Backtesting for the Optimum HBPP Allocations

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Re: Backtesting for the Optimum HBPP Allocations

Post by frugal » Tue Feb 12, 2013 4:14 pm

Peak2Trough

the most terrible thing investing is the monster DRAWDOWNS.

Can you please let me now the TOP 10 drawdowns of the HB PP ?


Thank YOU!
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Re: Backtesting for the Optimum HBPP Allocations

Post by rocketdog » Tue Feb 19, 2013 12:55 pm

rocketdog wrote:This is great stuff, but I'm confused about the SharpeMDD.  How exactly is that being calculated?  I can't seem to back into it using the Sharpe and MaxDD values.
Bump.
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Re: Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Tue Feb 19, 2013 3:15 pm

rocketdog wrote:This is great stuff, but I'm confused about the SharpeMDD.  How exactly is that being calculated?  I can't seem to back into it using the Sharpe and MaxDD values.
It's the same as the Sharpe ratio, but the denominator is the MaxDD for that allocation rather than the standard deviation.  In other words, it is:

(CAGR - RiskFreeCAGR) / MaxDD

If you want to double check it in the spreadsheet, you can do so using the current data since we know that the numerator for Sharpe and SharpeMDD are the same.  You would just multiple by the StdDev and divide by the MaxDD to arrive at the SharpeMDD.

Sharpe * StdDev / MaxDD * 100 = SharpeMDD

That help?
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Re: Backtesting for the Optimum HBPP Allocations

Post by rocketdog » Tue Feb 19, 2013 3:36 pm

I'm a bit of an Excel junkie, and I've been playing around with this data.  First, I discarded any rows where any of the indicators was in the bottom 50% of its own category.  Then, I ranked the remaining results for each indicator based on whether it was in the Top 10%, Top 20%, and so on. 

Then I filtered the data to find the best balance between performance and risk.  So far, no matter how I go about it I almost always get results that fall within these ranges:
T-bills = 15%-20%
T-bonds = 30%-35%
Gold    = 15%-20%
Stocks  = 30%-35%
These proportions generally result in the following indicator ranges:
CAGR      =  9.38%- 9.45%
StdDev    =  6.78%- 7.00%
MaxDD    = 17.35%-18.84%
Sharpe    =  0.53%- 0.54%
SharpeMDD = 19.53%-21.65%
These ranges are all better than a pure 4x25 PP (with only a very minor exception in the case of StdDev).  This suggests to me that we can take these ranges and use them as a starting point to build our PP.  Then, we can tilt it towards slightly less risk and lower returns (20/30/20/30) or slightly more risk and higher returns (15/35/15/35) depending on our tolerance.  But in the end, I would expect any PP that falls within these ranges to perform very similarly.

It's possible my logic is flawed, so feel free to see if you can find a better balance between performance and risk. 
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Re: Backtesting for the Optimum HBPP Allocations

Post by MachineGhost » Tue Feb 19, 2013 4:13 pm

rocketdog wrote: It's possible my logic is flawed, so feel free to see if you can find a better balance between performance and risk.
Your logic is sound.  The problem is the future will not repeat the past, exactly.  So anything but  a naive diversification risks being under or over weight any of the four asset classes.  It should already be obvious we are not repeating the 70's in exactly the same way.

There is room for debate on how to define the weight basis, though.
Last edited by MachineGhost on Tue Feb 19, 2013 4:15 pm, edited 1 time in total.
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Re: Backtesting for the Optimum HBPP Allocations

Post by rocketdog » Wed Feb 20, 2013 9:35 am

MachineGhost wrote:Your logic is sound.  The problem is the future will not repeat the past, exactly.  So anything but  a naive diversification risks being under or over weight any of the four asset classes.  It should already be obvious we are not repeating the 70's in exactly the same way.

There is room for debate on how to define the weight basis, though.
I totally agree.  This is only backtesting after all, and the next 40 years may favor different proportions. 

My personal take-away is that anyone who wishes to play around with the proportions of each holding in their PP would be wise to stay within these ranges (holding at least 15% of each investment, but no more than 35% of any investment). 

