## Rebalancing: adaptive bands (a new approach)

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Topic Author
siamond
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Joined: Mon May 28, 2012 5:50 am

### Rebalancing: adaptive bands (a new approach)

Let’s say that we have one asset category (or asset class) targeted at X% of the portfolio in a given Asset Allocation. Let’s say that after a significant price variation, the asset category of interest represents Y% of the portfolio. What could be a good criterion to decide to rebalance the portfolio?

The rebalancing wiki page describes deviations from the target by a certain absolute percentage:
=> ABS(Y-X) > 5% would be a typical formula to implement this, with a 5% threshold

The wiki page also describes deviations from the target by a certain relative percentage:
=> ABS(Y/X-1) > 15% would be a typical formula to implement this, with a 15% threshold

Let’s take a scenario where the asset category of interest varies by 25% (upwards or downwards). To keep the discussion symmetric, we need to remember that a 25% rise is the same variation as a 20% drop. (1/(1+25%)-1 = -20%). In other words, after a 25% rise, a 20% drop would bring the price to the same point, and conversely. Ok, so say we have a 25% price variation on our asset category (SCV, REIT, bonds, all equities, whatever), seems like time to rebalance!

On another thread, Kevin nicely illustrated the fact that both the absolute percentage approach and the relative percentage approach display idiosyncrasies, and that the outcome is quite dependent on the exact Asset Allocation (X%). Let me show the same effect while using slightly different graphs.

Let’s assume that the asset category varies by 25%, while the rest of the portfolio does nothing (not fully realistic, but this helps the thinking). See the first graph below, if the target allocation is less than 30% of the portfolio, the relative band threshold is reached. Otherwise, it is NOT. That doesn’t seem terribly satisfying; the price of the asset category tanked or increased by a good deal (25%), whether you have a small or a large investment in this category, it seems like time to rebalance. Even if we were to assume that the rest of the portfolio actually went up, the curve would shift a bit, but this remains unsatisfying, notably with high allocations.

Topic Author
siamond
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Joined: Mon May 28, 2012 5:50 am

### Re: Rebalancing: adaptive bands (a new approach)

Now let’s look at an absolute percentage approach. Same kind of graph, and here, when the price varies by 25%, we reach a 5% (absolute) threshold only if the target AA is between 40% and 70%. That is NOT satisfying either.

Now one could argue that combining both approaches would deliver a somewhat decent result, maybe use the absolute band approach when the AA is greater than 20%, and use the relative band approach otherwise. This is the idea behind the “5/25” method popularized by Larry Swedroe. This certainly could work, but remains somewhat ad hoc and approximate, as the graphs show.

Topic Author
siamond
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Joined: Mon May 28, 2012 5:50 am

### Re: Rebalancing: adaptive bands (a new approach)

Well, personally what I’d like to see is very simple, a formula that shows a FLAT LINE on such graph. Irrespective of the target AA for a given asset category (or class), if its valuation (price per share) varies by 25% (up or down), I’d like to see a criterion that tells me “threshold reached, time to rebalance” in any case.

Kevin actually pondered about such ‘flat line’ objective in the 5/25 thread, and Longinvest provided an answer that seemed a bit complicated at the first glance, with bands that would depend on the target allocation %, based on some clever math so that such bands would be reached by the same variation of price in any case.

I did a bit of algebra, and it turns out that Longinvest’s insight can be expressed with a simple formula in a spreadsheet. Let’s call this approach adaptive bands. If the target is X% and the current situation is Y%, then a 25% threshold would be tested by:

=> ( ABS(Y-X) / (MIN(X, Y) – X*Y) ) > 25%

Of course, I assembled the same type of chart as before, and we see that a 25% price variation (up or down) would indeed be captured by a 25% threshold. And this is true, IRRESPECTIVE of the target AA for a given asset category or asset class. Cool, isn’t it? This seems to me as an interesting new approach to rebalancing, more intellectually satisfying.

