The Swedroe 5/25 rebalancing bands restated

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livesoft
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The Swedroe 5/25 rebalancing bands restated

Post by livesoft » Fri Feb 26, 2016 7:35 pm

I think something like this may have been posted before, but so what!

I wanted to know how far equities would have to go down to trigger a rebalancing move given the 5/25 rule. Or conversely, if equities dropped D% then how would one's asset allocation shift?

The result to the nearest percent is rather trivial:
For typical asset allocations, it would take about a 20% drop in equities to hit a 5% rebalancing band. This assumes the fixed income side of the portfolio does not change.

Perhaps the 5% number from Mr Swedroe was not simply picked out of the air? Maybe he thought, "Ah, a 20% correction is when to rebalance!"

And if there was about a 10% drop in equities, then one's portfolio might drift only slightly less than 3% out-of-balance.

I use a tighter band than 5% along with another criteria. Nevertheless, I want to thank Mr Swedroe for making this band thing popular.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by LadyGeek » Fri Feb 26, 2016 10:36 pm

The band thing is in the wiki: Rebalancing "Different rebalancing approaches"
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Re: The Swedroe 5/25 rebalancing bands restated

Post by grabiner » Fri Feb 26, 2016 10:49 pm

Here are some numbers worked out. In each case, we assume that your starting portfolio was $100,000.

From 80/20, you would need to drop from $80,000 to $60,000; with $60,000 in stock and $20,000 in bonds, you are now 75/25. This is a 25% decline.

From 60/40, you would need to drop from $60,000 to $48,889, a 19% decline.

From 40/60, you would need to drop from $40,000 to $32,308, a 19% decline.

From 20/80, you would need to drop from $20,000 to $14,118, a 29% decline.

All of these hit the 5% limit. The 25% limit would be relevant in a 90/10 portfolio, as a drop from $90,000 to $70,000 makes the portfolio 87.5/12.5. This is a 29% decline, so 90/10 portfolios don't need to rebalance much even with the 25% rule. (I was 90/10 and did go over the band in October 2008, with the market down about 40% from the peak and 30% from my last rebalance.)
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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Fri Feb 26, 2016 11:21 pm

I have yet to understand the point of the "5" in the suggested approach... Why use an absolute percentage in addition to a relative percentage? I don't get it. A relative percentage sounds perfectly good enough (and is more consistent with all sizes and flavors of AAs).

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Re: The Swedroe 5/25 rebalancing bands restated

Post by DG99999 » Fri Feb 26, 2016 11:34 pm

I went through this exercise, along with others, years ago as I worked through the literature available to develop my rebalancing strategy. It came as a surprise to see this posted by such a strong BH contributor and rebalancing advocate as you, LS. I have always appreciated your many insightful posts, but have thought your rebalancing bands may be too tight. I would suggest you consider another exercise - looking at incremental and total losses incurred when rebalancing tightly over the course of a large drawdown as well as the resultant returns upon recovery. While it would not make sense to develop a strategy based on 50% market losses (since you might never implement it), this exercise might lead you to widen your bands a bit.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by dratkinson » Sat Feb 27, 2016 1:20 am

siamond wrote:I have yet to understand the point of the "5" in the suggested approach... Why use an absolute percentage in addition to a relative percentage? I don't get it. A relative percentage sounds perfectly good enough (and is more consistent with all sizes and flavors of AAs).
The way I understood it, and as explained in LadyGeek's link above... the 5% absolute is used with asset classes, and the 25% relative is used with investments in an asset class.

Example 1.
Equities (asset class)
--TSM
--TISM
Bonds (asset class)
--TBM
--munis

Given multiple investments in each asset class, it is possible a class could become unbalance (5% absolute) before any investment hits a rebalance band (25% relative).

Example 2.
Equities (asset class)
--TSM
Bonds (asset class)
--TBM

On the other hand, holding only one investment in each class might see the investment band (25% relative) hit before the class band (5% absolute).

That explanation satisfied me then so I didn't look any closer.

Recall a post by Swedroe since then in which he advocated 5/20 bands. Recall him saying 5/25 might expose one to more risk, but didn't attempt to work through the logic.

Disclosure. Originally coded 5/20 bands into my Excel tracking, but switched to 5/25 when 20% triggered an alert and I wasn't ready to rebalance. (Changing to 5/25 temporarily silenced Excel alert until I was ready to rebalance.)
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Re: The Swedroe 5/25 rebalancing bands restated

Post by larryswedroe » Sat Feb 27, 2016 9:17 am

Few thoughts
First, transactions costs and taxes matter, so you don't want to have very tight bands---though should always rebalance whenever have new cash.

Second, MOM is a factor we know exists (or at least has historically) so you don't want bands to be too tight.