The other interesting thing I wanted to point out is that the upper and lower bands in my findings (15% and 35%) happen to correlate perfectly with the rebalancing triggers recommended for the PP.  I wonder if we can extrapolate any significance from this, or if it's merely a happy coincidence? 
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Re: Backtesting for the Optimum HBPP Allocations

Post by Thomas Hoog » Wed Feb 20, 2013 9:38 am

I have also been playing around (great data) with set of allocations with round figures 0, 10, 20 etc.
and the 40 years periode and the 30 years period. In the 30 years period the HP allocation performs less compared to the 40 years period. However the final conclusion was a 10 % (cash), 20 % (Gold), 30 % (Bonds), 40 (Stocks) allocation for me. It give a slightly better CAGR and some more risk in MAXDD. And that is ok for me.
It also makes sense. The HP 25 % allocation presume an equal duration of the period a favourite asset.  However in the past the period of prosperity (stock) endures longer then p.e. recession (cash) or panic (gold).
I'm surprised that it falls out of your range
Could you run your allocations in the 30 years period ?
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Re: Backtesting for the Optimum HBPP Allocations

Post by rocketdog » Wed Feb 20, 2013 11:41 am

Thomas Hoog wrote: I have also been playing around (great data) with set of allocations with round figures 0, 10, 20 etc. and the 40 years periode and the 30 years period. In the 30 years period the HP allocation performs less compared to the 40 years period. However the final conclusion was a 10 % (cash), 20 % (Gold), 30 % (Bonds), 40 (Stocks) allocation for me. It give a slightly better CAGR and some more risk in MAXDD. And that is ok for me.
It also makes sense. The HP 25 % allocation presume an equal duration of the period a favourite asset.  However in the past the period of prosperity (stock) endures longer then p.e. recession (cash) or panic (gold).
I'm surprised that it falls out of your range
Could you run your allocations in the 30 years period ?
Your findings gave me a chuckle, because before I even started this I thought about a 10/20/30/40 allocation like the one you describe.  The reason it fell out of my findings is that the StdDev and MaxDD are in the bottom 50% of such an allocation, and I restricted my data set to only the top 50% in each criteria.  That's because I was trying to find the "sweet spot" between risk and reward, not simply mazimize my reward. 

For those who don't really care about one or more of the criteria, then they can exclude that criteria from their filter.  For instance, if I have more than 20 years before retirement, I might care more about CAGR than either StdDev or MaxDD, so I could exclude StdDev and MaxDD from my filtering criteria. 

You can data mine different scenarios all day long.  My objective was merely to see if I could find reasonable reward at a tolerable risk. 
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Re: Backtesting for the Optimum HBPP Allocations

Post by rocketdog » Thu Feb 21, 2013 9:01 am

Peak2Trough wrote:If you want to double check it in the spreadsheet, you can do so using the current data since we know that the numerator for Sharpe and SharpeMDD are the same.  You would just multiple by the StdDev and divide by the MaxDD to arrive at the SharpeMDD.

Sharpe * StdDev / MaxDD * 100 = SharpeMDD
I see now.  But why are we first multiplying the Sharpe by StdDev? 

Also, am I right in assuming that a higher SharpeMDD is better than a lower SharpeMDD? 
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Re: Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Thu Feb 21, 2013 9:10 am

rocketdog wrote:I see now.  But why are we first multiplying the Sharpe by StdDev?
Because StdDev is the denominator in the original Sharpe ratio.  We're trying to isolate the original numerator (CAGR - RiskFreeCAGR) and then divide by the MaxDD to create a new ratio which is functionally equivalent to the Sharpe ratio, but using MaxDD instead of StdDev.

I'm not convinced it has a lot of usefulness above and beyond that of the original Sharpe ratio, but some folks asked for it, and it was easy enough to add so there we have it.
Also, am I right in assuming that a higher SharpeMDD is better than a lower SharpeMDD?
Yes you are!  Well, assuming you like money.  ;D
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Re: Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Thu Feb 21, 2013 9:16 am

frugal wrote:the most terrible thing investing is the monster DRAWDOWNS.

Can you please let me now the TOP 10 drawdowns of the HB PP ?
I agree that drawdowns are often overlooked, even by the HBPP crowd. 

While I can't tell you what the 10 highest drawdowns were over a given period, you can do do the following on the website:

Enter all the dates, allocations, and other options like you would for a normal query on the site.  Then next to "DD count threshold" enter a number like 10%.  Then when you calculate the returns, look for the "DD > 15% Count" in the results.

What that number is telling you is how many > 15% drawdowns there were over the period and allocation you selected.  For example, if I enter:

01-01-1972
01-01-2013
25 / 25 / 25 / 25
1 yr Tr
30 yr Tr
Rebalance annually
Reinvest dividends
DD Count Threshold 10%

It will tell me there were 8 peak to trough drawdowns of > 10% from 1972-2013. 

