'm not going to take the time to refind and link more.
See below for response on that equation.
Last edited by breakingthemarkt on Tue Mar 10, 2020 9:01 pm, edited 1 time in total.

mjb
Posts: 168
Joined: Sat Nov 30, 2013 11:43 am

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

breakingthemarkt wrote:
Sat Feb 22, 2020 12:28 pm
mjb wrote:
Fri Feb 21, 2020 8:26 pm
breakingthemarkt wrote:
Fri Feb 21, 2020 5:45 pm
Uncorrelated wrote:
Wed Feb 19, 2020 3:37 pm
The academic approach is to use the arithmetic excess return, the return above the t-bill rate. This figure stays stable during periods of inflation/deflation.

I think the idea of calculating the arithmetic return based on anything less than the full sample is an extremely bad idea. There is a wide array of research that suggests that the monthly return of stocks has a correlation of zero with the return of the preceding month. Some academics claim it's impossible to create a better estimate than the average over the full sample.

What is the rationale for using gold, given that gold has a return and correlation with stocks/bonds that are statistically indistinguishable from zero. And that factors (for example, the value factor) have statistically significant positive return? How do you avoid survivorship bias with gold?

I don't think the graphs showing the rebalanced interval can be interpreted with any statistical confidence. The best resource I know about rebalancing is this page: https://www.aacalc.com/docs/when_to_rebalance. Don't forget transaction costs either, 0.5% per transaction seems to be a common figure.
jimbomahoney wrote:
Wed Feb 19, 2020 1:16 pm
Yes, I totally get that the arithmetic mean return is 7.6% (take the average of each year's returns).

I also totally get the geometric mean return is 3.1% (take the total period return and raise to one over the total period etc.)
His formula for calculating geometric from arithmetic assumes that the underlying distribution is normal and independently distributed. But if you are using a market timing algorithm, then chances are that you don't believe that returns are normal and independently distributed...
jimbomahoney wrote:
Wed Feb 19, 2020 11:30 am
6) No leverage, or possibly slightly small leverage using the remnants of a low-cost loan if I borrow to get the bathroom done or some such, or remortgage.
If your risk tolerance is so low you are unwilling to use 2-3x leverage, CAGR is unsuited as a performance metric.
Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.
Actually in some cases your equation is off by more than 50%
Ok. Please provide and example of one of those cases if you can? I really don't want to be off by 50%.
The issue arises when the variance exceeds the Arithmetic return by a significant percentage.

Here is an example

Assume years 1 to 6 with returns as an index {1, 0.85, 1.2, 0.9, 1.05, 1.07} for 0, -15%, 20%, -10%, 5%, 7%

Arithmetic mean return is 1.17%
Geometric mean return is 0.52%
STD dev is 12.6% with a variance of 1.6%
The Arithmetic mean - STD dev squared divided by 2 is 0.38%
While the absolute difference is only 0.14% the relative difference is 27%.

This scenario was very common in a pre Federal Reserve world but is not terribly different from a whipsaw drawdown.

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

breakingthemarkt wrote:
Sat Feb 22, 2020 3:26 pm

I'm intrigued though you think most of these players are creating alpha. I thought it was pretty well known they don't on average. Of all sites, I would have put this one near the top of understanding that.

Of course your not likely to find a way to beat the pros. But that doesn't mean you can't. And it doesn't mean the average investor can't learn why my strategy works and apply those principles to thier own investing strategies.
Oh, I'm not saying they're succeeding.

But they're trying. And sometimes they hit on something that works for a while, until it doesn't (e.g. Long Term Capital Management). And they have enough firepower to distort the markets that the average investor doesn't have insight into until it has already happened.

As for your strategy working.....well, no offense, backtesting doesn't prove much.

And you've been doing it since...what, March, 2019?

That's not even a year yet.

Seems to bit early to proclaim it "works".
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

mjb wrote:
Sat Feb 22, 2020 3:35 pm
breakingthemarkt wrote:
Sat Feb 22, 2020 12:28 pm
mjb wrote:
Fri Feb 21, 2020 8:26 pm
breakingthemarkt wrote:
Fri Feb 21, 2020 5:45 pm
Uncorrelated wrote:
Wed Feb 19, 2020 3:37 pm
The academic approach is to use the arithmetic excess return, the return above the t-bill rate. This figure stays stable during periods of inflation/deflation.

I think the idea of calculating the arithmetic return based on anything less than the full sample is an extremely bad idea. There is a wide array of research that suggests that the monthly return of stocks has a correlation of zero with the return of the preceding month. Some academics claim it's impossible to create a better estimate than the average over the full sample.

What is the rationale for using gold, given that gold has a return and correlation with stocks/bonds that are statistically indistinguishable from zero. And that factors (for example, the value factor) have statistically significant positive return? How do you avoid survivorship bias with gold?

I don't think the graphs showing the rebalanced interval can be interpreted with any statistical confidence. The best resource I know about rebalancing is this page: https://www.aacalc.com/docs/when_to_rebalance. Don't forget transaction costs either, 0.5% per transaction seems to be a common figure.

His formula for calculating geometric from arithmetic assumes that the underlying distribution is normal and independently distributed. But if you are using a market timing algorithm, then chances are that you don't believe that returns are normal and independently distributed...

If your risk tolerance is so low you are unwilling to use 2-3x leverage, CAGR is unsuited as a performance metric.
Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.
Actually in some cases your equation is off by more than 50%
Ok. Please provide and example of one of those cases if you can? I really don't want to be off by 50%.
The issue arises when the variance exceeds the Arithmetic return by a significant percentage.

Here is an example

Assume years 1 to 6 with returns as an index {1, 0.85, 1.2, 0.9, 1.05, 1.07} for 0, -15%, 20%, -10%, 5%, 7%

Arithmetic mean return is 1.17%
Geometric mean return is 0.52%
STD dev is 12.6% with a variance of 1.6%
The Arithmetic mean - STD dev squared divided by 2 is 0.38%
While the absolute difference is only 0.14% the relative difference is 27%.

This scenario was very common in a pre Federal Reserve world but is not terribly different from a whipsaw drawdown.
My formula says annual geo return is 0.38% vs 0.52%. As you said 0.14% difference in return.

How much would you change your portfolio allocation if an assets return was 0.14% higher than you thought it was?

And maybe more importantly, do you think your estimations for return are so precise that and error of 0.14% is anything more than noise?

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

watchnerd wrote:
Sat Feb 22, 2020 3:38 pm
breakingthemarkt wrote:
Sat Feb 22, 2020 3:26 pm

I'm intrigued though you think most of these players are creating alpha. I thought it was pretty well known they don't on average. Of all sites, I would have put this one near the top of understanding that.