Those two factors are what led me to recommend that broad band. Now what one should really do, but I wanted to keep it simple, is to have wider bands for more volatile asset classes like EM

Larry

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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Sat Feb 27, 2016 9:37 am

dratkinson wrote:
siamond wrote:I have yet to understand the point of the "5" in the suggested approach... Why use an absolute percentage in addition to a relative percentage? I don't get it. A relative percentage sounds perfectly good enough (and is more consistent with all sizes and flavors of AAs).
The way I understood it, and as explained in LadyGeek's link above... the 5% absolute is used with asset classes, and the 25% relative is used with investments in an asset class.
Actually, Larry defined 'asset class' as potentially anything (either coarse-grain or fine-grain) in his article. I would agree that your interpretation is more attractive. Still, in any case, I just don't see the rationale of using absolute percentages, while I see clear inconsistencies with doing so (results would significantly vary depending on one's AA - I gave a theoretical example here, I stretched the example to better illustrate the problem).

Larry, if you could clarify where you were coming from, this would be much appreciated. Why would we need an absolute criterion in addition to relative criteria?

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Re: The Swedroe 5/25 rebalancing bands restated

Post by fortyofforty » Sat Feb 27, 2016 10:25 am

This might explain why I never seemed to reach my "rebalancing trigger". I am thinking of moving to a quarterly rebalancing, to remove emotion and introduce additional simplicity.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by livesoft » Sat Feb 27, 2016 10:32 am

fortyofforty wrote:This might explain why I never seemed to reach my "rebalancing trigger". I am thinking of moving to a quarterly rebalancing, to remove emotion and introduce additional simplicity.
My "another criteria" is the RBD thing. It removes emotions and keeps things simple.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by dbr » Sat Feb 27, 2016 10:49 am

Larry will probably agree but lot's of "rule of thumb" approaches to things use simple ratios or fractions because why not when there is no particular algorithm that clearly optimizes something. 5's work pretty well. You can also look at the points of absurdity. 10% bands result in almost never rebalancing, so why bother. Less than a 25% change in something you hold 5% of can hardly matter very much, etc.

An alternative, of course, is to always use the rule of prime numbers. We can let the "5" ride, but the other one should be "23" not "25."

Another answer in this same spirit: When Lewis Carroll was asked why all the characters in his poem "The Hunting of the Snark" have names beginning with "B," his answer was "Why not?"

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Re: The Swedroe 5/25 rebalancing bands restated

Post by livesoft » Sat Feb 27, 2016 10:51 am

^grabiner did mention 19%, 19%, and 29%. :)
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Re: The Swedroe 5/25 rebalancing bands restated

Post by grabiner » Sat Feb 27, 2016 11:24 am

siamond wrote:I have yet to understand the point of the "5" in the suggested approach... Why use an absolute percentage in addition to a relative percentage? I don't get it. A relative percentage sounds perfectly good enough (and is more consistent with all sizes and flavors of AAs).
I would actually say that the absolute 5% matters more than the relative 25%. Having 4% more in stocks and 4% less in bonds doesn't change the risk and expected return of your portfolio that much, regardless of whether the change is from 60/40 to 64/36 or from 90/10 to 94/6.

In fact, I don't use the relative 25% myself for subclasses such as large-cap emerging markets, only for the major classes of US, foreign, bonds, and real estate. Again, the logic is that the difference doesn't really matter. If you want to hold 5% in large-cap growth stock and 5% in small-cap growth stock but hold 7% and 3%, you'll never notice this in your overall portfolio returns. If you want to hold 10% in bonds and 10% in REITs but hold 14% and 6%, you might notice this (and that happened to many portfolios in 2008.)
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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Sat Feb 27, 2016 11:41 am

dbr wrote:Larry will probably agree but lot's of "rule of thumb" approaches to things use simple ratios or fractions because why not when there is no particular algorithm that clearly optimizes something. 5's work pretty well. You can also look at the points of absurdity. 10% bands result in almost never rebalancing, so why bother. Less than a 25% change in something you hold 5% of can hardly matter very much, etc.

An alternative, of course, is to always use the rule of prime numbers. We can let the "5" ride, but the other one should be "23" not "25."

Another answer in this same spirit: When Lewis Carroll was asked why all the characters in his poem "The Hunting of the Snark" have names beginning with "B," his answer was "Why not?"
Ok, fair enough, this is indeed the only possible interpretation, a coarse rule of thumb that works ok-ish in most reasonable cases.

This still doesn't explain why would one *add* such approximate mechanism (absolute percentages) to a more rigorous mechanism (relative percentages) which works perfectly fine whether one uses it on fine-grain categories or coarse-grain classes? I don't mind rules of thumb to simplify, but here, this is just adding complexity (and inconsistencies). I don't know, it just hurts my math-inclined brain, I guess! :wink:

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Re: The Swedroe 5/25 rebalancing bands restated

Post by larryswedroe » Sat Feb 27, 2016 2:20 pm

The reason I recommend relative % also is that for asset classes with low allocations like 5%, I don't that you would want them to be allowed to double or go to zero

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Re: The Swedroe 5/25 rebalancing bands restated

Post by FoolStreet » Sat Feb 27, 2016 3:17 pm

This is really confusing to me to put it into practice, maybe because I luckily haven't been faced with a massive downturn since 08/09. Back then, I was 100% stocks because of age, so there was nothing to rebalance. I've now increased my FI % because I want to ease into a more conservative positionlittle by little by the time I am ready to retire.

