40/15 rebalancing bands?

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Pet Hog
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40/15 rebalancing bands?

Post by Pet Hog » Tue May 28, 2013 5:02 pm

Hi, I'm a new member and this is my first post.  I have lurked for a few months and have learned a lot.  Thank you all.

I have a question about rebalancing bands.  I'm curious whether 40/15 bands might be attractive for rebalancing events (rather than 35/15) and whether anyone has modeled them?  I'm considering 40/15 bands for two reasons: (i) they more accurately reflect a component halving or doubling in value and (ii) they might better balance volatility on the upside and downside.  Let me explain both.

(i) Consider a balanced PP with stocks, gold, cash, and bonds of $100 each:
100/100/100/100 = $400
If one component doubles in value (say stocks), with no change to the others (sure, unlikely in the real world), we would get:
200/100/100/100 = $500
In percentage terms,
40/20/20/20 = 100%
This situation would trigger a rebalance (40% band).

From the original balanced portfolio, if one of the components halved in value we would get:
50/100/100/100 = $350
In percentages,
14.3/28.6/28.6/28.6 = 100%
This situation would trigger the 15% rebalancing band.  I understand the logic of the PP having a 15% band: it corresponds to one of the components halving in value relative to all of the other components.  That makes sense to me.  But I would also expect -- for symmetry alone! -- to rebalance on the upside at 40%, not 35%.

(ii) Using Peak2Trough's data at http://www.peaktotrough.com/hbpp.cgi and looking at all of the historical rebalancing events for the 35/15 bands over the last 40+ years, it seems that there have been more rebalances triggered by a component reaching 35% than there have been by one reaching 15% (by about 2:1).  To my mind, you would want both events to be roughly equally distributed to catch volatility in both directions.  One way to even it out might be to increase the 35% band to 40% (so that rebalancing on the upside becomes less frequent) while keeping the 15% band where it is.  Unfortunately, Peak2Trough's algorithm doesn't allow 40/15 as an option for rebalancing bands.

I'm not trying to reinvent the wheel, but I am curious whether these bands have been tested before and what the numbers look like. If only to convince myself that there is no advantage!  Has there been a discussion like this before?  Does what I propose sound logical?
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Xan
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Re: 40/15 rebalancing bands?

Post by Xan » Tue May 28, 2013 5:19 pm

Welcome!

It sounds very logical indeed.  I believe Harry Browne never claimed there was anything scientific about 35/15.  The fact is that rebalancing more often is sometimes better, and rebalancing less often is sometimes better.  It's going to be hard to scientifically prove what bands are best, since that's a matter of predicting the future from past events.

But I'm sure that any testing or hard figures that you can come up with would be most welcome!
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smurff
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Re: 40/15 rebalancing bands?

Post by smurff » Tue May 28, 2013 5:34 pm

If a person looked at the portfolio only once a year, it's possible to be at 40% on the best performing asset.
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AdamA
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Re: 40/15 rebalancing bands?

Post by AdamA » Tue May 28, 2013 6:41 pm

It seems reasonable to me, especially if you have to pay taxes to rebalance.
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Re: 40/15 rebalancing bands?

Post by Khisanth » Tue May 28, 2013 10:45 pm

From posts I read a while back, the 35% rebalancing band represented a 40% increase in an asset. But that was basically taking 25 * 1.4 to equal 35. That's looking at that one asset in isolation to the rest of the portfolio. I hadn't actually put the pen to paper to make the calculations before.

100 / 100 / 100 / 100 = 400    100 / 400 = 25.00%

40% increase in one asset: 140 / 100 / 100 / 100 = 440    140 / 440 = 31.18%  100 / 440 = 22.72%
50% increase in one asset: 150 / 100 / 100 / 100 = 450    150 / 450 = 33.33%  100 / 450 = 22.22%

62% increase in one asset: 162 / 100 / 100 / 100 = 462    162 / 462 = 35.06%  100 / 462 = 21.64%

47% decrease in one asset: 53 / 100 / 100 / 100 = 353    53 / 353 = 15.01%    100 / 353 = 28.33%

So there isn't really any complete symmetry involved in the 15/35 rebalancing bands.

HOWEVER, the 15/35 bands were chosen to represent a significant imbalance in the ratio of the PP assets for portfolio protection as well. I'm pretty sure I wouldn't be comfortable with 40/20/20/20, as I'm already itching to rebalance when an asset hits 30% of the total portfolio.