Of course your not likely to find a way to beat the pros. But that doesn't mean you can't. And it doesn't mean the average investor can't learn why my strategy works and apply those principles to thier own investing strategies.
Oh, I'm not saying they're succeeding.

But they're trying. And sometimes they hit on something that works for a while, until it doesn't (e.g. Long Term Capital Management). And they have enough firepower to distort the markets that the average investor doesn't have insight into until it has already happened.

As for your strategy working.....well, no offense, backtesting doesn't prove much.

And you've been doing it since...what, March, 2019?

That's not even a year yet.

Seems to bit early to proclaim it "works".
I've been writing about it since March.

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

breakingthemarkt wrote:
Sat Feb 22, 2020 3:56 pm

I've been writing about it since March.
So how long has this experiment been going on?

70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

breakingthemarkt
Posts: 24
Joined: Fri Feb 21, 2020 5:23 pm

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

watchnerd wrote:
Sat Feb 22, 2020 3:58 pm
breakingthemarkt wrote:
Sat Feb 22, 2020 3:56 pm

I've been writing about it since March.
So how long has this experiment been going on?

The strategy is running at the top of the blog. I post the rebalanced portfolio (the trades) every week. And I posted the results from the account with pictures of the real statistics from IB. I'm trying to be transparent.

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

breakingthemarkt wrote:
Sat Feb 22, 2020 4:13 pm
watchnerd wrote:
Sat Feb 22, 2020 3:58 pm
breakingthemarkt wrote:
Sat Feb 22, 2020 3:56 pm

I've been writing about it since March.
So how long has this experiment been going on?

The strategy is running at the top of the blog. I post the rebalanced portfolio (the trades) every week. And I posted the results from the account with pictures of the real statistics from IB. I'm trying to be transparent.

So how long has it been?

Can you share the links to the data?

70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

mjb
Posts: 168
Joined: Sat Nov 30, 2013 11:43 am

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

breakingthemarkt wrote:
Sat Feb 22, 2020 3:54 pm
mjb wrote:
Sat Feb 22, 2020 3:35 pm
breakingthemarkt wrote:
Sat Feb 22, 2020 12:28 pm
mjb wrote:
Fri Feb 21, 2020 8:26 pm
breakingthemarkt wrote:
Fri Feb 21, 2020 5:45 pm

Why you think Arith mean – 0.5xSD^2 is bad approximation for the geometric mean. I understand that its not 100% perfect for investment returns (which are nearly normal but not normal) but you do know how small the error on that formula is right? If I say the geo return is 1.05% and it truly is 1.0495%, it’s not going to change the portfolio composition.

I absolutely think investment returns are i.i.d. and I think markets are efficient.
Actually in some cases your equation is off by more than 50%
Ok. Please provide and example of one of those cases if you can? I really don't want to be off by 50%.
The issue arises when the variance exceeds the Arithmetic return by a significant percentage.

Here is an example

Assume years 1 to 6 with returns as an index {1, 0.85, 1.2, 0.9, 1.05, 1.07} for 0, -15%, 20%, -10%, 5%, 7%

Arithmetic mean return is 1.17%
Geometric mean return is 0.52%
STD dev is 12.6% with a variance of 1.6%
The Arithmetic mean - STD dev squared divided by 2 is 0.38%
While the absolute difference is only 0.14% the relative difference is 27%.

This scenario was very common in a pre Federal Reserve world but is not terribly different from a whipsaw drawdown.
My formula says annual geo return is 0.38% vs 0.52%. As you said 0.14% difference in return.

How much would you change your portfolio allocation if an assets return was 0.14% higher than you thought it was?

And maybe more importantly, do you think your estimations for return are so precise that and error of 0.14% is anything more than noise?
However, from an algorthmic standpoint the relative difference of >20% would make a huge difference. And given that this occurs during wild swings in a sideways market where spreads in annual or monthly returns are in the single to double digits, you would likely be making false positive rebalances.

NotTooDeepLearning
Posts: 174
Joined: Wed Oct 24, 2018 2:04 pm

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

It's also possible to get leveraged returns similar to his with a upro/tmf strategy and hopping out of upro when stocks are below their 200 day moving average and unemployment ticks above its 10 months moving average. That yields returns in the low 20%s and a max draw down of ~30%. I did a fully reproducible backtest in R here (download the folder, make the folder your working directory, and install the correct packages before running the script):

ldyrland
Posts: 1
Joined: Sat Feb 22, 2020 2:54 pm

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

I understand how to get the allocation figures for 2 assets (from BreakingTheMarket blog), using the arithmetic values, standard deviation and covariance. Where I'm struggling is how to do it with 4 assets. Do you this calculation 6 times (4 choose 2 combinations) and then average somehow?

I'd appreciate anyone's kindness in explaining this, or at least leading me in the right direction.

Thanks,

Uncorrelated
Posts: 537
Joined: Sun Oct 13, 2019 3:16 pm

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

chi_capitalist wrote:
Sat Feb 22, 2020 2:29 pm
Uncorrelated wrote:
Sat Feb 22, 2020 1:11 pm
Sometimes I come across something that really doesn't make any sense. This is one of those cases.

In order to time the markets, there must be some elements that are predictable, meaning that the probability distribution of future returns on time A differs from time B. If returns are i.i.d., the best possible allocation is static.
Well, two things in reaction to the "doesn't make any sense." I agree it "doesn't make any sense for most people to execute" - but completely disagree it "doesn't make any sense"- in terms of logic or correctness of the math or in whether or not you can know the things you need to know for this to work.

1. If your expectations are static, then the right portfolio is static. Yes. However, you do have a choice re how to construct that static portfolio, and building it to explicitly plan for rebalancing returns, and to explicitly build it to grow as fast as possible, or to have a specific risk, or to maximize sharpe ratio, or whatever, is clearly a thing folks talk about here. There is a bunch of good thinking here that I think is interesting and useful even if you don't apply it as BTM does. Certainly between the geometric mean / maximum rebalanced growth ideas and the kelly betting ideas, there is some good raw material to incorporate in the next argument about 100% stocks vs. 70/30 or whatever.

2. There is quite a lot that is predictable in the financial markets, especially if you think about that in the useful sense of "this predicts a different random distribution of outcomes than that does". Some of these things are slow enough moving to impact people that are "near static BH", and some require faster actions to respond to - to each their own. But saying (as many do here) that things are not AT ALL predictable is just ignoring a ton of evidence.

Examples:
• Volatility clusters and is quite predictable (in a statistical sense) for at least 30 days
• Bond yields predict bond returns, even at quite long time periods
• CAPE does a sort of kind of OK job on equities over the long term
• If you compare E/P vs real rates you will see that that spread predicts VERY different relative stock/bond returns even at 1 month time horizon
• It at least appears there are asset class level momentum effects that everyone likes to talk about, but I personally draw the line there, as the idea of selling when things get cheap is something I just can't get my head around
There is more... but I assume you get my point.