Over the past few years, I log into my 401k account and click as if I was going to rebalance. It shows me my past AA in % form. If my original AA % is not 5% more or less, then I leave it alone. Admittedly, the recent drop in equities has helped me with my incremental increase of bonds due to age (age-20) over the last year or two.

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Re: The Swedroe 5/25 rebalancing bands restated

Post by fortyofforty » Sat Feb 27, 2016 4:08 pm

livesoft wrote:
fortyofforty wrote:This might explain why I never seemed to reach my "rebalancing trigger". I am thinking of moving to a quarterly rebalancing, to remove emotion and introduce additional simplicity.
My "another criteria" is the RBD thing. It removes emotions and keeps things simple.
I like that in theory, but it leaves me waiting to trigger my move, and it often seems that I am unable to access my account on such days due to work constraints. Then I feel like I missed a golden opportunity, which I did.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by 1210sda » Sat Feb 27, 2016 4:19 pm

Some financial advisers have a series of model portfolios they use for client presentations. These model portfolios usually have a 10% difference in AA. For example, Port A might be 80/20 AA (stock/bond); Port B could then be 70/30 AA; Port C 60/40 AA; Port D 50/50, etc. etc.

My view is that 5% represents the mid point between these portfolios. Re balancing at the 5% level would mean a 60/40 portfolio could go to 65/35 or 55/45 and still be OK. However, If not rebalanced at 5%, Port C could become Port B or Port D.

The 25% relative is for smaller allocations. If in your 60/40 portfolio you have a sub asset class of "cash" of 4%, the 25% relative means you should re- balance at 3% or 5%, not -1% or 9%.

1210

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Re: The Swedroe 5/25 rebalancing bands restated

Post by livesoft » Sat Feb 27, 2016 5:11 pm

fortyofforty wrote:
livesoft wrote:
fortyofforty wrote:This might explain why I never seemed to reach my "rebalancing trigger". I am thinking of moving to a quarterly rebalancing, to remove emotion and introduce additional simplicity.
My "another criteria" is the RBD thing. It removes emotions and keeps things simple.
I like that in theory, but it leaves me waiting to trigger my move, and it often seems that I am unable to access my account on such days due to work constraints. Then I feel like I missed a golden opportunity, which I did.
Your post prompted me to look at the "Alerts" that one can set at their broker. It turns out that TDAmeritrade* will send you an e-mail if a stock price (say an ETF) moves by more than 2.5% (or 5% or 10%) from its previous close. While this is not my definition of an RBD, an RBD will not have occurred unless this alert is triggered. I don't think one always needs to act promptly, so work constraints should not be much of an issue.

*Yes, Vanguard allows this as well.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by Bubbagump » Sun Feb 28, 2016 10:37 am

I question the band approach, especially on larger portfolios. A 5% in value (not AA) change as we have seen in recent months on a say $5MM portfolio is $250k. It seems to me rebalancing from bonds to equities at that level might make sense to snatch up deals? While we certainly don't want to time the market, this seems in line with the spirit of bands?

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Re: The Swedroe 5/25 rebalancing bands restated

Post by dbr » Sun Feb 28, 2016 11:04 am

Bubbagump wrote:I question the band approach, especially on larger portfolios. A 5% in value (not AA) change as we have seen in recent months on a say $5MM portfolio is $250k. It seems to me rebalancing from bonds to equities at that level might make sense to snatch up deals? While we certainly don't want to time the market, this seems in line with the spirit of bands?
Bands is about controlling risk as defined by keeping asset allocation near a defined target. Espeically it addresses what an investor should do if over time the asset allocation increases in stocks to a point of being very risky and in need of correcting. It has nothing to do with timing markets. There is no presumption that because stocks have declined some that there is a deal to be had.

The subject of "rebalancing bonus" can be studied to see how well the idea of deals does nor doesn't work out.

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Re: The Swedroe 5/25 rebalancing bands restated

Post by fortyofforty » Sun Feb 28, 2016 9:49 pm

livesoft wrote:
fortyofforty wrote:
livesoft wrote:
fortyofforty wrote:This might explain why I never seemed to reach my "rebalancing trigger". I am thinking of moving to a quarterly rebalancing, to remove emotion and introduce additional simplicity.
My "another criteria" is the RBD thing. It removes emotions and keeps things simple.
I like that in theory, but it leaves me waiting to trigger my move, and it often seems that I am unable to access my account on such days due to work constraints. Then I feel like I missed a golden opportunity, which I did.
Your post prompted me to look at the "Alerts" that one can set at their broker. It turns out that TDAmeritrade* will send you an e-mail if a stock price (say an ETF) moves by more than 2.5% (or 5% or 10%) from its previous close. While this is not my definition of an RBD, an RBD will not have occurred unless this alert is triggered. I don't think one always needs to act promptly, so work constraints should not be much of an issue.