(all credits to Kevin for defining a neat objective, and to Longinvest for articulating an elegant solution; I am just the messenger!).

Any thoughts?

PS1. All the math for this post can be found in this Excel file.
PS2. Of course, I backtested the whole thing! Questions welcome.
Last edited by siamond on Sun Mar 06, 2016 11:47 am, edited 1 time in total.

AtlasShrugged?
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### Re: Rebalancing: adaptive bands (a new approach)

siamond....Yowza! I would suggest adding a 'Read Me' tab at the start of the spreadsheet. But some questions.

Q: How does one 'operationalize' this?

Example: Consider a portfolio of the following index funds in these proportions

Index fund type Current
Large Cap 16.9%
Mid-Cap 30.5%
Small-Cap 6.6%
REIT 6.1%
Int'l 24.1%
Bond 15.5%

And the target allocations are these proportions.

Index fund type Target
Large Cap 17.0%
Mid-Cap 24.0%
Small-Cap 6.0%
REIT 7.0%
Int'l 25.0%
Bond 21.0%

My sense is that the 'core' is there, but it needs to be made 'idiot-proof' (for people like me) with directions on how to use it.
“If you don't know, the thing to do is not to get scared, but to learn.”

livesoft
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### Re: Rebalancing: adaptive bands (a new approach)

Ha! Idiots wouldn't use this anyways.
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Topic Author
siamond
Posts: 4928
Joined: Mon May 28, 2012 5:50 am

### Re: Rebalancing: adaptive bands (a new approach)

JCE66 wrote:Q: How does one 'operationalize' this?

Example: Consider a portfolio of the following index funds in these proportions [...]
Sure. Even livesoft can do it!

Here is a small table I added to the spreadsheet (new 1st tab), using your example. I also included aggregate asset classes.

This shows if a given rebalancing threshold is reached, and by how much. Using the absolute/relative/adaptive methods. I added conditional formatting to highlight when a threshold is reached.

Cell D18's formula is ABS(C18-B18)
Cell E18's formula is ABS(C18/B18-1)
Cell F18's formula is ABS(C18-B18)/(MIN(C18,B18)-C18*B18)

I also added the corresponding rise/drop, as the symmetric math of the adaptive approach is not always entirely intuitive.

(EDIT: restored the pic - was deleted by mistake)
Last edited by siamond on Sun Mar 06, 2016 1:37 pm, edited 1 time in total.

longinvest
Posts: 3851
Joined: Sat Aug 11, 2012 8:44 am

### Re: Rebalancing: adaptive bands (a new approach)

I would present it this way:

Code: Select all

``````Upper movement  25.00%

Fund Type       Target Lower Band Upper Band
Large Cap       17.00%     14.08%     20.38%
Mid-Cap         24.00%     20.17%     28.30%
Small-Cap        6.00%      4.86%      7.39%
REIT             7.00%      5.68%      8.60%
Int'l           25.00%     21.05%     29.41%
Bond            21.00%     17.54%     24.94%
``````
This seems simpler to me (I used my formulas with a 1.25 factor).
Bogleheads investment philosophy | single-ETF balanced portfolio (VBAL) | VPW accumulation

Rodc
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### Re: Rebalancing: adaptive bands (a new approach)

Other than for anesthetic niceness, to what degree is this likely to be significantly and reliably better than something far more simple like 5/25 or just annual rebalancing? Most studies show very little difference between methods. Is this really that much different in outcome?
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

Rodc
Posts: 13601
Joined: Tue Jun 26, 2007 9:46 am

### Re: Rebalancing: adaptive bands (a new approach)

longinvest wrote:I would present it this way:

Code: Select all

``````Upper movement  25.00%

Fund Type       Target Lower Band Upper Band
Large Cap       17.00%     14.08%     20.38%
Mid-Cap         24.00%     20.17%     28.30%
Small-Cap        6.00%      4.86%      7.39%
REIT             7.00%      5.68%      8.60%
Int'l           25.00%     21.05%     29.41%
Bond            21.00%     17.54%     24.94%
``````
This seems simpler to me (I used my formulas with a 1.25 factor).
Those bands are so close to symmetric it is hard to imagine this really matters. If one cannot optimize their allocation to four (!) significant digits, how can it make sense to set rebalance bands to four significant digits?

