"There is a rebalancing bonus ... false"

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Re: "There is a rebalancing bonus ... false"

Postby tadamsmar » Fri May 31, 2013 5:42 pm

camontgo wrote:
tadamsmar wrote:You have gone wrong with the statement "the average bonus over many trials is zero". You likely did not get exactly zero as the estimate from your simulations. And, in any case, you certainly did not prove that the average bonus was zero because it's not possible to do that with a simulation. You could design a simulation that rejects a hypothesis like "The average bonus is greater than N%" with some specific level of certainty, but that does not prove it's zero with any level of certainty. You might find that a sufficiently large simulation would tighten the uncertainty on the average bonus around a non-zero value sufficient to prove it was not zero.


I agree that my simulation doesn't amount to "proof" and the average for 1000 trials is not precisely zero....so I'd reword the statement to "very close to zero".

To be more specific, I just ran 1000 trials, and the average rebalancing bonus over 10 years for two assets with 10% return and 20% standard deviation was 0.05% per year. The simulation does show a rebalancing bonus about 2/3 of the time...and a penalty only about 1/3 of the time...but the penalties tend to be larger than the bonuses.


Try increasing the variance on the 2 assets and the number of years. My hunch it that will make the rebalancing bonus obvious.

Or try 1 no risk, no return asset and 1 high variance asset with some return. That will make it similar to the Shannon example.

My hunch is that in your scenario rebalancing is not much better as a Kelly money management strategy compared with no rebalancing.
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Re: "There is a rebalancing bonus ... false"

Postby camontgo » Fri May 31, 2013 9:15 pm

tadamsmar wrote:Try increasing the variance on the 2 assets and the number of years. My hunch it that will make the rebalancing bonus obvious.

Or try 1 no risk, no return asset and 1 high variance asset with some return. That will make it similar to the Shannon example.

My hunch is that in your scenario rebalancing is not much better as a Kelly money management strategy compared with no rebalancing.


Ok, I tried it, and I do see that the average annual bonus in the simulation gets bigger when the standard deviation is increased.

I'm still thinking it through, but my simulation (assuming I haven't made any errors) is showing that there is some positive bonus on average. It can be significant for extreme parameters, but it is tiny (close to zero) on average for parameters that seem realistic for diversified asset classes (i.e. u.s. and international; large cap and small cap; stocks and bonds). The "expected" bonus over reasonable horizons appears to be only a few basis points per year using volatilities and correlations typical of these asset classes....probably not enough to cover the additional costs.
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Re: "There is a rebalancing bonus ... false"

Postby tadamsmar » Sat Jun 01, 2013 9:04 am

camontgo wrote:
tadamsmar wrote:Try increasing the variance on the 2 assets and the number of years. My hunch it that will make the rebalancing bonus obvious.

Or try 1 no risk, no return asset and 1 high variance asset with some return. That will make it similar to the Shannon example.

My hunch is that in your scenario rebalancing is not much better as a Kelly money management strategy compared with no rebalancing.


Ok, I tried it, and I do see that the average annual bonus in the simulation gets bigger when the standard deviation is increased.

I'm still thinking it through, but my simulation (assuming I haven't made any errors) is showing that there is some positive bonus on average. It can be significant for extreme parameters, but it is tiny (close to zero) on average for parameters that seem realistic for diversified asset classes (i.e. u.s. and international; large cap and small cap; stocks and bonds). The "expected" bonus over reasonable horizons appears to be only a few basis points per year using volatilities and correlations typical of these asset classes....probably not enough to cover the additional costs.


It makes sense that the bonus due to Shannon/Kelly considerations is small because pretty good money management is already built into our strategy for diversified assets with lowish variance (money management as provided by the Kelly Criteria). Ed Thorpe used Kelly in running the world's first hedge fund and discussed it's application in "Beat the Market" but this must have been making much riskier bets in the markets.

This implies that Bernstein is right for typical mutual fund investing, but for the wrong reasons. It's not true that rebalancing provides no bonus for random markets, it's true that rebalancing provides no or a de minimis bonus for relatively low variance mutual funds in random markets. Hence, if there is a bonus in this situation, then its due to auto correlation (so called "mean reversion") and not due to superior Kelly-style money management. (Perhaps if one allocated to a leveraged small value fund and a leveraged long bond fund then Kelly considerations would come into play significantly, not sure.)

If you have an edge in a high stakes gambling game (you are card counting for instance) it's easy to see that rebalancing between on-table and off-table assets must be optimal relative to going all in. On-table assets may go to zero on the next bet. But we don't call this rebalancing, we use terms like "going all in", "letting it ride", "taking some off the table".

You can rebalance for free in tax-deferred accounts, with some rate limits depending on the fund company rules. Lots of us limit our rebalancing to those accounts.
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Re: "There is a rebalancing bonus ... false"

Postby camontgo » Sat Jun 01, 2013 9:59 am

tadamsmar wrote:
camontgo wrote:Ok, I tried it, and I do see that the average annual bonus in the simulation gets bigger when the standard deviation is increased.