*Yes, Vanguard allows this as well.
I agree that one doesn't "always need[] to act promptly", however, the notion of trying to capture the market movement of a RBD indicates that one should act promptly when the market reacts with extreme downward volatility. Otherwise we wouldn't even worry about RBDs.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by LadyGeek » Sun Feb 28, 2016 10:17 pm

The acronym RBD is in the wiki: Abbreviations and Acronyms
RBD - Really Bad Day. A Bogleheads' idiomatic term coined by forum member livesoft. An early mention is in this thread: Today was a Really Bad Day.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by larryswedroe » Mon Feb 29, 2016 8:39 am

fortyofforty
Not that I'm advocating market timing but volatility tends to cluster, meaning RBDs are more likely to be followed by more RBDs than reversals. Most RBDs happen in bear markets, though most of the really good days also happen in bear markets, But momentum is a factor that exists.

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Re: The Swedroe 5/25 rebalancing bands restated

Post by zengolf2011 » Mon Feb 29, 2016 1:58 pm

My sole personal reason to rebalance is to maintain my desired range of risk exposure. I expect to rebalance less than once a year. When my personal situation changes, I would reassess my desired bands.

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Re: The Swedroe 5/25 rebalancing bands restated

Post by Fat-Tailed Contagion » Mon Feb 29, 2016 2:57 pm

larryswedroe wrote:Few thoughts
First, transactions costs and taxes matter, so you don't want to have very tight bands---though should always rebalance whenever have new cash.

Second, MOM is a factor we know exists (or at least has historically) so you don't want bands to be too tight.

Those two factors are what led me to recommend that broad band. Now what one should really do, but I wanted to keep it simple, is to have wider bands for more volatile asset classes like EM

Larry
Hi Larry,

Was this 5/25 rebalance method designed to optimize Short-term Momentum and Long-term Reversions to the mean or was it more of just a ballpark guesstimate?

Are you aware of any studies that have used the data to optimize rebalancing methods that you find useful ?
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Re: The Swedroe 5/25 rebalancing bands restated

Post by larryswedroe » Mon Feb 29, 2016 4:01 pm

fat tailed
It was trying to find BALANCE between taking advantage of MOM, minimizing trade costs, and risk control
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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Mon Feb 29, 2016 4:07 pm

Fat-Tailed Contagion wrote:Are you aware of any studies that have used the data to optimize rebalancing methods that you find useful ?
I am not Larry, but let me answer nevertheless. Do check the wiki page on rebalancing. The best study by far is the one from Daryanani. The Vanguard papers also make for a good read (see the external links on the wiki page).

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Re: The Swedroe 5/25 rebalancing bands restated

Post by dratkinson » Mon Feb 29, 2016 5:57 pm

larryswedroe wrote:fat tailed
It was trying to find BALANCE between taking advantage of MOM, minimizing trade costs, and risk control
Larry
Clarification? Your "50% tolerance band" (rebalance half-way back to target AA after a rebalance band is crossed), was that for the same reason?
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Re: The Swedroe 5/25 rebalancing bands restated

Post by larryswedroe » Mon Feb 29, 2016 6:31 pm

dratkinson

First I tried to make rules relatively simple while adhering to the objectives.

Second, yes it was put there to also take more advantage of momentum but also to give people permission to not rebalance back all the way if their stomachs couldn't take it (:-))

Hope that helps
Larry

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Re: The Swedroe 5/25 rebalancing bands restated

Post by Rodc » Mon Feb 29, 2016 7:51 pm

larryswedroe wrote:Few thoughts
First, transactions costs and taxes matter, so you don't want to have very tight bands---though should always rebalance whenever have new cash.

Second, MOM is a factor we know exists (or at least has historically) so you don't want bands to be too tight.

Those two factors are what led me to recommend that broad band. Now what one should really do, but I wanted to keep it simple, is to have wider bands for more volatile asset classes like EM

Larry
Hi Larry,

One could also use asymmetrical bands since it takes a greater percentage to go from 5% down to even than from 5% up to even. (Drop 5% takes a gain of 5.3% to get back to even, but going from being up 5% to even takes a 4.8% haircut).

I did both early on but decided that the minor tweaks, given the basic set up (5% and 25%) is kind of a WAG, were basically working with noise. Certainly defensible and has some appeal, but given I don't really know if I should be 50/50 or 60/40 or 70/30 I decided to just keep it simple.

Rod
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Re: The Swedroe 5/25 rebalancing bands restated

Post by Kevin M » Mon Feb 29, 2016 8:38 pm

livesoft wrote: I wanted to know how far equities would have to go down to trigger a rebalancing move given the 5/25 rule. Or conversely, if equities dropped D% then how would one's asset allocation shift?
For a methodical treatment, see +/- 5% Rebalancing Bands.

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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Mon Feb 29, 2016 11:20 pm

Kevin M wrote:
livesoft wrote: I wanted to know how far equities would have to go down to trigger a rebalancing move given the 5/25 rule. Or conversely, if equities dropped D% then how would one's asset allocation shift?
For a methodical treatment, see +/- 5% Rebalancing Bands.