If this is just fun and games I like it. Why not play around and see what happens. Better than watching sitcoms on TV.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

Topic Author
siamond
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Joined: Mon May 28, 2012 5:50 am

### Re: Rebalancing: adaptive bands (a new approach)

Rodc wrote:Other than for anesthetic niceness, to what degree is this likely to be significantly and reliably better than something far more simple like 5/25 or just annual rebalancing? Most studies show very little difference between methods. Is this really that much different in outcome?
No, it's not that different in outcome. I ran a full gamut of backtesting experiments last night, comparing various methods (including this one) on diverse portfolios. I used weekly historical returns between 1985 and 2015 for US stocks, bonds, international, small-caps, small-value. I used several durations, several starting points for historical cycles.

When comparing the various approaches, the rebalancing bonus stays small (hard to go over 0.2% on average across all cycles for a given AA). Compared to annual rebalancing, that is. With the adaptive method, it seems that there is a bit more consistency in the bonus, across the various AAs I tested, which would make sense, but this is tenuous (and I am biased, as I like the idea!).

So yeah, this is more for intellectual satisfaction. Personally, I would much prefer using a method that makes sense to me, this helps in sticking with it. The relative rebalancing approach did make sense to me, but then Kevin demonstrated its short-comings. The 5/25 approach makes me roll my eyes. This new proposal could be a way to restore some kind of peace in my mind!

longinvest
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Joined: Sat Aug 11, 2012 8:44 am

### Re: Rebalancing: adaptive bands (a new approach)

Rodc wrote: Those bands are so close to symmetric it is hard to imagine this really matters. If one cannot optimize their allocation to four (!) significant digits, how can it make sense to set rebalance bands to four significant digits?

If this is just fun and games I like it. Why not play around and see what happens. Better than watching sitcoms on TV.
Rodc,

You always catch me, when I lazily let LibreOffice format my percentages by default to two decimals. You're right, of course; I should have trimmed a decimal or two. Anyway, I'm not sure if it really makes sense to have a 5% allocation to something, but I'm not a tilter.

For my defense, note that when I first presented the idea, I proposed simply adding a table into the Wiki indicating bands at each 10% AA allocation (but the factor was 1.2 instead of 1.25) and I had kept whole percentages:

viewtopic.php?f=10&t=185596#p2821061
longinvest wrote: ...

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%
``````
...
Here's a ready-to-use table, using a 1.25 factor and a 5% AA increment:

Code: Select all

``````AA	 Low	  Up
5%	 4.0% 	6.2%
10%	 8.2%	12.2%
15%	12.4%	18.1%
20%	16.7%	23.8%
25%	21.1%	29.4%
30%	25.5%	34.9%
35%	30.1%	40.2%
40%	34.8%	45.5%
45%	39.6%	50.6%
50%	44.4%	55.6%
55%	49.4%	60.4%
60%	54.5%	65.2%
65%	59.8%	69.9%
70%	65.1%	74.5%
75%	70.6%	78.9%
80%	76.2%	83.3%
85%	81.9%	87.6%
90%	87.8%	91.8%
95%	93.8%	96.0%
``````
This time, I kept one decimal, because, when you think about it, 1% of 10% is a pretty big error margin for the relative movement (e.g. stocks dropping 30% instead of 20%). Using one digit reduces the error margin to 1%. Of course, I could have rounded to the nearest 0.5%, instead, but I'm too lazy.
Bogleheads investment philosophy | single-ETF balanced portfolio (VBAL) | VPW accumulation

longinvest
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Joined: Sat Aug 11, 2012 8:44 am

### Re: Rebalancing: adaptive bands (a new approach)

Just in case...

If anybody uses "age in bonds", it could be useful to have 1% precision for the AA:

Code: Select all

