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[MachineGhost]

I am still not quite sure where you stand. You criticize the PP and call its followers muppets in one breath (alluding to a better quantitative solution that involves more transactions), but then you dismiss quantitative solutions in posts like this.

Where do you stand? What are you currently doing with your money?

You sound like doodle there!

I'm just saying that we must not lose sight that the PP is fundamentally about economic environments, not "holy grail" mathematical algorithms for portfolio optimization, and so long as historical data is limited, the two will not meet each other.  Heck, I will almost guarantee that the "optimal" allocation derived by any algorithm won't be a heuristic 25x4 in my natural lifetime!

I think the PP's theoretical basis comes into play when deciding what broad asset classes to include and when deciding whether or not a proposed "optimal" allocation is sensible.  Maybe if we could include T-Bond data back the the 1940's, the resulting algorithm weights would be more sensible than overweighting to interest/inflation risk, but we don't currently have the luxury of that certainty.

So, where I stand at present is that I believe what we are all really after is a maximally anti-correlated portfolio and I am only willing to accept the limited history of T-Bonds using that approach.  It is the only portfolio weighting scheme that seems to be in harmony with the PP's fundamentals: http://www.systematicportfolio.com/mincorr

[sophie]

MG, have you run any simulations with the min correlation calculator?  What did you come up with, by way improving on the PP's 25x4 allocations?

[MachineGhost]

MG, have you run any simulations with the min correlation calculator?  What did you come up with, by way improving on the PP's 25x4 allocations?

It took me two grueling days to code it up but unfortunately, it won't work on a bar to bar basis, only on the very last bar of data and won't go back more than 200 bars as I'm too stupid to know how to program competently.  The output (on 100 bars) doesn't match the version implemented in R, but it does match the manually inputted Excel spreadsheet (which I used to vet my code output).  So using the R version, I get these weights going back to 5/1973 for all four asset classes as of 04/05/13:

Stocks: 39.222%
Bonds: 17.6243%
Gold: 14.2257%
Notes: 28.9275%

P.S.  My use of "muppets" is sarcasm, people.  Chill!

[Ad Orientem]

MG, have you run any simulations with the min correlation calculator?  What did you come up with, by way improving on the PP's 25x4 allocations?

It took me two grueling days to code it up but unfortunately, it won't work on a bar to bar basis, only on the very last bar of data and won't go back more than 200 bars as I'm too stupid to know how to program competently.  The output (on 100 bars) doesn't match the version implemented in R, but it does match the manually inputted Excel spreadsheet (which I used to vet my code output).  So using the R version, I get these weights going back to 5/1973 for all four asset classes as of 04/05/13:

Stocks: 39.222%
Bonds: 17.6243%
Gold: 14.2257%
Notes: 28.9275%

P.S.  My use of "muppets" is sarcasm, people.  Chill!

So taking this rather complicated formula and turning it into something that an investor with a room temperature IQ could use/grasp you are basically saying that a good investment allocation would be to take 80% of your money and put it in a 50/50 Boglehead portfolio (ITT/TSM) with a roughly 20% slug for gold?

Edit: For the record my above question was not intended to come across as snarky or critical. The suggestion, if understood correctly, sounds fairly reasonable to me and I would not lose a ton of sleep with such a portfolio.

[rocketdog]

Interesting, MG.  I've been churning the data that Peak2Trough posted a while back on this thread; I just haven't had a chance to write up and post my findings in detail.  But here's a sneak peek...

I looked for any portfolio combination that outperformed the PP under every criteria.  In other words, it had to have a higher CAGR and Sharpe ratio, but lower StdDev and MaxDD.  I found only 354 portfolios that beat the PP across all categories.  That's out of 176,851 different portfolio combinations! 

Let me put it another way:  The PP's 4x25% approach beat 99.8% of all other portfolio combinations!  Here are the allocations of the portfolios that outperformed the PP:

Code: Select all

Tbill	17% - 25% (Avg. = 20%)
Tbond	21% - 44% (Avg. = 33%)
Gold	13% - 24% (Avg. = 19%)
SP500	19% - 36% (Avg. = 28%)

The one caution I would make is that these ranges do not mean that any portfolio that falls within these ranges will outperform a PP.  It means that the portfolios that did outperform the PP had allocations that fell within these ranges.  In other words, the winning portfolios are a subset of all the portfolios that fall within these ranges. 

The upshot is that if over the past 40 years you had a portfolio with allocations that fell outside these ranges, you would not have beaten the PP.  But if you had a portfolio with allocations that fell within these ranges, you might have beaten the PP, depending on the exact allocations you held. 