This is all academic of course. Choose what feels comfortable. The 15/35 is a guideline. I've chosen 20/30 as I'm a bit more conservative and tend to want to keep things as closely balanced as possible.
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Re: 40/15 rebalancing bands?

Post by Tortoise » Wed May 29, 2013 1:16 am

Welcome, Pet Hog!

I agree with your math; 15/40 rebalancing bands are more symmetric than 15/35 in the sense that asset price changes tend to be multiplicative rather than additive. But I suspect that, all other things being equal, there is no inherent advantage in using more symmetric rebalancing bands. I haven't run any numbers, but that's just my hunch.

As Xan pointed out, sometimes rebalancing more often helps, and sometimes it hurts--and there's no way to predict it. Because of that, I tend to share Khisanth's view that the main purpose of the rebalancing bands is to prevent the portfolio from becoming dangerously lopsided, not necessarily to optimize portfolio growth. If you're okay with losing 40% of your portfolio if one asset happens to nosedive, then a 40% upper band might be suitable for you. Others with less risk tolerance (and the PP is an inherently risk-averse strategy) are more comfortable with HB's recommended 35% or even 30% as the upper band.

(As an aside, here's yet another set of rebalancing bands with an interesting kind of "symmetry": If an asset exceeds an allocation of 33%, that means it's now greater than 1/3 of the portfolio, so the PP now has the downside risk of a 3-asset portfolio. Similarly, if an asset drops below 20%, that means it's now less than 1/5 of the portfolio, meaning the PP now has the limited upside potential of a 5-asset portfolio. So one could rebalance to keep the allocations X in the range 1/5 < X < 1/3, i.e., use 20/33 rebalancing bands.)
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Re: 40/15 rebalancing bands?

Post by Pet Hog » Thu May 30, 2013 2:24 am

Xan wrote: It sounds very logical indeed.  I believe Harry Browne never claimed there was anything scientific about 35/15.  The fact is that rebalancing more often is sometimes better, and rebalancing less often is sometimes better.  It's going to be hard to scientifically prove what bands are best, since that's a matter of predicting the future from past events
Thanks for your response, Xan.  My attraction to the PP is its cold, mechanical rules.  While we may not find a scientific proof, there must an optimal strategy.  It seems that 35/15 is pretty close.
smurff wrote: If a person looked at the portfolio only once a year, it's possible to be at 40% on the best performing asset.
Thanks, Smurff.  I think we would all agree that it would be time to rebalance in that case!
AdamA wrote: It seems reasonable to me, especially if you have to pay taxes to rebalance.
Yes, AdamA, less-frequent rebalancing might help for taxable accounts.
Khisanth wrote: 62% increase in one asset: 162 / 100 / 100 / 100 = 462    162 / 462 = 35.06%  100 / 462 = 21.64%

HOWEVER, the 15/35 bands were chosen to represent a significant imbalance in the ratio of the PP assets for portfolio protection as well. I'm pretty sure I wouldn't be comfortable with 40/20/20/20, as I'm already itching to rebalance when an asset hits 30% of the total portfolio.
Thanks, Khisanth, for your analysis of the 35% band (increase in one asset by 1.62-fold).  On the downside, using my previous approach, we should consider a decrease in one asset by 1.62-fold ($100/1.62 = $61.70):
61.7/100/100/100 = $361.7
61.7/361.7 = 17.1%
In other words, rebalancing with 35/17.1 bands would be more "symmetrical" -- and would trigger more rebalancing events on the downside than using a 15% band.

With regard to discomfort at 40/20/20/20, I suspect that most people would not be uncomfortable with a 14.3/28.6/28.6/28.6 scenario (with 35/15 bands), which is just the inverse state: one asset at half (double) the value of the average of the other three.  In my hypothesis, it would be time to rebalance in both cases.
Tortoise wrote: But I suspect that, all other things being equal, there is no inherent advantage in using more symmetric rebalancing bands. I haven't run any numbers, but that's just my hunch.
Thanks, Tortoise.  My original post is also a hunch and I, too, haven't run the numbers.  I was hoping someone already had!
Tortoise wrote:As I tend to share Khisanth's view that the main purpose of the rebalancing bands is to prevent the portfolio from becoming dangerously lopsided, not necessarily to optimize portfolio growth.
As I stated above, I consider 40/20/20/20 and 14/28/28/28 to be inversely related; that is, neither is more lopsided than the other.  Or to put it another way, with 35/15 bands, I consider 15/29/28/28 (one asset approximately half the average of the other three) to be more lopsided than 35/22/22/21 (one asset only 62% higher than the average of the other three).
Tortoise wrote:If an asset exceeds an allocation of 33%, that means it's now greater than 1/3 of the portfolio, so the PP now has the downside risk of a 3-asset portfolio. Similarly, if an asset drops below 20%, that means it's now less than 1/5 of the portfolio, meaning the PP now has the limited upside potential of a 5-asset portfolio. So one could rebalance to keep the allocations X in the range 1/5 < X < 1/3, i.e., use 20/33 rebalancing bands.
Excellent idea!  Has there been any number-crunching to support that approach?