``````AA 	Low  	Up
5%	 4.0%	 6.2%
6%	 4.9%	 7.4%
7%	 5.7%	 8.6%
8%	 6.5%	 9.8%
9%	 7.3%	11.0%
10%	 8.2%	12.2%
11%	 9.0%	13.4%
12%	 9.8%	14.6%
13%	10.7%	15.7%
14%	11.5%	16.9%
15%	12.4%	18.1%
16%	13.2%	19.2%
17%	14.1%	20.4%
18%	14.9%	21.5%
19%	15.8%	22.7%
20%	16.7%	23.8%
21%	17.5%	24.9%
22%	18.4%	26.1%
23%	19.3%	27.2%
24%	20.2%	28.3%
25%	21.1%	29.4%
26%	21.9%	30.5%
27%	22.8%	31.6%
28%	23.7%	32.7%
29%	24.6%	33.8%
30%	25.5%	34.9%
31%	26.4%	36.0%
32%	27.4%	37.0%
33%	28.3%	38.1%
34%	29.2%	39.2%
35%	30.1%	40.2%
36%	31.0%	41.3%
37%	32.0%	42.3%
38%	32.9%	43.4%
39%	33.8%	44.4%
40%	34.8%	45.5%
41%	35.7%	46.5%
42%	36.7%	47.5%
43%	37.6%	48.5%
44%	38.6%	49.5%
45%	39.6%	50.6%
46%	40.5%	51.6%
47%	41.5%	52.6%
48%	42.5%	53.6%
49%	43.5%	54.6%
50%	44.4%	55.6%
51%	45.4%	56.5%
52%	46.4%	57.5%
53%	47.4%	58.5%
54%	48.4%	59.5%
55%	49.4%	60.4%
56%	50.5%	61.4%
57%	51.5%	62.4%
58%	52.5%	63.3%
59%	53.5%	64.3%
60%	54.5%	65.2%
61%	55.6%	66.2%
62%	56.6%	67.1%
63%	57.7%	68.0%
64%	58.7%	69.0%
65%	59.8%	69.9%
66%	60.8%	70.8%
67%	61.9%	71.7%
68%	63.0%	72.6%
69%	64.0%	73.6%
70%	65.1%	74.5%
71%	66.2%	75.4%
72%	67.3%	76.3%
73%	68.4%	77.2%
74%	69.5%	78.1%
75%	70.6%	78.9%
76%	71.7%	79.8%
77%	72.8%	80.7%
78%	73.9%	81.6%
79%	75.1%	82.5%
80%	76.2%	83.3%
81%	77.3%	84.2%
82%	78.5%	85.1%
83%	79.6%	85.9%
84%	80.8%	86.8%
85%	81.9%	87.6%
86%	83.1%	88.5%
87%	84.3%	89.3%
88%	85.4%	90.2%
89%	86.6%	91.0%
90%	87.8%	91.8%
91%	89.0%	92.7%
92%	90.2%	93.5%
93%	91.4%	94.3%
94%	92.6%	95.1%
95%	93.8%	96.0%
``````
Of course, the tables are for die-hard pen and paper investors. Spreadsheet users would be best served by Siamond's formula and spreadsheet.
Bogleheads investment philosophy | single-ETF balanced portfolio (VBAL) | VPW accumulation

Rodc
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### Re: Rebalancing: adaptive bands (a new approach)

longinvest, siamond,

Thanks for the replies.

I do think the results are interesting.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

Topic Author
siamond
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Joined: Mon May 28, 2012 5:50 am

### Re: Rebalancing: adaptive bands (a new approach)

I improved a bit the first tab of the spreadsheet, with a better framework for checking your own AA, and for testing hypothetical scenarios.

I created two hypothetical scenarios, a big bear and a big bull, using high stock allocations and small tilts (to test the extremes). Click for a bigger display. The table on the right is the outcome of the hypothetical price variations. The table on the left assesses if rebalancing criteria are met.

The second scenario is the most interesting. When looking at asset classes, both the absolute and the relative approaches failed at 'noticing' the big bull market (see the variation column, I was pretty aggressive!) which should scream 'rebalance'. And even the analysis of asset categories is not terribly convincing as the absolute/relative criteria are barely reached. In all fairness, if I had plugged more of a drop for bonds, this wouldn't be the case, but heck, who knows what can happen in the future.

PS. when I ran my 1985-2015 weekly backtesting, I ended up with roughly one rebalancing event per year (on average) for each approach across all cycles, using those precise thresholds. In that sense, they do seem comparable. I only did the math on asset categories though, not asset classes.

Peter Foley
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### Re: Rebalancing: adaptive bands (a new approach)

Interesting work. Since I adopted the 5% band approach in the middle of the last recession, I have found few opportunities to rebalance. In 2012 I retired with an AA of 45/55 - purposefully on the conservative side after having seen how much our combined portfolio fell in 2009-2010.

The question I have is should I be looking for a method that would have me rebalance a little more frequently? The once a year method does not appeal to me because it is a timing approach, not strictly a market approach. Since I only rebalance stocks and bonds, perhaps a AA that is tied to market movement and not to a percentage of current AA is the answer. The market goes up or down 20%, rebalance to desired AA. Anything less than that, ignore.

Topic Author