My point is - I think everything BTM has discussed makes perfect sense, none of it requires making anything but the most aggregate/slow moving predictions, and all the data I can find backs BTM up 100%. However, the argument is a bit academic as I would say there are very few people who should be executing a monthly version of this strategy for all the behavioral reasons everyone discusses here, and REALLY few who should be leveraging this in a significant way and running it daily/weekly.

To each their own

Cheers

chi_capitalist
He is trying to time the market. He also said that he believes that markets are efficient, returns are independently and identically distributed. These statements are in direct conflict with one another, that's why I said it's not making any sense.

I've read most of the posts on the blog, but it's not really convincing. Most of the blog pages are based on misunderstandings, arbitrary assumptions that are not explained, and extremely complicated explanations of basic financial concepts. The most glaring misconception is about geometric vs arithmetic returns, there is no specific reason why optimizing for geometric returns is better than optimizing for arithmetic returns. Or why one should choose one of these return measurements instead of the infinitely many methods for quantifying expected return.

The blog would be a lot more useful if it actually explained how the algorithm works. How the volatility forecast works, how the volatility forecast was derived. How correlations are forecast, examining whether the forecasted correlations are actually statistically significant. Whether or not the strategy survives transaction costs, adverse selection costs, etc, etc. If you try to create a strategy without knowing all these things, the most likely result is that you're going to get murdered by the market maker.

Hydromod
Posts: 381
Joined: Tue Mar 26, 2019 10:21 pm

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

Uncorrelated wrote:
Sat Feb 22, 2020 5:32 pm
chi_capitalist wrote:
Sat Feb 22, 2020 2:29 pm
Uncorrelated wrote:
Sat Feb 22, 2020 1:11 pm
Sometimes I come across something that really doesn't make any sense. This is one of those cases.

In order to time the markets, there must be some elements that are predictable, meaning that the probability distribution of future returns on time A differs from time B. If returns are i.i.d., the best possible allocation is static.
Well, two things in reaction to the "doesn't make any sense." I agree it "doesn't make any sense for most people to execute" - but completely disagree it "doesn't make any sense"- in terms of logic or correctness of the math or in whether or not you can know the things you need to know for this to work.

1. If your expectations are static, then the right portfolio is static. Yes. However, you do have a choice re how to construct that static portfolio, and building it to explicitly plan for rebalancing returns, and to explicitly build it to grow as fast as possible, or to have a specific risk, or to maximize sharpe ratio, or whatever, is clearly a thing folks talk about here. There is a bunch of good thinking here that I think is interesting and useful even if you don't apply it as BTM does. Certainly between the geometric mean / maximum rebalanced growth ideas and the kelly betting ideas, there is some good raw material to incorporate in the next argument about 100% stocks vs. 70/30 or whatever.

2. There is quite a lot that is predictable in the financial markets, especially if you think about that in the useful sense of "this predicts a different random distribution of outcomes than that does". Some of these things are slow enough moving to impact people that are "near static BH", and some require faster actions to respond to - to each their own. But saying (as many do here) that things are not AT ALL predictable is just ignoring a ton of evidence.

Examples:
• Volatility clusters and is quite predictable (in a statistical sense) for at least 30 days
• Bond yields predict bond returns, even at quite long time periods
• CAPE does a sort of kind of OK job on equities over the long term
• If you compare E/P vs real rates you will see that that spread predicts VERY different relative stock/bond returns even at 1 month time horizon
• It at least appears there are asset class level momentum effects that everyone likes to talk about, but I personally draw the line there, as the idea of selling when things get cheap is something I just can't get my head around
There is more... but I assume you get my point.

My point is - I think everything BTM has discussed makes perfect sense, none of it requires making anything but the most aggregate/slow moving predictions, and all the data I can find backs BTM up 100%. However, the argument is a bit academic as I would say there are very few people who should be executing a monthly version of this strategy for all the behavioral reasons everyone discusses here, and REALLY few who should be leveraging this in a significant way and running it daily/weekly.

To each their own

Cheers

chi_capitalist
He is trying to time the market. He also said that he believes that markets are efficient, returns are independently and identically distributed. These statements are in direct conflict with one another, that's why I said it's not making any sense.

I've read most of the posts on the blog, but it's not really convincing. Most of the blog pages are based on misunderstandings, arbitrary assumptions that are not explained, and extremely complicated explanations of basic financial concepts. The most glaring misconception is about geometric vs arithmetic returns, there is no specific reason why optimizing for geometric returns is better than optimizing for arithmetic returns. Or why one should choose one of these return measurements instead of the infinitely many methods for quantifying expected return.

The blog would be a lot more useful if it actually explained how the algorithm works. How the volatility forecast works, how the volatility forecast was derived. How correlations are forecast, examining whether the forecasted correlations are actually statistically significant. Whether or not the strategy survives transaction costs, adverse selection costs, etc, etc. If you try to create a strategy without knowing all these things, the most likely result is that you're going to get murdered by the market maker.
I agree that the blog is hard to follow and needs to cut to the chase. He's clearly not an academic, as he's pointed out, and I suspect that some nuances are lost. With that said, I think that he's trying his best to explain concepts that may not come naturally to him and some of these comments are a bit over the top.

He's using a formula for optimal weights, at least for two assets, that is taken from a paper that assumes normally distributed and correlated returns with different means and variances. Not independent and identically distributed. One needs to go to the original source to get the theory. I'm wondering what one would get assuming the Laplace distribution instead.

The cited paper discusses multi-asset portfolios, but it doesn't give an explicit formula for determining the optimal weighting.

The most recent blog post goes through some of the mechanics of calculating volatility/correlation. I think that some of the tabulated numbers are copied from the wrong place though. As folks have pointed out, it takes quite a lot of data to determine a robust correlation coefficient. A different blog entry points out that the weights are not very sensitive to the correlation coefficient until the correlation coefficient approaches one; he specifically selects assets that do not have large positive correlation.

I think that the optimizing for geometric mean comes out of the Kelly criterion. He has some early posts that show why the geometric mean is favored over the arithmetic mean. I don't fully understand the approach, though, which is why I have been following the blog. Of dollars and data just had an illustration of why one might need to be careful of the arithmetic mean.

I'm always offput by the term "timing the market." My impression is that "timing the market" means trying to predict market high and low points in the cycle in order to sell and buy, but the terminology seems to be thrown out in this forum whenever an asset allocation is adjusted for any reason other than changes in life circumstances. It doesn't seem to be very useful when it is so loosely thrown about.