Kevin
That's a good read. And another reason for which a rule using an absolute percentage (the "5%") seems unwieldy. And unnecessary in presence of a relative percentage rule (the "25%") anyway. Except that the 25% number is quite wide. 15% or 20% would seem more reasonable, based on history. As to asymmetric bands or volatility-based bands, I see the point, but this is where I would choose simplicity over more elegant math (in practice, this will not change much).

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Re: The Swedroe 5/25 rebalancing bands restated

Post by Kevin M » Tue Mar 01, 2016 2:44 pm

siamond wrote: And another reason for which a rule using an absolute percentage (the "5%") seems unwieldy. And unnecessary in presence of a relative percentage rule (the "25%") anyway. Except that the 25% number is quite wide. 15% or 20% would seem more reasonable, based on history.
Siamond, are you proposing using the same percentage (e.g., 15%-25%) regardless of the allocation, or using a different percentage depending on the allocation?

I don't know if this will help, and perhaps you've already looked at it yourself, but using just a fixed percentage point (or as some have referred to it, absolute percent) or just a fixed percent results in very different rebalancing events.

Image

Note that at allocations of 80% or above, the 25% rule is nonsensical on the upside, as your allocation would need to increase to 100% or more to trigger rebalancing. Of course I'm assuming no leverage here. This could be one reason for not using just a fixed percent at higher allocations.

I'm not saying that one or the other is better, just that they would result in very different rebalancing events.

Of course a 20% allocation is the point of indifference with the 5pp/25% rebalancing strategy. For allocations higher than 20%, the 5 percentage point limit results in more frequent rebalancing, and for allocations lower than 20%, the 25% limit results in more frequent rebalancing.

Using your lower limit of 15%, we see these comparative results:

Image

Note that I added in a row for an allocation of 33.4%, since this is the point of indifference with respect to a 5pp/15% rebalancing strategy. Even a 15% limit doesn't work on the upside for 90% allocation, since this would require an allocation of 103.5% of target to trigger rebalancing. Again, I'm assuming no leverage here.

Looking at the charts in tfb's blog post, I wonder if it makes sense for a rebalancing strategy to factor in how much stocks increase or decrease in value. I know that I'm going to do at least some rebalancing if one of my risky asset classes is down 20%-30% from its 52 week highs, although perhaps not fully back to target allocation.

This is one reason I used some of the cash from maturing CDs to add to stocks in recent months, more to international stocks (and a even a little more to emerging market stocks relative to their target allocation), even though I was not 5 percentage points or more below target. Because my stock allocation wasn't very close to 5 percentage points below target allocation, I did this patiently over time as stocks hit new 52-week lows, and did not rebalance all the way back to target at any point. Then stocks went up, and a couple of nice CD deals came along (7-year at 3% and 5-year at 2.5%), so much of the cash I was holding back to rebalance into stocks went into the CDs.

Due to the opportune rebalancing and partial recovery in stocks, I am less than 1 percentage point below target for stocks, even though US stocks are still almost 10% below 52-week highs. And even though international stocks still are a bit more than 20% below 52-week highs and emerging market stocks are almost 30% below 52-week highs, I'm less than 50 basis points below my portfolio allocation to international stocks, both at the portfolio level and as a percent of stocks, and am actually a smidge above my emerging markets target allocation at both portfolio level and percent of international stocks.

Kevin
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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Tue Mar 01, 2016 4:12 pm

Kevin M wrote:Siamond, are you proposing using the same percentage (e.g., 15%-25%) regardless of the allocation, or using a different percentage depending on the allocation?
Kevin, yes, I was suggesting to simply ditch the absolute % rule, and settle for a lower relative % rule, e.g. 20%. Use a weighted % band, in other words. And yes, regardless of the allocation, use the same relative % for all asset categories (or aggregates).

I agree with you that if a given asset category is more than 85% of your portfolio, then no rebalancing event will occur on the upside, but I don't see that this is an issue (who in their right mind would have such low level of diversification? plus the smaller asset categories will probably trigger something).

And sure, a relative rule would result in a pattern which is quite different from an absolute rule, but this is the entire point, it seems to me that the pattern of an absolute rule is simply not satisfying, as was clearly shown by the nice write-up you quoted (which I think we should add to the wiki, btw).

I know all too well that we're splitting hairs because the rebalancing bonus (compared to a simple systematic rebalance every year approach) is small anyway, therefore pretty much whatever one does (within reason!) will work, but I just cannot see why one would want to use multiple types of rules and introduce weird patterns. What am I missing? :confused
Kevin M wrote:I wonder if it makes sense for a rebalancing strategy to factor in how much stocks increase or decrease in value.
Exactly! Say one has a two funds portfolio, US stocks and US bonds. Say the portfolio is rebalanced at T0. Then VTI shoots up or drops 20%. Whether one's target AA is 30/70, 50/50, or 70/30 should be irrelevant, everyone should probably rebalance by then, right? Hence a relative % rule.