siamond
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### Re: Rebalancing: adaptive bands (a new approach)

Peter Foley wrote:The question I have is should I be looking for a method that would have me rebalance a little more frequently?
As I mentioned, with the thresholds I've used, we seem to end up rebalancing roughly once a year on average, but of course more frequently during big market hiccups and less frequently in steadier time. If you were to use lower thresholds, you'll get more rebalancing events, and this will probably cost you a tiny bit of rebalancing bonus. With higher thresholds, you may get a slightly higher bonus, but your AA may drift for a long time, which is probably not the intent in your IPS. Anyhoo, since said bonus is very small (0.2% annual is real good, 0.1% isn't unusual, if I did the backtesting properly), it doesn't really matter much.

What I like about the adaptive method is that this probably will make you rebalance when you feel the urge to do so (i.e. big market variation), irrespective of your exact AA. On the other hand, it may seem more complicated or possibly less intuitive than the absolute/relative methods. Although frankly, it's just one pre-canned Excel formula (check my spreadsheet), not the end of the world! Way less complicated than calculating your current AA!

Now, those threshold methods are (a tad) more effective if you monitor the market on a weekly or monthly basis, or at least when the headlines get all screechy. Which may seem a burden, and prone to emotional reactions. One can get fancy, and develop a Google spreadsheet that does all the work for you, even generate an e-mail when a threshold is reached. I did it, mostly for the fun of it, but then it does require appropriate skills.

Kevin M
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### Re: Rebalancing: adaptive bands (a new approach)

Kudos to siamond and longinvest for their work on this; quite interesting.

To clarify the thrust of my replies in the other thread, linked by siamond above, I was first trying to explain to siamond why you probably need the 5 percentage point (pp) (aka absolute) rule in addition to the 25% (aka relative) rule, since siamond was asking why not just the (relative) 25% rule (or 15% or 20%). I showed graphically how the 25% rule (or 15% or 20%) alone breaks down for larger allocations. So yes, I pointed out how the 25% rule alone probably was insufficient.

Similarly, the 5pp rule alone breaks down for smaller allocations, so yes, I pointed out the potential flaw of using just that rule.

In working on the charts to clarify this, it struck me how nicely the 5/25 rule (or perhaps 5/20) provides a reasonable approximation of what siamond is achieving with the more complex approach (although admittedly pretty simple if you use a spreadsheet). To illustrate, first is a chart of the 5pp and 20% rules shown on a single chart:

(Terminology note: the "b+0%" in the legend indicates that this model assumes that the bond portion of the portfolio changes by 0%, assuming that the asset class being examined is a risky asset class like stocks. The formulas used in the spreadsheet model accommodate using a different assumption about the bond portion; e.g., increasing by 2% when stocks decline enough to trigger rebalancing).

This shows the allocations at which each rule "breaks down", but also you can trace the maximum values of both curves to see how combining them achieves a reasonable approximation to a flattish line in the range of about 20% to 25% drop in the asset value across allocations from 10% to 80%. To make it easier to see this, here is the chart showing a single curve for the combined 5/20 rule:

Really quite elegant that such a simple rule achieves such a nice approximation of the flat line siamond is striving for for allocations between 10% and 80%.

As a side note, this rule doesn't look very good for allocations above about 80%, but then the 20% (relative) rule applied to the bond allocation of 20% or less would trigger rebalancing for more modest stock declines than the 37% indicated on the chart. For example, with a 90/10 initial stock/bond allocation, a stock decline of 19% results in an allocation of 88/12, and the 20% rule applied to the bond target of 10% would trigger rebalancing.