In this case, he is saying that (i) the daily market returns can be adequately represented as normally distributed, (ii) the covariances for the next week can be adequately estimated using the returns from the 30 to 50 trading days, and (iii) the difference in expected returns for the next week can be estimated from some "long" lookback (with an as yet unrevealed duration). Given the current volatility state, he expects that there is an asset allocation that will optimally balance gains and losses over many repetitions, and sets the portfolio to that allocation. I don't seen any hint of predicting a market cycle in this application, and he specifically stated that that is not the intent.

Topic Author
jimbomahoney
Posts: 29
Joined: Wed Feb 12, 2020 5:51 am

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

ldyrland wrote:
Sat Feb 22, 2020 5:13 pm
I understand how to get the allocation figures for 2 assets (from BreakingTheMarket blog), using the arithmetic values, standard deviation and covariance. Where I'm struggling is how to do it with 4 assets. Do you this calculation 6 times (4 choose 2 combinations) and then average somehow?

I'd appreciate anyone's kindness in explaining this, or at least leading me in the right direction.

Thanks,
Yes, it is more difficult with more than two assets.

Since cash is constant (zero SD, fixed return), I don't use it in the correlation calculations. That leaves three assets, which is also three asset pairs. (However, my code is generalised so that it can handle any number of assets).

You're right that there could be more than one set of correlations at play. For example, if all assets are somewhat correlated at one point in time, then you could end up with multiple calls to reduce the allocation to the underperforming asset in each pair.

Here's an example:

At one point in time, Gold is underperforming (geometrically) and correlated with both Stocks and Bonds.

E.g. the correlation calls for a 60% reduction relative to Bonds and a 10% reduction relative to Stocks. Rather than take the average, I multiply to get a ~64% reduction (0.4 * 0.9 = 0.36) in gold overall. I tested taking the mean or the median, but I believe the product is the correct way to do it, and this is borne out in the backtests.

Hope that helps?
Last edited by jimbomahoney on Sun Feb 23, 2020 7:31 am, edited 2 times in total.

Topic Author
jimbomahoney
Posts: 29
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### Re: Fascinating take on a rebalanced Permanent Portfolio - BreakingTheMarket.com

Uncorrelated wrote:
Sat Feb 22, 2020 5:32 pm
He is trying to time the market.
I don't agree at all.

Where I do agree with both you and BTM is that market-timing doesn't work.

I was first attracted to market-timing by the epic (infamous) post here by market-timer who, IIRC, was using Mebane Faber's "Tactical Asset Allocation" model. At the time, I was also convinced by it, but having done a LOT of testing with various SMA / EMA / MACD methodologies come to the conclusion that the market is entirely random and that it's just "luck" as to whether a particular moving average / time period works. i.e. backtesting allows one to cherry-pick the EMA/SMA that works for that period of time.

Granted, MT was also using leverage, but irrespective of that, I believe that market-timing is simply luck.

BTM is not timing the market. He's using good-enough estimates of current market conditions and historical expectations to reduce volatility and drive up returns.
Uncorrelated wrote:
Sat Feb 22, 2020 5:32 pm
The blog would be a lot more useful if it actually explained how the algorithm works. How the volatility forecast works, how the volatility forecast was derived. How correlations are forecast, examining whether the forecasted correlations are actually statistically significant. Whether or not the strategy survives transaction costs, adverse selection costs, etc, etc. If you try to create a strategy without knowing all these things, the most likely result is that you're going to get murdered by the market maker.
As I've said before, despite only having a few months of R coding experience, I've managed to implement it all in a script that allows me to test any market ticker as an asset that can be downloaded from Yahoo / alphavantage.

I believe that BTM is also using this for real, and has stated as much.

Yes, it's true that he could be lying, as anyone can on the internet, and it's impossible to know for sure.

However, I've done enough testing of market strategies to know when the model is "good enough" and not subject to look-back bias or look-ahead bias. I'm continuing to refine the model and find that I get similar results to BTM.

Again, I could be lying, but I will implement this in real-life once I'm happy with the model, and this will be used for my entire portfolio. However, only time will tell if it was the correct thing to do!

I suspect we will end up agreeing to disagree, and that's cool.

Topic Author
jimbomahoney
Posts: 29
Joined: Wed Feb 12, 2020 5:51 am

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

I've been working on refining my model of BTM's theory so that it suits my situation and my beliefs about the world.

I've taken what BTM has done and modified it thus:

1) Cannot trade in "real-time" - i.e. must wait until at least the next day. This is partly due to the availability of real-time data on the assets I wish to use and partly because I do not want to trade daily. Therefore my model adds one day of lag so that it only trades based on yesterday's close. In code, I'm added a "lag" variable, which will basically offset the dataframe by n days.

2) Cannot trade too frequently - this is similar to the previous constraint, but additionally, I do not want to be trading daily. In code, I've added a "rebalance frequency" variable, which will basically extend the daily weights found from #1 by an additional n days.

3) UK assets - Long UK Gilts, Gold in GBP, Global Stock Market. I don't believe in investing in a single stock market index, hence prefer a global tracker, which is of course even more diversified than the S&P. I'm using Long UK Gilts only because I cann't find a suitable global bond index to test data on.

4) Moving arithmetic return window. I believe this differs from BTM's theory, but perhaps he will correct me if I'm wrong. As previously stated, I believe he uses a "fixed" value for the arithmetic return based on a long history of returns. Because of my beliefs about the future, I don't want to use a "fixed" arithmetic return as basis on which to derive expected returns, no matter how long the data from which that return is based.

UPDATE 27th Feb - Actually, I'm now deeply suspicious about using a rolling window as this leads to large swings in returns and asset weights depending on the length of that window.

My model allows me to vary the following:
• Arithmetic return window
• SD window
• Correlation window
• Rebalance frequency
• Risk-free rate
• Leverage cost
• Cap on gold (from 0 - 100%)
This has allowed me to do extensive testing on the effects of each, both on the data I will use to execute my trades (a short dataset), the same assets that BTM uses (TLT, GLD, S&P, Cash, but again, over a relatively short timeframe of ~13 years) and also over a large dataset using only GLD, S&P and Cash (almost 40 years).

I'll try and explain each and the results of my testing:

Arithmetic Return Window

As I've stated numerous times, I really don't like the idea of a fixed value for the arithmetic return. On the other hand, if the period of time is too short (as BTM has also stated), the estimate will basically be garbage. So, using the largest dataset I have (40 years of gold and S&P), I tested the effect of using a moving arithmetic return:

The X axis is in years.

Just as BTM suggests, anything less than ~2 years is garbage. However, there is a pattern here (see the curve of best fit I've plotted), which I don't believe is "random".

Yes, the returns I'm getting jump around, but I believe that, as long as the window over which to calculate arithmetic returns is "sensible" (between about 2.5 and 8 years), it can be used.

The same pattern emerges using the assets I plan on using, however, because my dataset is so short, as I increase the window, I "crop" my dataset, so have fewer years on which to test.

