Market Change needed to trigger Rebalance with 5/25 rule

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diasurfer
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Market Change needed to trigger Rebalance with 5/25 rule

Post by diasurfer »

I noticed that the market drop of about 10% since Jan 1, 2008 had a quite noticeable impact on my account balance but a small impact on my asset allocation. I'm not even close to Larry Swedroe's rebalancing triggers of 5% absolute change in any asset or 25% of any asset's allocation. I am invested 90% in equities and 10% in bonds. Obviously if I was 100% equities it would not change my AA at all, but I was expecting more impact. I decided to quantify the effect of market changes on AA in a very simple way.

The very simple way I calculated it is to assume AA that are composed entirely of stocks and bonds, and to assume that the value of the bonds does not change. TSM has dropped 10% since Jan 1 while TBM has risen 1.5% so its not a perfect assumption but good enough. .

The plot below (click on thumbnail - hope this works!) shows the percentage change in AA (- eq. %, + bond %) for market losses of 10% and 20% (again, with no change in bond value). These are shown in red. Note that for the 10% drop, no AA is even close to the 5/25 rebalancing triggers (shown in black).

Interesting, those with 40/60 - 60/40 AA are the most likely to have rebalance triggered. At 20% market loss, rebalance is triggered for these investors but not for more conservative or more aggressive investors.

Note that the curves are not symmetrical. The maximum change in AA occurs at 53% equities.


Image

The second plot shows the amount of market change needed to trigger rebalancing as a function of equity percentage. Bull market (gain) is in black and bear (loss) is in red, again assuming no change in bond value.

Note the asymmetry between losses and gains when comparing the rebalance triggers for 80/20 and 20/80 portfolios. Also note that the 80/20 portfolio (where the 5% rule meets the 25% rule) is the least likely to be rebalanced of all portfolios with equity greater than 40%.

Image

I realize this isn't rocket science but I thought some readers would find it interesting. Apparently, rebalancing by the 5/25 rule will occur much less often that I thought it would. It would take a very large drop or gain in a short time span. Over a long time span, the assumption of fixed bond value is more of a problem, but I think you get the point.

Edited several times for grammar.
Topic Author
diasurfer
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Post by diasurfer »

With all the recent threads, polls, etc on rebalancing, was no one was surprised that the drop since Jan 1 has not been nearly large enough to trigger a rebalance in average stock/bond portolios, according to these charts?

Was it already obvious and hence un-comment-worthy?
dbr
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Post by dbr »

It shows the 25/5 rule is robust against noise.

For a more formal analysis of such problems it might be interesting to peruse the literature in statistical process control regarding methods to know when to interfere with a process in the presence of both noise and special causes for which corrections should be applied. There are people who apply such methods to business processes and to processes for which steady state includes a modelable trend.

I am sorry I do not have refences at hand.
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diasurfer
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Post by diasurfer »

dbr wrote:It shows the 25/5 rule is robust against noise.

For a more formal analysis of such problems it might be interesting to peruse the literature in statistical process control regarding methods to know when to interfere with a process in the presence of both noise and special causes for which corrections should be applied. There are people who apply such methods to business processes and to processes for which steady state includes a modelable trend.

I am sorry I do not have refences at hand.
Hey a reply! :wink:

There seem to be a range of opinions on when to rebalance. "Strategic rebalancing", moveable bands, etc etc. I wonder how many, if any, are based on statistical process control, and how many are based on backtesting various methods or simple gut-feeling rules-of-thumb.

Perhaps if Larry Swedroe was reading this he could comment on the source of his 5/25 rule.

Again, the surprising thing to me was that (if the 5/25 rule has merit) the volatility of the past year has merely been, as you put it, "noise".
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mas
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Post by mas »

I did find this interesting. Here is a sense of the frequency (at calendar year intervals - based on Ken French's data) for the 80% equity case:

Code: Select all

          SV    LG
> +40%    24%    9%
< -25%     8%    5%
This is only based on that one year's move, so a few year's cumulative movements would be even more likely to breach these thresholds.
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diasurfer
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Post by diasurfer »

mas wrote:I did find this interesting. Here is a sense of the frequency (at calendar year intervals - based on Ken French's data) for the 80% equity case:

Code: Select all

          SV    LG
> +40%    24%    9%
< -25%     8%    5%
This is only based on that one year's move, so a few year's cumulative movements would be even more likely to breach these thresholds.
Thanks.

Although it doesn't necessarily follow from your numbers, adopting annual rebalancing for an 80/20 results in more frequent rebalancing than with 5/25, because it will take a few years to reach +40/-25%, and sudden drops of this magnitude are rare.
dbr
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Post by dbr »

Just as examples, typical process control rules indicate interference with the process according to schemes such as the following:

"There are 4 basic rules with respect to how the data is situated on a control chart to indicate if it is not in statistical control (i.e. special causes of variation are present instead of random sources). These are as follows:

Rule 1: Any single data point falls outside the 3-sigma limit from the centerline (i.e., any point falls outside Zone A, beyond either the upper or lower control limit);
Rule 2: Two out of three consecutive points fall beyond the 2-sigma limit (in zone A or beyond), on the same side of the centerline;
Rule 3: Four out of five consecutive points fall beyond the 1-sigma limit (in Zone B or beyond), on the same side of the centerline;
Rule 4: Nine consecutive points fall on the same side of the centerline (in Zone C or beyond);"

Note 1-sigma means one standard deviation of the process (lots of caveats about what data to use and how to calculate same).

I would have to believe the academic guru's have assessed whether or not it makes sense to apply such concepts to the stock market, but I would guess it is a certainty someone has looked. It is truly interesting to look at how such concepts apply to the sales and profits of corporations and why monthly and quarterly results are more noise than anything else most of the time.
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diasurfer
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Post by diasurfer »

I guess if Taleb is right, Rule 1 is going to be triggered a lot more often than we would expect!
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mas
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Post by mas »

diasurfer wrote:Although it doesn't necessarily follow from your numbers, adopting annual rebalancing for an 80/20 results in more frequent rebalancing than with 5/25, because it will take a few years to reach +40/-25%, and sudden drops of this magnitude are rare.
Yes my numbers are a little bit of apples to the 5/25's oranges, but it gives a ballpark. Plus I don't have the desire to be more thorough :)
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