Change the DD threshold to 15% and there is only 1.
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Re: Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Thu Feb 21, 2013 9:23 am

Thomas Hoog wrote:Could you run your allocations in the 30 years period ?
Interesting point... I actually ran every decade independently when I started this and, as you would expect, got significantly different results for each.  I rather liken it to an exponential moving average vs a normal weight moving average in that we should apply more weight to the more recent results, given that they are the result of particular economic climates.

Having said that, I'm not sure running it for 30 years vs 40 is all that helpful... if we agree more recent data is 'better' then we would eventually narrow it down further and further, and yet still probably wouldn't have a better understanding of what the future may bring. 

I tend to look at the data more as a way to ferret out what effect changes in allocations actually have over time than an attempt to answer what allocation to adopt going forward.
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Re: Backtesting for the Optimum HBPP Allocations

Post by Thomas Hoog » Thu Feb 21, 2013 10:17 am

rocketdog wrote:
Thomas Hoog wrote: I have also been playing around (great data) with set of allocations with round figures 0, 10, 20 etc. and the 40 years periode and the 30 years period. In the 30 years period the HP allocation performs less compared to the 40 years period. However the final conclusion was a 10 % (cash), 20 % (Gold), 30 % (Bonds), 40 (Stocks) allocation for me. It give a slightly better CAGR and some more risk in MAXDD. And that is ok for me.
It also makes sense. The HP 25 % allocation presume an equal duration of the period a favourite asset.  However in the past the period of prosperity (stock) endures longer then p.e. recession (cash) or panic (gold).
I'm surprised that it falls out of your range
Could you run your allocations in the 30 years period ?
Your findings gave me a chuckle, because before I even started this I thought about a 10/20/30/40 allocation like the one you describe.  The reason it fell out of my findings is that the StdDev and MaxDD are in the bottom 50% of such an allocation, and I restricted my data set to only the top 50% in each criteria.  That's because I was trying to find the "sweet spot" between risk and reward, not simply mazimize my reward. 

For those who don't really care about one or more of the criteria, then they can exclude that criteria from their filter.  For instance, if I have more than 20 years before retirement, I might care more about CAGR than either StdDev or MaxDD, so I could exclude StdDev and MaxDD from my filtering criteria. 

You can data mine different scenarios all day long.  My objective was merely to see if I could find reasonable reward at a tolerable risk. 
Ok, now I understand your method. And yes it has a StD below 50 % average.
Using your method and some logical allocations (C= Cash, B= Bonds, G=Gold, S = Stocks)
you get the folowing results

C B G S CAGR StD MAXDD Sharpe SharpeMDD
10 30 20 40 9,8 7,6 19,9% 0,54 20,60
25 25 25 25 9,3 6,8 20,2% 0,52 16,21
20 30 20 30 9,4 6,8 18,8% 0,54 15,35
15 35 15 35 9,5 7,0 17,4% 0,54 26,47
10 40 20 30 9,7 7,3 20,1% 0,55 19,90


and now to put them in your "order". The % means p.e first row 19 % in CAGR that there are 18 % better and 81 % less allocations
Red means last, Green best
C   B   G   S    CAGR StD MAXDD Sharpe SharpeMDD
10 30 20 40 19% 57%    31%     2%     4%
25 25 25 25 45% 29% 33%     5%   22%
20 30 20 30 39% 28% 26%     1%     9%
15 35 15 35 35% 32% 19%     2%     1%
10 40 20 30 23% 37% 32%     0%     7%

So you can choose according to your whishes.
The last one: 10 % TBills, 40 % Bonds, 20 % Gold, 30 % Stocks has a great Sharpe ratio
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Re: Backtesting for the Optimum HBPP Allocations

Post by rocketdog » Thu Feb 21, 2013 11:46 am

Thomas Hoog wrote:The last one: 10 % TBills, 40 % Bonds, 20 % Gold, 30 % Stocks has a great Sharpe ratio
OK, get ready for this...

I did some more in-depth number crunching using a different methodology, and I came up with similar but different bands than I did the first time.  I feel better about these results so I thought I'd share them here. 