UPDATE 27th Feb - Actually, I'm now deeply suspicious about using a rolling window as this leads to large swings in returns and asset weights depending on the length of that window.

I've also tested this to examine the annual returns I get vs. BTM, since he's posted his results a few times on his blog:

Bearing in mind that those results are with the constraints of lagging the market by one day, I think that's a pretty good match. Yes, his volatility is better than mine, but I strongly suspect that's because he's responding faster. The advantage that, I believe, my method has is faster response to changing asset returns - for example, I don't want to use a 30 year average return for bonds if they've been in a 30 year bull market... I'd rather move my expectations with the recent past to accomodate changes.

SD Window and Correlation Window

Initially, I was simply using the same length of time to calculate the SD and the correlation, which is what BTM insinuated was sufficient (i.e. around 20 - 50 days was enough for both).

My results agree with this, but with an interesting refinement. Below is how the returns / Sharpe is affected by varying the SD and correlation window together (i.e. each are equal in length).

Notice there is a rapid increase as this window is increased, peaking in this case at 23 days. However, there is a second peak out towards the long-term - in this case, 813 days!

I thought that was pretty interesting and decided to try varying the SD and correlation windows independently. It turns out that the second peak is caused by the extended correlation window, not the SD.

Keeping the SD window short (23 days), but varying the correlation window independently reveals that longer periods are superior and that the second peak in the previous plot is entirely due to the "better" correlation calculations:

Rebalance Frequency

I've updated a previous post, so check that for my results and opinions.

Summary: shorter = better, just like BTM says. Anything shorter than 80 days is "good enough" if you're lagging the market, as I am.

Gold Cap

Because I'm using a moving arithmetic return for my model, the swings in asset weights can be huge. I noticed that BTM's model never went more than 32% in GLD over the entire period, so I thought about implementing a limit manually. The risk in doing this of course is that you're basically placing more constraints on the model, such that you "break" its asset weights.

UPDATE 27th Feb - Actually, I'm now deeply suspicious about using a rolling window as this leads to large swings in returns and asset weights depending on the length of that window.

This (rapid change in asset weights) is partly mitigated by the reduced rebalance frequency I'm using, but can also be manually overridden by using a cap on the maximum allocation to gold. In general, I don't use this cap, but the code provides it and essentially reallocates anything above the gold cap into the other assets according to the same rules.

Here's an example done using the assets I wish to use, and using a moving arithmetic return window, rebalance frequency of 12 days and a gold cap of 20%:

Here's the same done with no limit on how much to weight towards gold:

You can clearly see GLD can quite happily go wherever it wants with no limit...

(Incidentally, the CAGR over this period was 9% without a cap on gold and 8.2% with a cap of 20%, but I realise that the dataset is too short to know what is "correct". I don't think I'm happy about applying artificial caps in this way, but I know that some people would be uncomfortable with so much in "a barbarous relic" )

Leverage

Since I'm lagging the market and trading less frequently, my results with leverage are very hit and miss. As BTM has commented in a previous post, leverage requires a faster response time to be effective, so I'm not going to use it. In my testing, using a 12 day rebalance window and a 1 day lag, leveraged "BTM" beats buy n hold, which is nice, but loses out to a non-leveraged BTM because it cannot respond fast enough to nasty corrections (e.g. stocks in 2000, 2008 and gold in 2011/12).

Putting it all together

So, in summary, I'm now in a place where I have code that replicates what BTM has outlined, but tweaked for my personal beliefs and situation.

The settings I plan to use are:

1) 23 day SD window.
2) ~4 year arithmetic return window. UPDATE 27th Feb - Actually, I'm now deeply suspicious about using a rolling window as this leads to large swings in returns and asset weights depending on the length of that window.
3) ~4 year correlation window.
4) 12 day rebalance frequency (I might increase this to 20, 40 or even 80, but I want to "play" and testing suggests that shorter is better).
5) Always use yesterday's close (largely mitigated by a reduced rebalance frequency).

Testing this on ~40 years of data, but only for three assets (Gold, Cash, Stocks) gives me the following:

10.9% CAGR
0.731 Sharpe

Compared with a rebalanced equal split (33/33/33):

5.5% CAGR
0.695 Sharpe

Or 60/40 Stocks/Gold:

8% CAGR
0.658 Sharpe

Over the 40 years of data, my implementation of BTM's method beats a rebalanced 60/40 over 80% of the time.

Testing this on ~13 years and the same assets as BTM (GLD in USD, TLT, S&P):

10.5% CAGR
0.731 Sharpe

vs. an equal split (basically a rebalanced Permanent Portfolio):

6.1% CAGR
0.934 Sharpe

vs. a 60/20/20 rebalanced split of S&P/Bonds/Gold:

6.2% CAGR
0.718 Sharpe

Again, the BTM method beats a 60/20/20 split more often than not (61% in this short dataset). My Sharpe is never as good as BTM's, but as outlined above, that's because I'm trading on a lag and less frequently.

Testing this on my actual assets (a very short dataset of only the last 4 years):

9% CAGR
1.275 Sharpe

vs. equal split:

7.3%
1.443 Sharpe

vs. 60/20/20:

10.4% CAGR
1.683 Sharpe

Pretty happy with that. The data is short enough that a fixed ratio could beat my method due to chance.

Let's go and do this for real...
Last edited by jimbomahoney on Thu Feb 27, 2020 3:39 am, edited 5 times in total.

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

jimbomahoney wrote:
Sun Feb 23, 2020 7:09 am

I believe that BTM is also using this for real, and has stated as much.
But for how long?

The posts only go back to March, 2019.

The public record isn't even a year old.

I've asked for sharing of the records going back prior to that. Nothing shared yet.

As you yourself just said, backtesting can prove pretty much any algorithm works if you pick the right data set. The real world tends to pan out differently.
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

Topic Author
jimbomahoney
Posts: 29
Joined: Wed Feb 12, 2020 5:51 am

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

watchnerd wrote:
Sun Feb 23, 2020 10:38 am
But for how long?

The posts only go back to March, 2019.

The public record isn't even a year old.

I've asked for sharing of the records going back prior to that. Nothing shared yet.

As you yourself just said, backtesting can prove pretty much any algorithm works if you pick the right data set. The real world tends to pan out differently.
I don't believe that backtesting is at the same risk of bias with the volatility-targetting method (aka "BTM method") than a momentum method, and BTM has explained much more eloquently why on his blog.

I think you posted your comment before my (epic) post above, which goes over why I believe this is the case.

Uncorrelated
Posts: 537
Joined: Sun Oct 13, 2019 3:16 pm

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

Hydromod wrote:
Sat Feb 22, 2020 11:11 pm
I agree that the blog is hard to follow and needs to cut to the chase. He's clearly not an academic, as he's pointed out, and I suspect that some nuances are lost. With that said, I think that he's trying his best to explain concepts that may not come naturally to him and some of these comments are a bit over the top.

