Backtesting for the Optimum HBPP Allocations

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Peak2Trough
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Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Fri Dec 28, 2012 3:26 pm

Some of you are aware I have been working on some backtesting code for the HBPP.  I've been able to put together something that allows me to choose arbitrary dates and spit out the CAGR, max draw down, standard deviation, etc for the portfolio over a given time period.

Having built and tested that to my satisfaction, I decided to take it a step further.  I recently posted in another thread that I decided to iterate using that same code and price data over the 176,000-ish ways one could allocate 0-100% of capital over the 4 assets.  In effect, I wanted to answer the following questions: 

1) What have been the optimum performing allocations among the 4 assets of the permanent portfolio since 1972?
2) In what ways has changing the allocation affected performance and volatility of the portfolio?

I'm aware that doesn't answer what will be the future most efficient allocation, but I think the results can be instructive nonetheless.

A few folks expressed interest in seeing the results, so I'm posting them here, along with a CSV file with the full results of every iteration.  I think the columns are self-explanatory, but if anyone has questions, by all means post them here and I'll try to answer.  Here's the results:

http://www.peaktotrough.com/download/hb ... v.zip  [ 3 MB ]

Here are the parameters for each run of this simulation:

- Start date:  01/01/1972
- End date:  12/06/2012
- Reinvest all dividends and interest payments into their respective assets
- Rebalance on 35/15 bands
- Cash in 1 year T-bills
- Treasury bonds are all 30 years when they were historically available, 20 years otherwise
- Stock allocation in the S&P 500

Interesting (albeit, somewhat random) observations:

- Sorting for highest CAGR gives us:  10.3% CAGR and 11.12% annualized standard deviation with an allocation of 0% Tbills, 6% Tbonds, 50% gold, 44% S&P500.

- Sorting for highest max drawdown yields a 100% allocation to gold.  It takes the... ahem... gold medal with a 70.26% max dd over the period.  Yikes.

- Sorting for highest Sharpe ratio gives us 0.6167 with an allocation of:  20% Tbills, 23% Tbonds, 34% Gold, 23% S&P500.  CAGR of 10.21% and standard deviation of 7.3%.

- Second highest Sharpe ratio is 0.6166:  27% Tbills, 25% Tbonds, 21% Gold, 27% S&P500.  CAGR of 9.7% and standard deviation of 6.5%.  Two things noteworthy here... a significant difference in allocation, but similar results in sharpe ratios.  Also, this is substantially similar to the standard 4x25 portfolio.

- Looking at gold specifically, in the top 100 results sorted by Sharpe ratio, the low gold allocation is 18%, CAGR is 9.6%.  The high gold allocation is 35% with a CAGR of 10.3%. 

- The standard 4x25 allocation is remarkably close to the optimal allocation with a CAGR of 9.6%, standard deviation of 6.8% and Sharpe ratio of 0.57.  I personally find this fascinating.

Some of you guys are MUCH better at data crunching with Excel than I am, so have at it... let us know if you find anything interesting. 

Also, it goes without saying that I do not claim these results to be error-free, and I highly recommend everyone verify the results and perform their own due diligence before using anything contained herein for investment purposes.

Thanks,
P2T
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frugal
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Re: Backtesting for the Optimum HBPP Allocations

Post by frugal » Fri Dec 28, 2012 4:26 pm

Great job!

What I also would like to have is a daily chart of HBPP performance for the same period. Can you publish it?

Regards


I've found it over your FANTASTIC personal web-site. Another GREAT GREAT work!
Last edited by frugal on Sat Dec 29, 2012 2:53 am, edited 1 time in total.
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buddtholomew
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Re: Backtesting for the Optimum HBPP Allocations

Post by buddtholomew » Fri Dec 28, 2012 6:13 pm

Thank you for producing this content. I too find it fascinating that the 4x25 configuration is close to the optimal allocation.

Happy Holidays!
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whatchamacallit
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Re: Backtesting for the Optimum HBPP Allocations

Post by whatchamacallit » Fri Dec 28, 2012 8:32 pm

Thank you for sharing.

I was wondering how the rebalance bands were applied in these different scenarios.

Wouldn't 15/35 rebalance bands only apply to the 25x4 portfolio?
Peak2Trough
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Re: Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Sat Dec 29, 2012 7:27 am

frugal wrote:What I also would like to have is a daily chart of HBPP performance for the same period. Can you publish it?
I'll do one better... you can generate your own here:

http://www.peaktotrough.com/hbpp.cgi

Have fun.  ;)
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Re: Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Sat Dec 29, 2012 7:34 am

whatchamacallit wrote: I was wondering how the rebalance bands were applied in these different scenarios.