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Re: The Swedroe 5/25 rebalancing bands restated

Post by Kevin M » Wed Mar 02, 2016 1:39 pm

siamond, your replies to my questions make me think that perhaps what you're referring to as relative percent is not the same as the 25% part of the 5/25 guideline. With the latter, you would rebalance if a target 10% allocation dropped to 7.5% ( 10% x (1-25%) ), regardless of the percentage decline of that asset class. If you replaced 5/25 with say NA/15 (NA = not applicable), then for a 10% target allocation you would rebalance if the allocation dropped to 8.5% ( 10% x (1-15%) ).

This has nothing to do with the alternate or additional "rule" of rebalancing I suggested of rebalancing when any asset class drops by 20% or more from its 52-week high.

To illustrate, here is a chart of percentage drops required to trigger rebalancing with NA/15 rebalancing guideline (i.e., 15% "relative" with no "absolute" component).

Image

For example, with a 70/30 stock/bond portfolio, a stock drop of 37% would be required to trigger rebalancing, which would occur when stocks dropped to 70% x (1 - 15%) = 60% of the portfolio (a decline of 10 percentage points).

By contrast, similar to the chart in the tfb blog post, this chart shows the percentage drops required for rebalancing with a 5/NA rule (5 percentage point drop, no "relative" percent component):

Image

What is strikingly different is how flat the drop-required line is between allocations of 30% and 70% for the 5 percentage point rule relative to the 15% rule. For the former, the range is 18% to 22% (a 4 pp spread), while for the latter it is 20% to 37% (a 17 pp spread). In other words the "5" part of the 5/25 rule results in fairly consistent rebalancing for a wide range of portfolios given a drop of about 20% in stocks, whereas using just a relative percent results in a much wider range of drops required to trigger rebalancing.

Kevin
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Re: The Swedroe 5/25 rebalancing bands restated

Post by longinvest » Wed Mar 02, 2016 3:23 pm

Kevin M wrote: ...
For example, with a 70/30 stock/bond portfolio, a stock drop of 37% would be required to trigger rebalancing, which would occur when stocks dropped to 70% x (1 - 15%) = 60% of the portfolio (a decline of 10 percentage points).
...
What is strikingly different is how flat the drop-required line is between allocations of 30% and 70% for the 5 percentage point rule relative to the 15% rule. For the former, the range is 18% to 22% (a 4 pp spread), while for the latter it is 20% to 37% (a 17 pp spread).
...
So, why not base the rebalancing rule on the relative movement of an asset? In other words, make the trigger allocation dependent.

For example, if the goal is to rebalance after a relative movement of +20% and -16.67%*, we get:

* If we're going to design something symmetric, we might as well make it fully symmetric!

Code: Select all

Allocation LowerTrigger UpperTrigger
90%        88%          92%
80%        77%          83%
70%        66%          74%
60%        56%          64%
50%        45%          55%
40%        36%          44%
30%        26%          33%
20%        17%          23%
10%         8%          12%
For the curious, here are the spreadsheet formulas:

Code: Select all

A1: =90
B1: =(A1/1.2)/(A1/1.2+100-A1)*100
C1: =(A1*1.2)/(A1*1.2+100-A1)*100
As you can see, the rebalancing band adapts for each specific allocation. One could change the band size by choosing different relative movement sizes:
  • Wider: +25% and -20%
  • Narrower: +15% and -13%
That would make for nice Bogleheads-designed rebalancing bands to add to the Wiki. :wink:
Last edited by longinvest on Wed Mar 02, 2016 3:27 pm, edited 1 time in total.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by larryswedroe » Wed Mar 02, 2016 3:24 pm

Note that IMO the specific rule is FAR LESS IMPORTANT than having a RULE and sticking to it.
Dancing on the head of a pin here IMO

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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Wed Mar 02, 2016 4:30 pm

Kevin M wrote:siamond, your replies to my questions make me think that perhaps what you're referring to as relative percent is not the same as the 25% part of the 5/25 guideline. With the latter, you would rebalance if a target 10% allocation dropped to 7.5% ( 10% x (1-25%) ), regardless of the percentage decline of that asset class. If you replaced 5/25 with say NA/15 (NA = not applicable), then for a 10% target allocation you would rebalance if the allocation dropped to 8.5% ( 10% x (1-15%) ).
Hm. I did the math with the NA/15 rule (which was indeed what I meant, but thanks for giving me the benefit of the doubt!), and figured out how you got to your charts. And you're right, my previous post was somewhat hasty.

I am not drawing the same conclusion as you did though. Let's look at your absolute % chart to start with. Very few people go with two asset categories. Purists like Taylor would go with three. I chose to use some tilts, I have 8 categories, and my largest one is close to 25%. And well, the 20% to 30% part of the chart is clearly NOT unsatisfying. Even if one has only 4 or 5 categories, clearly something will not work right, even with the 'hack' of saying that such absolute % rule doesn't apply for asset categories under 20%. Unless one interprets the absolute-AA rule as applying only to coarse asset classes, but even then, it stays dubious.