He's using a formula for optimal weights, at least for two assets, that is taken from a paper that assumes normally distributed and correlated returns with different means and variances. Not independent and identically distributed. One needs to go to the original source to get the theory. I'm wondering what one would get assuming the Laplace distribution instead.

The cited paper discusses multi-asset portfolios, but it doesn't give an explicit formula for determining the optimal weighting.

The most recent blog post goes through some of the mechanics of calculating volatility/correlation. I think that some of the tabulated numbers are copied from the wrong place though. As folks have pointed out, it takes quite a lot of data to determine a robust correlation coefficient. A different blog entry points out that the weights are not very sensitive to the correlation coefficient until the correlation coefficient approaches one; he specifically selects assets that do not have large positive correlation.

I think that the optimizing for geometric mean comes out of the Kelly criterion. He has some early posts that show why the geometric mean is favored over the arithmetic mean. I don't fully understand the approach, though, which is why I have been following the blog. Of dollars and data just had an illustration of why one might need to be careful of the arithmetic mean.

I'm always offput by the term "timing the market." My impression is that "timing the market" means trying to predict market high and low points in the cycle in order to sell and buy, but the terminology seems to be thrown out in this forum whenever an asset allocation is adjusted for any reason other than changes in life circumstances. It doesn't seem to be very useful when it is so loosely thrown about.

In this case, he is saying that (i) the daily market returns can be adequately represented as normally distributed, (ii) the covariances for the next week can be adequately estimated using the returns from the 30 to 50 trading days, and (iii) the difference in expected returns for the next week can be estimated from some "long" lookback (with an as yet unrevealed duration). Given the current volatility state, he expects that there is an asset allocation that will optimally balance gains and losses over many repetitions, and sets the portfolio to that allocation. I don't seen any hint of predicting a market cycle in this application, and he specifically stated that that is not the intent.

Do you mean https://papers.ssrn.com/sol3/papers.cfm ... id=2927791? I thought that was a bad paper, honestly. With Shannon's demon, they forget to mention that the buy and hold investor has an higher average balance than an optimal rebalancing agent after N trials. With Pandorro's paradox they make exactly the same mistake. In chapter 5 discussing Samuelson's fallacy, they appear to misunderstand the fallacy. The real fallacy is not (as they say) that Samuelson dismissed log utility because it may lead to ruin, but that there is no convincing reason to choose to optimize for geometric growth rate in the first place. They wrote a whole page on Samuelson's fallacy while falling victim to Samuelson's fallacy

The problem for selecting the optimal portfolio given assumptions about the expected return and correlations is quite trivial to solve, for example by using the SLSQP solver in scipy. The real question is: which assumptions are reasonable?

Using the geometric returns because the kelly criterion maximizes the geometric returns is circular logic. A necessarily condition for making the kelly criterion optimal is that you have a logarithmic utility function. Optimizing for the max log utility results in the portfolio that maximizes geometric growth rate. The log utility is a special case of the constant relative risk aversion. If you are risk-neutral, it is better to optimize for arithmetic growth. If you are more risk averse than log utility (most people are), then using the kelly criterion is not appropriate.

My definition of timing the market is using return assumptions that are not static. If the assumption is that correlations are time-varying, then that is market timing. I'm not for or against market timing, but it's important to recognize what it is.

Allow me to disagree with the assumption that covariances for the next week can be adequately estimated based on 30 to 50 trading days... but I would like to be proven wrong. I can't find any papers on this subject that I can understand.

Lastly, returns on long time scales (annual) are very close to normally distributed, but daily returns are not normal at all. Most statistical tools assume a normal distribution and may end up failing catastrophically when used on non-normally distributed daily data.

Uncorrelated
Posts: 537
Joined: Sun Oct 13, 2019 3:16 pm

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

jimbomahoney wrote:
Sun Feb 23, 2020 7:09 am
Uncorrelated wrote:
Sat Feb 22, 2020 5:32 pm
He is trying to time the market.
I don't agree at all.

Where I do agree with both you and BTM is that market-timing doesn't work.
It appears that we disagree on the definition of market timing, and also whether it is possible. If you are varying your asset allocation as a result in economic conditions, that is market timing.

It's not that I don't believe you or BtM, just that the arguments are either nonexistent or poor. This makes it nearly impossible to evaluate the strategy.
jimbomahoney wrote:
Sun Feb 23, 2020 10:38 am
Long post
Some comments here. You might not be able to answer all of them, but it's good to think about them.

Are you accounting for trading costs? Using a time lag is a good start, common academic practice is to also subtract 0.5% per trade to account for spread/friction costs and adverse selection bias. If you are trading highly liquid ETF's in small sizes (less than millions), using something in the range of 0.2% might be more accurate.

The "optimal" window for calculating the arithmetic return with your data is 2.5-8 years. Are you calculating this based on the nominal returns, real returns, or the excess returns? What is the theoretical basis for this window size? What are the objections against using a window spanning the entire data period? I fear that using a short window may (accidentally) result in exploitation of momentum effects, you don't seem to believe in momentum.

Regarding the SD and correlation window length, the longer the correlation window is, the better the results. Doesn't that imply that the best estimate for correlation is an estimate over the full sample? (i.e. correlation is not time-varying). The results when varying the SD look pretty random and statistically insignificant. If you can't find a theoretical explanation why an 23-day SD window is better than a 10-day or 40-day SD window, I think there is a large chance that this is a result of overfitting.

You are currently estimating the return, correlation and SD in your trading strategy. It might be interesting to run a few backtests with only one of these enabled. I suspect that the return estimation window is the main driver of returns, via momentum effect.

Hydromod
Posts: 381
Joined: Tue Mar 26, 2019 10:21 pm

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

Uncorrelated wrote:
Sun Feb 23, 2020 10:51 am
Do you mean https://papers.ssrn.com/sol3/papers.cfm ... id=2927791? I thought that was a bad paper, honestly. With Shannon's demon, they forget to mention that the buy and hold investor has an higher average balance than an optimal rebalancing agent after N trials. With Pandorro's paradox they make exactly the same mistake. In chapter 5 discussing Samuelson's fallacy, they appear to misunderstand the fallacy. The real fallacy is not (as they say) that Samuelson dismissed log utility because it may lead to ruin, but that there is no convincing reason to choose to optimize for geometric growth rate in the first place. They wrote a whole page on Samuelson's fallacy while falling victim to Samuelson's fallacy

The problem for selecting the optimal portfolio given assumptions about the expected return and correlations is quite trivial to solve, for example by using the SLSQP solver in scipy. The real question is: which assumptions are reasonable?