This time, I wanted to find the portfolios that gave me the best of all worlds.  So I filtered for the Top 40% under each criteria:

40% Highest CAGR
40% Lowest StdDev
40% Lowest MaxDD
40% Highest Sharpe
40% Highest SharpeMDD

In other words, I was looking for the intersection of just those portfolios that were "best of breed" in each of the given criteria.  What I got in return was 17 portfolios.  Here are the bands for those portfolios:

T-Bills =  9% - 13%
T-Bonds = 32% - 44%
Gold    = 18% - 21%
SP500  = 29% - 35%

Notice anything?  Yes they all encompass the 10/40/20/30 portfolio that Gerard homed in on! 

My new bands result in the following criteria ranges:

CAGR      =  9.66 -  9.70
StdDev    =  7.24 -  7.29
MaxDD    = 19.08 - 20.02
Sharpe    =  0.54 -  0.55
SharpeMDD = 19.84 - 20.80

As you can see, we are splitting hairs here, with most of the criteria differing by only a few tenths -- or even hundredths -- of a percent. 

I'm not suggesting this is the "perfect" portfolio, and clearly the past 40 years is not likely to be repeated.  But I thought it was interesting that these ranges generally indicate that holding less cash and gold but more bonds and stocks has historically provided the best balance between performance and risk.
Last edited by rocketdog on Thu Feb 21, 2013 11:49 am, edited 1 time in total.
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Re: Backtesting for the Optimum HBPP Allocations

Post by annieB » Thu Feb 21, 2013 11:56 am

Great analysis.Fun to follow..
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Re: Backtesting for the Optimum HBPP Allocations

Post by Peak2Trough » Thu Feb 21, 2013 2:05 pm

rocketdog wrote:But I thought it was interesting that these ranges generally indicate that holding less cash and gold but more bonds and stocks has historically provided the best balance between performance and risk.
Fantastic work!  It seems to me the hypothesis above is fairly intuitive as well, given the volatility of gold, and the lack thereof of cash.  In fact, I wonder how close that allocation is to a HBPP allocation equally weighted on volatility.
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Re: Backtesting for the Optimum HBPP Allocations

Post by MachineGhost » Thu Feb 21, 2013 3:09 pm

Peak2Trough wrote: I'm not convinced it has a lot of usefulness above and beyond that of the original Sharpe ratio, but some folks asked for it, and it was easy enough to add so there we have it.
It has use in that it is a number you can actually relate to in practical terms, as opposed to volatility.  But the reason Sharpe and MaxDD are rather similar on a relative basis is because the highest high above a mean to the lowest low below the mean is essentially a peak-to-trough drawdown.
Last edited by MachineGhost on Thu Feb 21, 2013 3:11 pm, edited 1 time in total.
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Re: Backtesting for the Optimum HBPP Allocations

Post by MachineGhost » Thu Feb 21, 2013 3:15 pm

rocketdog wrote: I'm not suggesting this is the "perfect" portfolio, and clearly the past 40 years is not likely to be repeated.  But I thought it was interesting that these ranges generally indicate that holding less cash and gold but more bonds and stocks has historically provided the best balance between performance and risk.
That would make plenty of sense with secular bull markets in stock and bonds since 1980.  If Japan is a taste of our future, such a portfolio may underperform versus naive diversification.
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Re: Backtesting for the Optimum HBPP Allocations

Post by rocketdog » Thu Feb 21, 2013 3:30 pm

MachineGhost wrote:
rocketdog wrote: I'm not suggesting this is the "perfect" portfolio, and clearly the past 40 years is not likely to be repeated.  But I thought it was interesting that these ranges generally indicate that holding less cash and gold but more bonds and stocks has historically provided the best balance between performance and risk.
That would make plenty of sense with secular bull markets in stock and bonds since 1980.  If Japan is a taste of our future, such a portfolio may underperform versus naive diversification.
Absolutely, which is why I qualified my statement.  No telling what will happen over the next "X" number of years.  This is just a fun "rearview mirror" exercise. 

Another thing to consider is that my analysis looked at the entire 40-year period.  But if you're close to (or in) retirement, you don't have the luxury of 4 decades to smooth things out.  So you may want to shift yourself towards a portfolio that has lower StdDev and/or MaxDD readings, even though it wil likely come at the expense of CAGR.  Most retirees don't need any major surprises in their portfolio.
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Re: Backtesting for the Optimum HBPP Allocations

Post by frugal » Thu Feb 21, 2013 3:45 pm

Peak2Trough wrote:
frugal wrote:the most terrible thing investing is the monster DRAWDOWNS.

Can you please let me now the TOP 10 drawdowns of the HB PP ?
I agree that drawdowns are often overlooked, even by the HBPP crowd. 