As to the first graph (relative %), if one were to take a simple 70/30 portfolio, and stocks drop 37%, then the bonds side will not stay flat (as a flight to safety will occur). Actual numbers may vary for sure, but the first graph you assembled would clearly be flatter. Let's take a simplified world where bonds go up as much as stocks go down (or the rest of your portfolio goes up as much as the asset category dropping). Here is the outcome, first chart is same as yours, 2nd one is the 'flight to safety' theory. I know, I am simplifying a lot, as nobody has a perfectly diversified portfolio and some may view cash as safety, so the truth probably sits in-between the two extreme charts.

Image

This being clarified, you're absolutely right that the relative rule is more AA-dependent than I originally perceived. Even while noting that the 5% to 40% AA allocations are by far the most meaningful (the flatter part of both of our graphs).

Ok, thank you for opening my eyes, at least, I finally somewhat understand where the 5/25 logic is coming from. The whole thing isn't quite satisfying though, and I still don't see that the "5" part is adding much, unless maybe if one just uses it for coarse asset classes. I think I'll stick to my NA/20 rule for my own portfolio. Seems good enough.

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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Wed Mar 02, 2016 4:36 pm

larryswedroe wrote:Note that IMO the specific rule is FAR LESS IMPORTANT than having a RULE and sticking to it.
Dancing on the head of a pin here IMO
Yes, I certainly wouldn't disagree with you here. This being said, to have a rule and stick to it, one has to wholeheartedly endorse it, and therefore it has to make intuitive sense to some, factual sense to others, and intuitive+factual to some Excel crazies... :wink: I think this is the crux of the issue we're discussing here.

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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Wed Mar 02, 2016 4:41 pm

longinvest wrote:That would make for nice Bogleheads-designed rebalancing bands to add to the Wiki. :wink:
Well, there is a 'spreadsheet' section in the corresponding Wiki page. What are you waiting for? :wink:

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Re: The Swedroe 5/25 rebalancing bands restated

Post by Kevin M » Thu Mar 03, 2016 3:33 pm

I thought it would be interesting to show on one chart the percentage drop required for both the 5 percentage point rebalancing threshold and the 25% rebalancing threshold. I also included 15% and 20% "relative" thresholds:

Image

This shows us the intersections of the two rules, i.e.:
  • 29% drop for 20% allocation using 5/25
  • 25% drop for 25% allocation using 5/20
  • 21% drop for a 34% allocation using 5/15.
Using 5/20 comes the closest to a flat line between 5% and 70% allocations, with 5/25 allowing for more volatility before rebalancing small allocations, accounting for the likelihood of more volatile assets having smaller allocations. Using 5/15 allows a little opportunity to rebalance small, volatile allocations more frequently, which some people may enjoy.

At any rate, I think this graphically shows the elegance of something like a simple 5/25 or 5/20 rebalancing guideline.

Kevin
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Re: The Swedroe 5/25 rebalancing bands restated

Post by Fat-Tailed Contagion » Thu Mar 03, 2016 3:43 pm

Thanks Kevin,

You are right people are probably anxious to rebalance or tinker more often, a human behavioral bias.

An argument for 5/25 and less often rebalancing may be that it helps with the Momentum effect to let an asset class 'run' to the upside before selling to soon and letting it 'fall' before rebuying and exposing yourself to additional losses.

This is intuition, I have not data to back it up but it would make a nice study.
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Re: The Swedroe 5/25 rebalancing bands restated

Post by livesoft » Thu Mar 03, 2016 3:48 pm

But how many people actually rebalanced in 2016? This is a serious question. I don't think too many folks hit rebalancing bands, yet hindsight does show that rebalancing in January or February was a great time to do so. Did Swedroe 5/25 prevent some rebalancing?
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Re: The Swedroe 5/25 rebalancing bands restated

Post by acr123 » Thu Mar 03, 2016 3:51 pm

Not sure I understand your 5 pp graph. For 50% target allocation , a 5% drop goes to 45%. That is a 10% decrease but your graph shows closer to ~18%. What am I missing?

Thanks,

Al

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Re: The Swedroe 5/25 rebalancing bands restated

Post by Kevin M » Thu Mar 03, 2016 4:06 pm

acr123 wrote:Not sure I understand your 5 pp graph. For 50% target allocation , a 5% drop goes to 45%. That is a 10% decrease but your graph shows closer to ~18%. What am I missing?

Thanks,

Al
Your stocks go down so your portfolio is smaller. Stocks are numerator, and portfolio is the denominator, so with both numerator and denominator going down,
numerator must go down more for percentage point decline to reach target.
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What is PP?

Post by EyeDee » Thu Mar 03, 2016 5:12 pm

.
Kevin,

What does the pp stand for? I believe I follow from the context what is generally meant. What I am asking is what does the abbreviation represents. I am guessing one of the p's is percent or percentage, but what does the other p stand for or what do the both stand for if one of them is not percent or percentage?