Thanks for all the replies.  I am amazed at the high level of discussion on these forums -- and by the high quality of the language!
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Re: 40/15 rebalancing bands?

Post by Tortoise » Thu May 30, 2013 10:18 pm

Pet Hog wrote:
Tortoise wrote:If an asset exceeds an allocation of 33%, that means it's now greater than 1/3 of the portfolio, so the PP now has the downside risk of a 3-asset portfolio. Similarly, if an asset drops below 20%, that means it's now less than 1/5 of the portfolio, meaning the PP now has the limited upside potential of a 5-asset portfolio. So one could rebalance to keep the allocations X in the range 1/5 < X < 1/3, i.e., use 20/33 rebalancing bands.
Excellent idea!  Has there been any number-crunching to support that approach?
I doubt it; it's just an idea that occurred to me as I was writing the reply :)

As far as number-crunching goes, these sorts of questions about rebalance bands and strategies for new contributions (add to cash, equal split, proportional adding, or buy the lagging asset) come up often enough on this forum that I'm starting to think it would be fun to code up a Monte Carlo simulator to test all of these ideas. Ideally, it would have two modes:
  1. Back-testing Mode: Use stock/bond/gold/cash data back to 1972 to see how various strategies would have performed in the past
  2. Prediction Mode: Use a statistical model of stock/bond/gold/cash price movements to predict how various strategies should perform in some probabilistic sense going forward (e.g., show a random distribution of returns for each strategy or set of rebalance bands, highlighting the mean and standard deviation)
If someone has already created a tool like that with a user-friendly GUI, I'll pay money for it!
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Re: 40/15 rebalancing bands?

Post by Pointedstick » Thu May 30, 2013 10:50 pm

Tortoise, I believe these sites get pretty close:
1. http://www.longtermreturns.com/p/histor ... turns.html
2. http://firecalc.com
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Re: 40/15 rebalancing bands?

Post by Tortoise » Fri May 31, 2013 12:00 am

Very cool, thanks PS!
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Re: 40/15 rebalancing bands?

Post by tennpaga » Fri May 31, 2013 7:23 am

Pet Hog wrote: This situation would trigger the 15% rebalancing band.  I understand the logic of the PP having a 15% band: it corresponds to one of the components halving in value relative to all of the other components.  That makes sense to me.  But I would also expect -- for symmetry alone! -- to rebalance on the upside at 40%, not 35%.
Numbers are just numbers, and there are lots of different ways to define symmetry.  HB's 25% +/- X (where X is 10%) is one type of symmetry.  Your post defines another.

Another would be to define rebalance bands at 25% * (1 + x) and 25% / (1 + x).  With x = 0.4, the bands work out to 35% and 18%; with x = 0.667 (2/3), the bands are 42% and 15%.

FWIW, I did a rebalancing backtest study 1.5 years ago, though I only looked at upper and lower bands at 25% +/- X (i.e. using Harry Browne's version of symmetry), and X = 10 (i.e. rebalance bands at 35/15) turned out to be optimal.

http://gyroscopicinvesting.com/forum/ht ... 933#p16933

My advice would be not to overthink this.  I'm sure one could find an after-the-fact "optimal" rebalancing strategy, but it would seem unlikely to me that the future would behave identically.
Last edited by tennpaga on Fri May 31, 2013 8:40 am, edited 1 time in total.
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Re: 40/15 rebalancing bands?

Post by smurff » Sat Jun 01, 2013 1:20 am

Pet Hog wrote:
Thanks for all the replies.  I am amazed at the high level of discussion on these forums -- and by the high quality of the language!
That's because MediumTex does not allow cussing'. :)
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