Of course, this is based on 40 years worth of backward-looking data provided by Peak2Trough, so take it FWIW. 

[MachineGhost]

So taking this rather complicated formula and turning it into something that an investor with a room temperature IQ could use/grasp you are basically saying that a good investment allocation would be to take 80% of your money and put it in a 50/50 Boglehead portfolio (ITT/TSM) with a roughly 20% slug for gold?

Its not a complicated formula, just complicated to implement for a non-programmer like me.  In actual practice, its a simple breeze to use in Excel assuming the R version outputs correctly.

But, I am uncomfortable with the heuristic rounding up or down that people like to do in making assumptions about portfolio weights.  Small changes in riskier assets can have huge long-term consequences.  So 20% is a huge difference from gold's 14.2257%  Same likewise for 50% vs stock's 39.22%.  It's not the upfront value weights that are important, but the "hidden" underlying risk exposure and its correlation to the other assets.  That being said, unlike other weighting schemes, minimum correlation is robust in the way that equal weight is...  it relies on heuristic "fuzzy logic" and is "anti-fragile".  Small changes in portfolio weights won't blow it up.

Out of curiosity, I did a backtest rebalancing annually using the ex-post-ante weights and achieved 8.34% CAR and -19.17% MaxDD with transaction costs (I plan to include taxes soon).

[rocketdog]

Just a quick addendum to my previous post... 

Here are the criteria ranges for the 354 portfolios that outperformed the PP across all criteria:

Code: Select all

	  MIN	  MAX	  AVG
CAGR	 9.26 	 9.40 	 9.31 
StdDev	 6.58 	 6.79 	 6.72 
MaxDD	16.27 	20.21 	18.32 
Sharpe	 0.53 	 0.55 	 0.54 

[MachineGhost]

Interesting, MG.  I've been churning the data that Peak2Trough posted a while back on this thread; I just haven't had a chance to write up and post my findings in detail.  But here's a sneak peek...

I looked for any portfolio combination that outperformed the PP under every criteria.  In other words, it had to have a higher CAGR and Sharpe ratio, but lower StdDev and MaxDD.  I found only 354 portfolios that beat the PP across all categories.  That's out of 176,851 different portfolio combinations!

I remember that thread!  It was some some sort of Monte Carlo/bootstrapping exercise, but please remember that covariance is not correlation (nor is correlation cointegration), volatility is not risk and Sharpe does not measure risk, duration or market timing ability.

So, it isn't hard to beat equal weight which ranks dead last on any weighting scheme...  for example, just weight inversely by the MaxDD or volatility and normalize all assets to 1.  The problem is how to adjust those weights for the cross correlations to the other assets in a robust manner.  The sloppiness in not adjusting is where the larger risk comes from when equal weighting because it is always out of sync with past human behavior and thus, the future.  Equal weight is just a concentration risk limiter.  Nothing else.

[rocketdog]

But, I am uncomfortable with the heuristic rounding up or down that people like to do in making assumptions about portfolio weights.  Small changes in riskier assets can have huge long-term consequences.  So 20% is a huge difference from gold's 14.2257%  Same likewise for 50% vs stock's 39.22%.  It's not the upfront value weights that are important, but the "hidden" underlying risk exposure and its correlation to the other assets.  That being said, unlike other weighting schemes, minimum correlation is robust in the way that equal weight is...  it relies on heuristic "fuzzy logic" and is "anti-fragile".  Small changes in portfolio weights won't blow it up.

So then how do you feel if we rounded your weightings as below, just to make it easier for all us muppets to remember:

Stocks: 40%
Bonds: 15%
Gold: 15%
Notes: 30%

[Dieter]

Technically, 50% of 80% gives you the 40% total in stock, so that's a match.

20% gold is high vs 15ish%, although I'd assume still within the rebalance band.... (40% of allocation?, so rebalance at 9% and 21% for a 15% allocation?)

Definitely something I've been tinkering with....

[Ad Orientem]

So taking this rather complicated formula and turning it into something that an investor with a room temperature IQ could use/grasp you are basically saying that a good investment allocation would be to take 80% of your money and put it in a 50/50 Boglehead portfolio (ITT/TSM) with a roughly 20% slug for gold?

But, I am uncomfortable with the heuristic rounding up or down that people like to do in making assumptions about portfolio weights.  Small changes in riskier assets can have huge long-term consequences.  So 20% is a huge difference from gold's 14.2257%  Same likewise for 50% vs stock's 39.22%.  It's not the upfront value weights that are important, but the "hidden" underlying risk exposure and its correlation to the other assets.  That being said, unlike other weighting schemes, minimum correlation is robust in the way that equal weight is...  it relies on heuristic "fuzzy logic" and is "anti-fragile".  Small changes in portfolio weights won't blow it up.