Using the geometric returns because the kelly criterion maximizes the geometric returns is circular logic. A necessarily condition for making the kelly criterion optimal is that you have a logarithmic utility function. Optimizing for the max log utility results in the portfolio that maximizes geometric growth rate. The log utility is a special case of the constant relative risk aversion. If you are risk-neutral, it is better to optimize for arithmetic growth. If you are more risk averse than log utility (most people are), then using the kelly criterion is not appropriate.

My definition of timing the market is using return assumptions that are not static. If the assumption is that correlations are time-varying, then that is market timing. I'm not for or against market timing, but it's important to recognize what it is.

Allow me to disagree with the assumption that covariances for the next week can be adequately estimated based on 30 to 50 trading days... but I would like to be proven wrong. I can't find any papers on this subject that I can understand.

Lastly, returns on long time scales (annual) are very close to normally distributed, but daily returns are not normal at all. Most statistical tools assume a normal distribution and may end up failing catastrophically when used on non-normally distributed daily data.
Thanks for explaining further. This is how I learn.

I agree about solving the problem with a minimization package; I use Matlab to solve multi-asset risk parity problems. I'm just waiting to see the assumptions that he used. I suspect it will be done pairwise, like jimbomahoney does, rather than considering all assets simultaneously.

The point about the 30-50 day lookback: it's not that the correlation is accurately measured, but that he did tests that suggest that the calculated weights only become sensitive to a correlation that is "near" one. So presumably one would start to fret about accuracy when the calculated correlations are greater than, say, 0.3 to 0.5 (picking values out of thin air...), rather than when they are in the range of -1 to 0.1.

My feel is that the key driver of improved returns is more due to the adaptive adjustment of weights up and down based on market volatility than due to the precise values of the weights. I would probably not worry too much about the precise value for a weight within a range of +/- 0.05 to 0.1, perhaps larger. Anyone have a narrower or wider range?

We went over the frequent rebalancing issue with HEDGEFUNDIE's threads. Using just UPROSIM and TMFSIM, I found a significant increase in CAGR with rebalancing every day or two (~100 bp ignoring costs), but the benefit dropped off rapidly with duration between rebalances. By two weeks the rebalancing bonus was down an order of magnitude. I've since implemented a more complete model for trading in backtests that randomly selects the trading prices during the day, but I haven't tried it again for a frequent trading analysis. It occurs to me that if the end-of-day prices are negatively correlated, presumably the intra-day prices are also negatively correlated, which might provide a little extra bump that partially offsets trading costs.

Any thoughts on how an implementation would be different assuming a Laplace distribution instead of a normal distribution?

Topic Author
jimbomahoney
Posts: 29
Joined: Wed Feb 12, 2020 5:51 am

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

Uncorrelated wrote:
Sun Feb 23, 2020 11:25 am
It appears that we disagree on the definition of market timing, and also whether it is possible. If you are varying your asset allocation as a result in economic conditions, that is market timing.

It's not that I don't believe you or BtM, just that the arguments are either nonexistent or poor. This makes it nearly impossible to evaluate the strategy.
That's a very fair point, and I do agree that choosing a window of a fixed period is equivalent to market timing. UPDATE 27th Feb - Actually, I'm now deeply suspicious about using a rolling window as this leads to large swings in returns and asset weights depending on the length of that window.

However, even a "window" of the entire dataset equates to the same thing. I'm not happy using a 30 or 100 year "window" to form an expectation of future returns. I've no idea what future reaturns are going to be, so any "window" is, at best, a guide.

I'm just going to have to accept the risk either way. A "fixed" expectation will not respond to changes. A moving window will be "biased" to whatever the dataset has tended towards.

The reason I like a moving window of returns, and the reason I'm fairly confident about it is two-fold:

1) My returns are similar to BTM, who as far as I can tell, is using a fixed return value for ~70+ years of data. I'm using a ~3-4 year moving window and getting similar returns, albeit with more volatility.
2) The fact that there is a pattern, similar to the rebalance frequency, that tends to be noisy for short periods (and therefore unreliable) but clearly trails off at longer periods. Yes, the short periods tend towards chance and the particularities of that dataset / time period. But there is, I believe, a trend. Short = random, but higher likelihood of being "optimal". Long = less noisy, but higher likelihood of lower returns. See some of the plots in my long post.

This is my justifcation anyway. I totally appreciate that it could be chance that 2 - 8 years just happens to work best for this time period.
Uncorrelated wrote:
Sun Feb 23, 2020 11:25 am
Some comments here. You might not be able to answer all of them, but it's good to think about them.

Are you accounting for trading costs? Using a time lag is a good start, common academic practice is to also subtract 0.5% per trade to account for spread/friction costs and adverse selection bias. If you are trading highly liquid ETF's in small sizes (less than millions), using something in the range of 0.2% might be more accurate.
Again, a fair point. I'll try and model it. Since I'm using (mostly) OEICs, there is no explicit trading cost, but I understand that there's almost certainly a spread and I'm getting hit there.
Uncorrelated wrote:
Sun Feb 23, 2020 11:25 am
The "optimal" window for calculating the arithmetic return with your data is 2.5-8 years. Are you calculating this based on the nominal returns, real returns, or the excess returns? What is the theoretical basis for this window size? What are the objections against using a window spanning the entire data period? I fear that using a short window may (accidentally) result in exploitation of momentum effects, you don't seem to believe in momentum.
I'm taking the arithmetic mean daily return for the period and converting it to an annual return. i.e. this should be the arithmetic annual return. I guess this is the nominal return.

I've explained my thoughts about the specific window above.
Uncorrelated wrote:
Sun Feb 23, 2020 11:25 am
Regarding the SD and correlation window length, the longer the correlation window is, the better the results. Doesn't that imply that the best estimate for correlation is an estimate over the full sample? (i.e. correlation is not time-varying). The results when varying the SD look pretty random and statistically insignificant. If you can't find a theoretical explanation why an 23-day SD window is better than a 10-day or 40-day SD window, I think there is a large chance that this is a result of overfitting.
Again, there is a trend. The results from SD window length become more stable as they get longer, but there is, as BTM says, not much difference once it's sufficiently long (e.g. 20 - 50 days). See my analysis in the long post.
Uncorrelated wrote:
Sun Feb 23, 2020 11:25 am
You are currently estimating the return, correlation and SD in your trading strategy. It might be interesting to run a few backtests with only one of these enabled. I suspect that the return estimation window is the main driver of returns, via momentum effect.
I'd also considered that and can show some results. I'd deliberately designed in various checks as the code executes so that I can see what it's doing.

Here is the arithmetic return of each of BTM's assets using my moving window. This serves as the starting point for weighting decisions:

The next step is to take the voltaility (SD) into account, which subtracts weight from those assets that are "currently" volatile, resulting in the next weighting:

Yes, there is a clear strong influence from the return estimates, as you say, and it's the main driver.