Pretty darn cool for a simple rule if you ask me. Of course siamond's and longinvest's complementary work is cool too.

Kevin
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Topic Author
siamond
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### Re: Rebalancing: adaptive bands (a new approach)

Thanks for the context, Kevin, and for opening my eyes to the shortcomings of absolute & relative rules.

I could assert that one consistent rule is simpler than two polar opposite rules cobbled together, but that would just be me teasing you!

Note that Kevin's charts are a tiny bit different from mine because I used the symmetric math described in the first post (plus I didn't use the same metric on the 'Y' axis anyway!), but the conclusions remain exactly the same.

livesoft
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### Re: Rebalancing: adaptive bands (a new approach)

Peter Foley wrote:The question I have is should I be looking for a method that would have me rebalance a little more frequently? The once a year method does not appeal to me because it is a timing approach, not strictly a market approach. Since I only rebalance stocks and bonds, perhaps a AA that is tied to market movement and not to a percentage of current AA is the answer. The market goes up or down 20%, rebalance to desired AA. Anything less than that, ignore.
FWIW, I want to rebalance not only on bands that are rarely, if ever, triggered, but also based on market movements. In 2016, there have been some market movements called RBDs (you probably know of the term) that have turned out to be great days to rebalance. Some of my purchases are up more than 15% so far this year alone. I'm hitting rebalancing bands on the upside and now have to sell equities to get back into balance.
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Clive
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### Re: Rebalancing: adaptive bands (a new approach)

The optimal rebalance point is at the peak (trough) of turning points. If the prior trend continues after rebalancing then having delayed rebalancing would have been better.

Turning points are unpredictable and vary.

PnF, MACD, ma crossovers etc can all be potential indicators, but also throw off false signals.

Adaptive weightings is a alternative choice. I like a log stochastic measure

( log(current) - log(bottom) ) / ( log(top) - log(bottom) )

[limited 0..1]

where bottom and top are x standard deviation around the mean. That will have you all in at the lower, all out at the upper. Supplement that dynamic weighting with a fixed weighting i.e. Ben Graham min of 25% stock plus 50% allocation to log stochastic will have you min 25%, max 75%. Given a measure of how much to hold, the only other factor is when to realign (potential turning point).

Only problem then is that standard deviations are dynamic, such that top and bottom also have to be dynamic.

All told - does adaptive do any better/worse than simple fixed time point, fixed weighting (simple) rebalancing?

Peter Foley
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### Re: Rebalancing: adaptive bands (a new approach)

livesoft wrote:
FWIW, I want to rebalance not only on bands that are rarely, if ever, triggered, but also based on market movements.
Me too, although not too often. Rather than use really bad days, which seem all too frequent, I was thinking of rebalancing every time the S&P 500 moved xxx points. During the recession that was roughly how I approached rebalancing. Every 100 point drop resulted in some rebalancing . . . . . until it got down to about 900 at which point I had reached the limit of my risk tolerance.

Now in hindsight . . . .

Topic Author
siamond
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Joined: Mon May 28, 2012 5:50 am

### Re: Rebalancing: adaptive bands (a new approach)

Clive wrote:All told - does adaptive do any better/worse than simple fixed time point, fixed weighting (simple) rebalancing?
I provided some information about the backtesting I ran in this post.