Thank you.
Kevin M wrote: Of course a 20% allocation is the point of indifference with the 5pp/25% rebalancing strategy. For allocations higher than 20%, the 5 percentage point limit results in more frequent rebalancing, and for allocations lower than 20%, the 25% limit results in more frequent rebalancing.
Randy

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Re: The Swedroe 5/25 rebalancing bands restated

Post by Kevin M » Thu Mar 03, 2016 5:17 pm

Kevin M wrote:
acr123 wrote:Not sure I understand your 5 pp graph. For 50% target allocation , a 5% drop goes to 45%. That is a 10% decrease but your graph shows closer to ~18%. What am I missing?

Thanks,

Al
Your stocks go down so your portfolio is smaller. Stocks are numerator, and portfolio is the denominator, so with both numerator and denominator going down, numerator must go down more for percentage point decline to reach target.
This reply was from my phone, so terse. To illustrate with some formulas and numbers ...

Let's take an initial allocation to the risky asset class and call it "a", and assume the other portion of the portfolio is in cash, so no change in value (the assumptions in all of these charts is no change in value in the other asset(s)). So your allocation to cash is 1 - a.

With a decrease, "d", in the risky asset class, your new allocation to the risky asset is this:

a * (1 - d) / ( a * (1 - d) + (1 - a) )

Note that (1 - a) in the denominator is the cash portion, which does not change, and the a * (1 - d) term, which does change, appears in both numerator and denominator.

Plugging in your numbers, so a decrease of 10% in the risky asset with initial allocation of 50% (d = 10%, a = 50%), the new allocation to the risky asset is:

50% * (1 - 10%) / ( 50% * (1 - 10%) + (1 - 50%) )

The resulting value is 47.4%. You can actually copy the formula above and paste into a Google search or URL field to calculate the result.

So both numerator and denominator go down, but denominator goes down more slowly due to the fixed cash allocation, so allocation to the risky asset goes down, but not by the 5 pp you might expect. This is the "surprise" of these equations and charts--how much an asset must decline to trigger rebalancing with one of these rules.

Plugging in the 18% decline

50% * (1 - 18%) / ( 50% * (1 - 18%) + (1 - 50%) )

Which gives the trigger value of 45%.

The percentage point curve in the charts is created by creating an equation with the formula above set equal to a - r, where r is the rebalancing threshold, solving for d in terms of a, and then plugging that formula in for a given r (in this case, 0.05) and various values of a. The (relative) percent curves are created by setting the formula above equal to a * (1 - r), solving for d in terms of a, and then plugging that formula in for the three different values of r (15%, 20%, 25%) and the various values of a.

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Re: What is PP?

Post by Kevin M » Thu Mar 03, 2016 5:29 pm

EyeDee wrote:.
What does the pp stand for?
Percentage point.

When adding and subtracting with percents you actually are working with percentage points. When multiplying or dividing you are working with percents. Larry and others refer to percentage points as "absolute percent/percentage" and percent as "relative percent/percentage".

So with a target allocation of 50%, a 5pp drop gives you an allocation of 50% - 5pp = 45%. A 5% drop results in an allocation of 50% * (1 - 5pp) = 50% * 95% = 47.5%. A 10% drop results in an allocation of 50% * 90% = 45%. So in this case, a 5pp drop is equal to a 10% drop.

Often people express something in percent when they really mean percentage point, but the context usually makes it clear. It's done so commonly that I sometimes do it myself, although I often write something like, "a decrease of 1% (percentage point)" to clarify.

When dealing with small numbers, as with fixed-income interest rates, it makes a huge difference. A decline of 1pp from 2% to 1% is a 50% decline, but typically people will refer to it as a 1% decline, the context hopefully making it clear.

Make sense?

Kevin
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Re: The Swedroe 5/25 rebalancing bands restated

Post by siamond » Thu Mar 03, 2016 7:41 pm

livesoft wrote:But how many people actually rebalanced in 2016? This is a serious question. I don't think too many folks hit rebalancing bands, yet hindsight does show that rebalancing in January or February was a great time to do so. Did Swedroe 5/25 prevent some rebalancing?
Any rule with large bands would probably have missed this 'opportunity', you're right. Trouble is if one uses smaller bands, you might rebalance too early, and you might miss a BIGGER opportunity! When I backtested various types of rules with monthly and weekly returns (cf. the thread you initiated), it was clear that larger bands win (not by much, mind you, but they do). But one has to stay within reason, or you end up rarely rebalancing and letting your AA drift too far from your target.

I agree with Kevin that the "20%" relative band seems like a decent compromise (actually, this is what I've been doing for a while!). I still shake my head at the 5% absolute band idea (as previously explained, I don't quite agree with Kevin's graphs, this neglects the fact that in reality, when some assets go down, others go up), but frankly, it really doesn't matter very much. As Larry said, just pick something you like, and stick with it. And even if you make an odd decision every now and then (don't know, perception of an RBD, maybe? :happy), you're not going to hurt yourself.

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