The next stage is to account for correlation. In my case, I'm using a rolling window of ~3 years (the same as the returns estimate).

The dotted lines represent the same as the previous graph. The solid lines are the new weights when correlation is taken into account. There's some reasonably chunky adjustments at times.

I can do the same using a "fixed" arithmetic return of whatever I want. As previously detailed, I can use what might be deemed "reasonable" fixed expectations of 9.1% for stocks, 6.8% for long bonds, 4% for gold and 1% for cash and I get the following (let me know if you want me to use some other fixed values):

This results in similar asset allocations to BTM - about 50% stocks, 35% bonds and 15% gold with occassional large swings. However, because of the "fixed" return expectation, the allocations aren't as wild as mine.

But I still really don't like saying "for as long into the future as I care about, stocks will return 9.1%, bonds 6.8% and gold 4%".

Again, only time will tell if my take on BTM's method is better / worse than his and/or some other fixed asset allocation.

I enjoy tinkering and care more about other things in life than money. As long as I have a roof over my head, food on the table, water from the tap and a loving partner / family, nothing else really matters.

Is more money better? Sure it is! That's why we're all on this board. But it's just a game to me, and one I'm willing to play around with and potentially, do worse than buy 'n' hold.

Last edited by jimbomahoney on Thu Feb 27, 2020 3:40 am, edited 3 times in total.

Topic Author
jimbomahoney
Posts: 29
Joined: Wed Feb 12, 2020 5:51 am

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

Hydromod wrote:
Sun Feb 23, 2020 1:17 pm
The point about the 30-50 day lookback: it's not that the correlation is accurately measured, but that he did tests that suggest that the calculated weights only become sensitive to a correlation that is "near" one. So presumably one would start to fret about accuracy when the calculated correlations are greater than, say, 0.3 to 0.5 (picking values out of thin air...), rather than when they are in the range of -1 to 0.1.
Bingo.

Correlation only has significant effects at high correlations.

The equation I'm using is adopted from BTM's post here.

Scroll almost to the bottom and you can see the effect.

I modeled that in Excel and fitted a curve to extract the equation, which is what I'm using to adjust weights:

1) I intially used a very approximate equation, which was Y = (1-X^7) where Y is the asset weight and X is the correlation between the asset pairs.

For example, if correlation is 0.9, this results in ~52% reduction in the underperforming asset's weight.

With a correlation of 0.5, it's almost negligle.

2) I'm now using a better fit, which is:

Y = -19.292* X^6 + 41.836*X^5 - 33.542*Xx^4 + 11.833*X^3 - 1.8904*X^2 + 0.0177 * X + 1.0003

This results in, for example, a correlation of 0.9 resulting in a ~55% reduction in the underperforming asset.

Or, for a 0.5 correlation, about a 7% reduction.

This performs better than the former simplistic method.

Hope this helps!

watchnerd
Posts: 5495
Joined: Sat Mar 03, 2007 11:18 am
Location: Seattle, WA, USA

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

jimbomahoney wrote:
Sun Feb 23, 2020 1:39 pm

Is more money better? Sure it is! That's why we're all on this board. But it's just a game to me, and one I'm willing to play around with and potentially, do worse than buy 'n' hold.

I'm curious how much of your portfolio % you're investing in this particular style of the game.
70% Global Market Weight Equities | 15% Long Treasuries 15% short TIPS & cash || RSU + ESPP

Uncorrelated
Posts: 537
Joined: Sun Oct 13, 2019 3:16 pm

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

Hydromod wrote:
Sun Feb 23, 2020 1:17 pm
Uncorrelated wrote:
Sun Feb 23, 2020 10:51 am
...
Thanks for explaining further. This is how I learn.

I agree about solving the problem with a minimization package; I use Matlab to solve multi-asset risk parity problems. I'm just waiting to see the assumptions that he used. I suspect it will be done pairwise, like jimbomahoney does, rather than considering all assets simultaneously.

The point about the 30-50 day lookback: it's not that the correlation is accurately measured, but that he did tests that suggest that the calculated weights only become sensitive to a correlation that is "near" one. So presumably one would start to fret about accuracy when the calculated correlations are greater than, say, 0.3 to 0.5 (picking values out of thin air...), rather than when they are in the range of -1 to 0.1.

My feel is that the key driver of improved returns is more due to the adaptive adjustment of weights up and down based on market volatility than due to the precise values of the weights. I would probably not worry too much about the precise value for a weight within a range of +/- 0.05 to 0.1, perhaps larger. Anyone have a narrower or wider range?

We went over the frequent rebalancing issue with HEDGEFUNDIE's threads. Using just UPROSIM and TMFSIM, I found a significant increase in CAGR with rebalancing every day or two (~100 bp ignoring costs), but the benefit dropped off rapidly with duration between rebalances. By two weeks the rebalancing bonus was down an order of magnitude. I've since implemented a more complete model for trading in backtests that randomly selects the trading prices during the day, but I haven't tried it again for a frequent trading analysis. It occurs to me that if the end-of-day prices are negatively correlated, presumably the intra-day prices are also negatively correlated, which might provide a little extra bump that partially offsets trading costs.

Any thoughts on how an implementation would be different assuming a Laplace distribution instead of a normal distribution?
If I remember correctly, the confidence interval on correlations is quite bad. For example, the 95% confidence interval of the correlation between stocks and gold over the last 50 years is around (-.5, .5). Even if the true underlying correlation is zero, that implies that 5% of the time, you're estimating below -.5 or above .5. It might be worth looking into statistical tests to estimate the confidence interval. The idea that the correlation can be accurately estimated with 30-50 data points almost sounds like a joke.

I don't think you can reliable trade on the end of day price. That's the domain of high frequency traders. I don't like to speak in absolutes, but you will lose if you try to compete with them. If you want to win, you'll have to do it in a way that avoids competing with them, probably by looking at longer timescales.

There are two advantages to using a normal distribution. First is that the normal distribution is a stable distribution, this means that linear combinations of normal distributions are also a normal distribution. This makes it easy to mix different assets. The second advantage is that the math for optimizing for geometric returns (or any other return measurement) is well-understood. Concretely, maximizing (mean(X) - .5 * var(X)) will give you the asset allocation with the max geometric return. The Laplace distribution is not stable, if we assume that stocks and bonds have a Laplace distribution, stocks + bonds has an unknown distribution. If you want to maximize the geometric growth rate (log utility) with a Laplace distribution, you'll probably have to work with a discrete approximation. It can definitely work, but requires bit more code.

I'm not an expert on probability, but it also appears that the method for estimating the variance differs between normal and Laplace distributions. This might break some of the assumptions used for calculating the kelly criterion.