Bottomline is that all bands-based algorithms, assuming frequent (e.g. weekly) monitoring, do seem to extract a small bonus compared to a time-based (e.g. annual) rebalancing. My findings are similar to Daryanani, although I didn't use the same funds nor the same time periods.

But the adaptive bands approach, although more intellectually satisfying (at least to me), does not seem to present an advantage over the other bands-based algorithms. I think it's more a matter of choosing an algorithm that you resonate with and will use with confidence.

AlohaJoe
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### Re: Rebalancing: adaptive bands (a new approach)

An additional interesting consequence of using adaptive bands is that they appear to add another kind of symmetry.

As I pointed out in a related thread, you need to look at all asset classes when deciding whether a rebalance is triggered.

When you just use symmetric triggers (+15%/-15%) and look at the entire portfolio there are some scenarios were a change in your portfolio triggers rebalancing in one asset but not in another. Imagine you have a 60/40 portfolio and are using 15% bands. Then stocks go up 30%, your portfolio looks like:

Stocks are 66.1%, which is still within the 51-69 band that +/-15% establishes. So you don't rebalance.
Bonds are 33.9%, which is outside of the 34-46 band that +/-15% establishes. So you do rebalance.

It isn't like there is anything objectively wrong with this but it still feels a bit weird from a purely obsessive-compulsive maths perspective.

edit: The more I think about this, the less I like it. We are saying "oh no, I don't have enough bonds!" But in a 2-asset world that means you must have too much of something else. But you don't. You still have the "right" amount of stocks. If you have too much of one thing, then you must have too little of another. But relative percentage bands don't work like that. (Disclaimer: again: this is more a theoretical/OCD concern than anything that affects the real world.)

And it isn't caused by the asymmetry of geometric returns. If you use -15%/+17.6% as your bands the same thing happens: bonds trigger rebalancing but stocks don't.

By contrast, when using the adaptive band method it is symmetric. If one asset triggers rebalancing then all assets trigger rebalancing. Here's an example, again with a 60/40 portfolio. With adaptive bands with a 20% factor that give stocks a band of 55.56% - 64.29% and bonds a band of 35.71% - 44.44%.

If stocks go up 20% then stocks are at 64.29% and bonds are at 35.71%...so both assets are sitting right at a trigger threshold -- the high threshold for stocks and the low threshold for bonds.
Last edited by AlohaJoe on Wed Nov 09, 2016 1:21 am, edited 2 times in total.

grabiner
Posts: 25110
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

### Re: Rebalancing: adaptive bands (a new approach)

The reason I prefer fixed bands is that what matters is not how the market changes, but how much it affects your portfolio. This is particularly important in a taxable account, when you would have to pay a capital-gains tax to rebalance out of stocks.

If you are 50% stock, and the stock market rises 22%, you are now 55% stock, which is a noticeable increase in your risk; you may want to sell some stock. If the stock market rises 50%, you are 60% stock, and should sell.

If you are 80% stock, and the stock market rises 22%, you are now 83% stock, which makes less of a difference in risk. It takes a 42% rise in the market to move you to 85%, which is the same risk increase as moving from 50% to 55% stock. And if you don't rebalance when you hit 83%, you may be able to get back down to 80% on your own, by using dividends and new investments to buy bond funds.
David Grabiner

Lieutenant.Columbo
Posts: 1178
Joined: Sat Sep 05, 2015 9:20 pm
Location: Cicely AK

### Re: Rebalancing: adaptive bands (a new approach)

grabiner wrote:The reason I prefer fixed bands is that what matters is not how the market changes, but how much it affects your portfolio. This is particularly important in a taxable account, when you would have to pay a capital-gains tax to rebalance out of stocks.

If you are 50% stock, and the stock market rises 22%, you are now 55% stock, which is a noticeable increase in your risk; you may want to sell some stock. If the stock market rises 50%, you are 60% stock, and should sell...