I think I expressed myself rather poorly. What I as suggesting was more of a 40-40-20 portfolio.

[melveyr]

MG,

How does the min correlation solution differ from the equal risk contribution (Thierry Roncalli). Equal risk contribution gets all of the asset classes so that they contribute an equal amount of covariance to the portfolio...  So asset classes with low correlation and low volatility get higher weightings.

Mincorr seems like a similar objective but with a totally different process. What subtle differences am I missing in the objectives?

[MachineGhost]

Code: Select all

	  MIN	  MAX	  AVG
CAGR	 9.26 	 9.40 	 9.31 
StdDev	 6.58 	 6.79 	 6.72 
MaxDD	16.27 	20.21 	18.32 
Sharpe	 0.53 	 0.55 	 0.54 

I don't trust the numbers.  The MIN is simply not possible with the PP, so I suspect the MaxDD is being understated.  Just to be sure, I ran an optimization over the ranges you choose using TBills.  16.5% MaxDD simply isnt reached until the CAR drops below 8% CAR at (21/13/19).  And this is without transaction costs included.  There's a remote possibility the MaxDD is less using rebalancing bands instead of annual rebalancing, but I seriously doubt it.

[MachineGhost]

Stocks: 40%
Bonds: 15%
Gold: 15%
Notes: 30%

What's wrong with simple rounding?  39%, 18%, 14%, 29%.  Surely us muppets can handle 39% vs 40%!

[MachineGhost]

Mincorr seems like a similar objective but with a totally different process. What subtle differences am I missing in the objectives?

Covariance isn't correlation, although they are similar.  And one of the simpler variations is sort of identical to ERC but doesn't require a supercomputer to calculate.  And some "fuzzy" smoothing and weighting is done to the correlations to make them more robust ala simple equal weight.  You need to read the white paper.

Stefan over in the Engineering thread actually pointed the way with his latest formula.  Its referenced in the paper as a portfolio's risk in reality is essentially: K * Average Risk * Average Corrrelation of the components or something like that where K is the inverse volatility as a initial weight.

[stuper1]

I have a question about all of this minimizing correlation and maximizing volatility analysis.  Shouldn't the analysis also include weighting to address the long-term expected upside of each investment class?  In other words, over the very long term, isn't it expected that say stocks will outperform bonds, and therefore we'd be better off overweighting stocks a bit?  Or maybe I'm way out in right field.

[melveyr]

I have a question about all of this minimizing correlation and maximizing volatility analysis.  Shouldn't the analysis also include weighting to address the long-term expected upside of each investment class?  In other words, over the very long term, isn't it expected that say stocks will outperform bonds, and therefore we'd be better off overweighting stocks a bit?  Or maybe I'm way out in right field.

Theoretically you are totally correct and that's what traditional MPT is all about (mean variance optimization). However, in reality this mean variance optimization has burned many investors because it causes them to buy whatever has done well in the recent past and extrapolate that out into the future.

Risk parity is popular because it doesn't require you to forecast the expected returns, and it keeps you disciplined by focusing on risk. The risk parity (and other risk frameworks that MG is posting about) are all about managing your downside, and letting the upside take care of itself. I guess you could see that following risk parity you are less likely to make a greedy mistake.

[melveyr]

Mincorr seems like a similar objective but with a totally different process. What subtle differences am I missing in the objectives?

Covariance isn't correlation, although they are similar.  And one of the simpler variations is sort of identical to ERC but doesn't require a supercomputer to calculate.  And some "fuzzy" smoothing and weighting is done to the correlations to make them more robust ala simple equal weight.  You need to read the white paper.

Stefan over in the Engineering thread actually pointed the way with his latest formula.  Its referenced in the paper as a portfolio's risk in reality is essentially: K * Average Risk * Average Corrrelation of the components or something like that where K is the inverse volatility as a initial weight.

Hmm okay. I think I still like the covariance ERC method. Its really not that bad. Solver in excel does it in seconds. You just make a cell that is the standard deviation of the risk weightings, and tell solver to find the weightings that makes that stdev 0. Another iterative process you can do in any language (I did it in Python) is that you start with 1% in each asset class, and then add 1% to whichever asset has the lowest weighted covariance to the total portfolio. You keep doing that until your portfolio is at 100% 

The mincorr method just strikes me as an inferior way of getting at the same ends, but maybe I am missing something...