Wouldn't 15/35 rebalance bands only apply to the 25x4 portfolio?
That is an excellent question!  And to be honest, one I hadn't given a whole lot of thought before running this simulation...

Here's the way it works currently:  The 35/15 points are simple "triggers" that, when hit, cause a rebalance action to occur.  The rebalance action itself will rebalance the portfolio back to its *original* allocation.  So if you started out with 20/30/16/34 that's what you'll have after the rebalance is completed.

Upon reflection, this means that many allocations are being rebalanced too much, and many are probably not being rebalanced enough, based upon the magnitude of the move required to hit the 35/15 trigger from the original allocation.  But then again, I suspect most of the ones any of us would actually consider are being rebalanced sufficiently often.

Maybe I'll start a new one on Jan 1, 2013 with annual rebalancing instead and see how that changes things...

Good comment, thanks!

P2T
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Re: Backtesting for the Optimum HBPP Allocations

Post by pugchief » Sat Dec 29, 2012 7:46 am

Awesome stuff. Thanks for sharing.
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Re: Backtesting for the Optimum HBPP Allocations

Post by MachineGhost » Sat Dec 29, 2012 7:54 am

I wouldn't say the optimal allocation is close to 25/4, but it depends on how you define risk.  Volatility is not risk.  If you use max drawdown for your risk criteria in Sharpe, then the optimal allocation will be much different as I posted in another thread (probably gone due to the forum software change).  For the average investor though, 25/4 is fine but there will be scary interyear periods of 20% max drawdowns, possibly higher in the next "tight money recession".

Frankly, I think you get more out of worrying about market timing than portfolio allocation.  There's not always a guaranteed inversely correlated asset that will go up in any given market condition.  For instance, a "tight money recession" is the worst for the PP because cash has no ability to move up, so avoiding losses in the other three assets is critical to managing overall portfolio risk.
Last edited by MachineGhost on Sat Dec 29, 2012 7:56 am, edited 1 time in total.
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Re: Backtesting for the Optimum HBPP Allocations

Post by Desert » Sat Dec 29, 2012 7:59 am

MG, that's interesting.  Do you recall what the optimum allocation was, using max drawdown in Sharpe? 
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Re: Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Sat Dec 29, 2012 8:17 am

MachineGhost wrote: I wouldn't say the optimal allocation is close to 25/4, but it depends on how you define risk.  Volatility is not risk.  If you use max drawdown for your risk criteria in Sharpe, then the optimal allocation will be much different as I posted in another thread (probably gone due to the forum software change).
Interesting.  Everything I have seen so far has shown standard deviation to be a good proxy for max drawdown.  In fact, what I've seen so far indicates that the relationship is, more or less, linear.  Sorting by max drawdown in my csv file and taking a quick look at the standard deviation column to the left also appears to confirm this.

Perhaps the standard deviations you've seen used for sharpe ratios in the past were calculated differently, used poor data sources, or extrapolated fewer data points.  Mine is a daily standard deviation which is then annualized, which should give as close an approximation to max drawdown as possible.

For that matter, download the file and test it... just multiply the sharpe ratio column by the StdDev column, and then divide the result by the MaxDD column.  That should give you what you're asking for above...
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Re: Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Sat Dec 29, 2012 8:42 am

Following up from my reply to MG above...

I took a moment and did what you suggested and created a new column using MaxDD as the risk component.  It turns out that it does materially change the optimum allocations using that ratio, and that the standard deviation and max drawdown do not have a linear relationship as I suggested earlier.

Most interesting is that the gold allocation varies from only 14-18% in the 100 most efficient allocations using this ratio.  The best is:

35% Tbill, 23% Tbond, 14% Gold, 28% S&P500 - CAGR 9.1%, 13.2% Max DD

I'd certainly take that deal.    ;)
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Re: Backtesting for the Optimum HBPP Allocations

Post by possum » Sat Dec 29, 2012 10:04 am

Peak2Trough wrote: Following up from my reply to MG above...

I took a moment and did what you suggested and created a new column using MaxDD as the risk component.  It turns out that it does materially change the optimum allocations using that ratio, and that the standard deviation and max drawdown do not have a linear relationship as I suggested earlier.

Most interesting is that the gold allocation varies from only 14-18% in the 100 most efficient allocations using this ratio.  The best is:

35% Tbill, 23% Tbond, 14% Gold, 28% S&P500 - CAGR 9.1%, 13.2% Max DD

I'd certainly take that deal.    ;)
FWIW, I've played around with different allocations and have also found that 15% gold and 30% equities is in the sweet spot.
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