David,
I understand your rationale for taking taxation into account when determining rebalancing bands.
Would you use different fixed band/s...
1. ... for an asset class that is ALL in Taxable and whose target within the portfolio is 25%...
...versus...
2. ... for an asset class that is 75% in Taxable (25% Tax-Deferred) and whose target within the portfolio is 50%?
Thank you.
Lt. Columbo: Well, what do you know. Here I am talking with some of the smartest people in the world, and I didn't even notice!

grabiner
Posts: 25110
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

### Re: Rebalancing: adaptive bands (a new approach)

Lieutenant.Columbo wrote:
grabiner wrote:The reason I prefer fixed bands is that what matters is not how the market changes, but how much it affects your portfolio. This is particularly important in a taxable account, when you would have to pay a capital-gains tax to rebalance out of stocks.

If you are 50% stock, and the stock market rises 22%, you are now 55% stock, which is a noticeable increase in your risk; you may want to sell some stock. If the stock market rises 50%, you are 60% stock, and should sell...
David,
I understand your rationale for taking taxation into account when determining rebalancing bands.
Would you use different fixed band/s...
1. ... for an asset class that is ALL in Taxable and whose target within the portfolio is 25%...
...versus...
2. ... for an asset class that is 75% in Taxable (25% Tax-Deferred) and whose target within the portfolio is 50%?
Thank you.
I would use the same band regardless of whether an asset class is in taxable or tax-deferred, but a different strategy.

What I do in my own Investment Policy Statement is to rebalance my tax-deferred accounts fully every year, since that is free. I will only sell for a capital gain to rebalance in taxable if I am outside a band, and even then, I will rebalance only to the band boundary. (I have never had to sell to rebalance in taxable; I have hit bands twice and rebalanced in tax-deferred.)

Since I hold bonds in a retirement plan, I can buy or sell bonds to rebalance with no tax consequences, and this is the most important rebalance. Since I hold US stocks in both my retirement accounts and my taxable accounts, I can sell them in my tax-deferred account to rebalance, but I will do my best to avoid selling my taxable Total Stock Market which has huge capital gains.
David Grabiner

HammerJoe
Posts: 1
Joined: Tue Oct 08, 2019 7:15 pm

### Re: Rebalancing: adaptive bands (a new approach)

I am sorry for bringing back an old discussion but I need help understanding how to use this adaptive Band.

I have a cryptocurrency portfolio of with several currencies and I would like to apply this strategy to it.
If I understood correctly this adaptive band determines when a rebalance is required right?
But how is calculation done to find out which assets need to be sold and bought to rebalance the portfolio?
Thats the part that I dont understand about the sheet provided because these portfolios are closed in nature, meaning that no fresh money comes in or comes out so to rebalance its assets need to be sold in order to buy others.

It would be nice if I could get an example of a portfolio like this:
Asset Allocation
BTC 30%
ETH 25%
LTC 20%
XRP 15%
NEO 10%

longinvest
Posts: 3851
Joined: Sat Aug 11, 2012 8:44 am

### Re: Rebalancing: adaptive bands (a new approach)

HammerJoe wrote:
Tue Oct 08, 2019 8:44 pm
I am sorry for bringing back an old discussion but I need help understanding how to use this adaptive Band.

I have a cryptocurrency portfolio ...
Bogleheads invest into stock and bond portfolios. So, here are the rebalancing triggers for an internationally-diversified balanced portfolio using the adaptive band table found in this post:
• Domestic stocks (VTI) target allocation 36%: low 31.0% high 41.3%
• International stocks (VXUS) target allocation 24%: low 20.2% high 28.3%
• Domestic bonds (BND) target allocation 28%: low 23.7% high 32.7%
• International bonds (BNDX) target allocation 12%: low 9.8% high 14.6%
Bogleheads investment philosophy | single-ETF balanced portfolio (VBAL) | VPW accumulation