While I can't tell you what the 10 highest drawdowns were over a given period, you can do do the following on the website:

Enter all the dates, allocations, and other options like you would for a normal query on the site.  Then next to "DD count threshold" enter a number like 10%.  Then when you calculate the returns, look for the "DD > 15% Count" in the results.

What that number is telling you is how many > 15% drawdowns there were over the period and allocation you selected.  For example, if I enter:

01-01-1972
01-01-2013
25 / 25 / 25 / 25
1 yr Tr
30 yr Tr
Rebalance annually
Reinvest dividends
DD Count Threshold 10%

It will tell me there were 8 peak to trough drawdowns of > 10% from 1972-2013. 

Change the DD threshold to 15% and there is only 1.
10-15% is already tough to feel.

but

we have to be prepared.

Thank you again!
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Re: Backtesting for the Optimum HBPP Allocations

Post by Thomas Hoog » Tue Feb 26, 2013 9:34 am

You could plan your financial life with it. The changeover is rather smooth.

Age     Invest period           Style         Cash LT Bonds   Gold     Stocks
20 - 50 > 30 years           aggressive   10       30           20       40
50 - 70 10 / 30 years       equable         10       40           20       30
70 - ~ less then 10 years   relax           15       35           15       35

Age       Invest period     CAGR   StD   MAXDD   Sharpe   SharpeMDD
20 - 50 > 30 years           19%   57%   31%       2%           4%
50 - 70 10 / 30 years       23%   37%   32%       0%           7%
70 - ~ less then 10 years 35%   32%   19%       2%           1%
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Re: Backtesting for the Optimum HBPP Allocations

Post by rocketdog » Tue Feb 26, 2013 9:59 am

Thomas Hoog wrote: Age       Invest period     CAGR   StD   MAXDD   Sharpe   SharpeMDD
20 - 50 > 30 years           19%   57%   31%       2%           4%
50 - 70 10 / 30 years       23%   37%   32%       0%           7%
70 - ~ less then 10 years 35%   32%   19%       2%           1%
That seems weird, that CAGR increases as you approach retirement.  Are you sure that's right?  I would want a high CAGR early in my life and more safety as I age. 

On a related note, I've decided that I'm going to put the same % of my investments into the PP as my current age.  Then each year when I rebalance, I'll add another 1% to one of my PP holdings, thus keeping my PP % equal to my age. 

That seems like a fair compromise to me, increasing my PP while simultaneously decreasing my VP as retirement approaches. 
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Re: Backtesting for the Optimum HBPP Allocations

Post by Thomas Hoog » Wed Feb 27, 2013 6:44 am

sorry, misinterpretation
I have used your "rangorder", so 19 % CAGR means it belongs to the top 19% on CAGR. The actual CAGR is stated somewhere in earlier posts.
The objective is  a decrease in CAGR en increase in safety (in terms of StD en MAXDD).

Your strategy on  ratio VP and PP seems to me a bit weird. VP is some strange invention to satisfy your emotional behaviour. If your behaviour is related to your age, it make sense. But I doubt that.
For me, I don't use a VP. I really have no idea what the future brings.
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Re: Backtesting for the Optimum HBPP Allocations

Post by rocketdog » Wed Feb 27, 2013 2:55 pm

Thomas Hoog wrote:Your strategy on  ratio VP and PP seems to me a bit weird. VP is some strange invention to satisfy your emotional behaviour. If your behaviour is related to your age, it make sense. But I doubt that.
For me, I don't use a VP. I really have no idea what the future brings.
Well, I consider the PP to be a somewhat conservative allocation portfolio.  I have a long investing time horizon, so I'm willing to take higher risks with some of my portfolio (the VP portion).  Since the longer the time horizon you have the more risk you can afford to take, it stands to reason that when I'm young my VP should be larger than my PP, and as I approach retirement I should shift funds from my VP to my PP. 

I'm not recommending that everyone do that, mind you.  It's just the approach I've come up with that fits my investing style.  If my PP repeatedly outperforms my VP over the next 5-10 years, I may reconsider this tactic and start shifting my VP funds into my PP at a faster rate. 
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Re: Backtesting for the Optimum HBPP Allocations

Post by Kriegsspiel » Wed Feb 27, 2013 6:27 pm

I was thinking about skewing the ratios for whatever reason, but it hurt my brain too much.  I just "increased" the size of my non-PP holdings. 
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