[MachineGhost]

The mincorr method just strikes me as an inferior way of getting at the same ends, but maybe I am missing something...

Well, I think the point is an iterative process like ERC is computationally inefficient and can really lever up the processor load when run on a basket of instruments, nor is it amenable to the additional levered processor load of optimization techniques for finding a local maximum (robust) as opposed to a global maximum (fragile).  Plus, using Solver restricts you from dynamically doing it point-in-time during backtests (unless you fancy doing it all by hand!), plus imagine how long that would take having to do an iterative process every x periods.

Also, if you look at the diversification index as well as the gini coefficient, which measures diversification effect as well as concentration risk in a portfolio, it will be higher for mincorr than the other weighting schemes.  I've never seen the diversification index applied anywhere else before except in Geoff Considine's proprietary portfolio management software** where it was not revealed.  So to have the use of the Composite Diversification Indicator is a huge boon for comparing weighting schemes.

[align=center][/align]

**  Who was the first to criticize the PP's real interest rate/gold overexposure here:
http://www.advisorperspectives.com/news ... o.pdf  The main driver of Considine's approach is the use of correlation and forward-looking volatility.  While I don't believe volatility = risk, it is the only forward-looking risk metric that we can actually measure from the marketplace.

He also wrote this:

As far as interest rate exposure, the 4×25 has a very strong negative correlation to 10-year Treasury bond yield (source: my calculations). PRPFX has almost a zero correlation to ten-year Treasury yield (source: my calculations). The higher return of the 4×25 in 2011 would seem to be related to this difference.

[MachineGhost]

Took me a while to figure out what changed, but using 90-day T-Bills instead of 3-year T-Notes:

Stocks: 9.96%
Bonds: 10.95%
Gold: 2.44%
Cash: 76.65%

And a spot check using ETF's back to 2004:

Stocks: 12.61%
Bonds: 8.81%
Gold: 5.49%
Cash: 73.10%

Close enough.  I'm not sure I understand the why under the mincorr framework.  Is characteristics between T-Bills and T-Notes really that great?

Without cash, it is:

Stocks: 59.06%
Bonds: 27.70%
Gold: 13.24%

Which is rather remarkably like the 60/40 portfolio that Wall Street promoted as optimal back in the mid-60's.

[rocketdog]

Code: Select all

	  MIN	  MAX	  AVG
CAGR	 9.26 	 9.40 	 9.31 
StdDev	 6.58 	 6.79 	 6.72 
MaxDD	16.27 	20.21 	18.32 
Sharpe	 0.53 	 0.55 	 0.54 

I don't trust the numbers.  The MIN is simply not possible with the PP, so I suspect the MaxDD is being understated.  Just to be sure, I ran an optimization over the ranges you choose using TBills.  16.5% MaxDD simply isnt reached until the CAR drops below 8% CAR at (21/13/19).  And this is without transaction costs included.  There's a remote possibility the MaxDD is less using rebalancing bands instead of annual rebalancing, but I seriously doubt it.

That's something you'll have to take up with Peak2Trough.  I'm just using the data he provided. 

[rocketdog]

Stocks: 40%
Bonds: 15%
Gold: 15%
Notes: 30%

What's wrong with simple rounding?  39%, 18%, 14%, 29%.  Surely us muppets can handle 39% vs 40%!

Because "true" muppets find nice round multiples of 5 appealing, that's why. 

[dragoncar]

Stocks: 40%
Bonds: 15%
Gold: 15%
Notes: 30%

What's wrong with simple rounding?  39%, 18%, 14%, 29%.  Surely us muppets can handle 39% vs 40%!

Because "true" muppets find nice round multiples of 5 appealing, that's why. 

Because tighter rounding implies a level of accuracy that doesn't exist.  I personally think muppets are more likely to blindly adopt a very scientific sounding 39.22% than the made up sounding 40% (which would require more critical thought and understanding of the information source)

[rocketdog]

What's wrong with simple rounding?  39%, 18%, 14%, 29%.  Surely us muppets can handle 39% vs 40%!

Because "true" muppets find nice round multiples of 5 appealing, that's why. 

Because tighter rounding implies a level of accuracy that doesn't exist.  I personally think muppets are more likely to blindly adopt a very scientific sounding 39.22% than the made up sounding 40% (which would require more critical thought and understanding of the information source)

Good point.  HB knew that intuitively, which is why he settled on the 4x25% formula: easy peasy for us muppets to deal with.  Numbers like 39 and 18 make my muppet head hurt.