I'm still thinking it through, but my simulation (assuming I haven't made any errors) is showing that there is some positive bonus on average. It can be significant for extreme parameters, but it is tiny (close to zero) on average for parameters that seem realistic for diversified asset classes (i.e. u.s. and international; large cap and small cap; stocks and bonds). The "expected" bonus over reasonable horizons appears to be only a few basis points per year using volatilities and correlations typical of these asset classes....probably not enough to cover the additional costs.


It makes sense that the bonus due to Shannon/Kelly considerations is small because pretty good money management is already built into our strategy for diversified assets with lowish variance (money management as provided by the Kelly Criteria). Ed Thorpe used Kelly in running the world's first hedge fund and discussed it's application in "Beat the Market" but this must have been making much riskier bets in the markets.

This implies that Bernstein is right for typical mutual fund investing, but for the wrong reasons. It's not true that rebalancing provides no bonus for random markets, it's true that rebalancing provides no or a de minimis bonus for relatively low variance mutual funds in random markets. Hence, if there is a bonus in this situation, then its due to auto correlation (so called "mean reversion") and not due to superior Kelly-style money management. (Perhaps if one allocated to a leveraged small value fund and a leveraged long bond fund then Kelly considerations would come into play significantly, not sure.)

If you have an edge in a high stakes gambling game (you are card counting for instance) it's easy to see that rebalancing between on-table and off-table assets must be optimal relative to going all in. On-table assets may go to zero on the next bet. But we don't call this rebalancing, we use terms like "going all in", "letting it ride", "taking some off the table".

You can rebalance for free in tax-deferred accounts, with some rate limits depending on the fund company rules. Lots of us limit our rebalancing to those accounts.


Well, I'm still not convinced there is a true bonus on average. I'm still working on it.

I do see a rebalancing bonus, on average, for very high variance cases, when I average the annualized returns across all outcomes...rebalance vs. non-rebalanced.

However, I think that method of averaging the outcomes is wrong. If I average the final dollar outcomes for rebalancing vs. no-rebalancing, I get no consistent winner...even with high variance and 10,000 trial simulations.

EDIT: From the simulation, I do find that the average CAGR is higher for rebalancing...though it takes some extreme parameters for this to be obvious. However, the distribution of CAGR for all trials is different for rebalancing vs. no rebalancing. The no-rebalancing distribution is more positively skewed than the distribution with rebalancing..especially when variance is very high. The result seems to be that in terms of average total ending wealth...neither strategy has the advantage. In terms of total wealth, rebalancing usually outperforms by a little, but sometimes underperforms by a lot. I'm happy to post code or try some other scenarios if you think this result may be wrong.

EDIT2: Rebalancing brings the median outcome (in terms of wealth) closer to the average outcome....but it doesn't seem to change the expected wealth....however, if you frame things in terms of average CAGR rather than total wealth or total return then there is a difference. For an extremely skewed distribution of wealth outcomes (such as in the Shannon's demon example) the results are dramatic because the expected value of the game where you flip a single coin 200 times with 100% gain or 50% loss is enormous, but the median outcome is that you end up with a gain of zero. Rebalancing across three coins, as in the rmelvey spreadsheet, brings the median outcome closer to the average outcome...so there is a dramatic rebalancing bonus the vast majority of the time...though there are still extremely rare scenarios where there is a rebalancing penalty which is many orders of magnitude larger than the typical bonus.
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Re: "There is a rebalancing bonus ... false"

Postby tadamsmar » Tue Jun 04, 2013 10:42 am

Thorpe did the math for asset allocation to the SP500 and T-bills here:

http://edwardothorp.com/sitebuildercont ... Market.pdf

But he ended up with zero allocation to T-Bills. He concluded that you could buy SP500 on margin up to 169% of your bankroll, assuming you are immortal and paid no fees.
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Re: "There is a rebalancing bonus ... false"

Postby camontgo » Tue Jun 04, 2013 11:53 am

tadamsmar wrote:Thorpe did the math for asset allocation to the SP500 and T-bills here:

http://edwardothorp.com/sitebuildercont ... Market.pdf

But he ended up with zero allocation to T-Bills. He concluded that you could buy SP500 on margin up to 169% of your bankroll, assuming you are immortal and paid no fees.


So, in Thorpe's calculation, his rebalancing strategy is maximizing expected log of wealth, which is the same as maximizing expected continuously compounded return....but, it is not the same thing as maximizing expected wealth. In many scenarios, rebalancing reduces the right tail of the distribution of final wealth, and raises the median value. In the case where two assets have the same expected return, the average wealth is the same, but average log of wealth is greater for the rebalanced portfolio.

I think this makes sense, and maximizing log of wealth is probably the best objective in many situations. The problem is that in most realistic situations, the expected benefit in terms of CAGR from the effect is extremely small (as in a few basis points...not the 0.5 to 1.5% mentioned in the title of a related thread).
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Re: "There is a rebalancing bonus ... false"

Postby boggler » Thu Jun 27, 2013 8:57 pm

camontgo wrote:
tadamsmar wrote:Thorpe did the math for asset allocation to the SP500 and T-bills here:

http://edwardothorp.com/sitebuildercont ... Market.pdf

But he ended up with zero allocation to T-Bills. He concluded that you could buy SP500 on margin up to 169% of your bankroll, assuming you are immortal and paid no fees.


So, in Thorpe's calculation, his rebalancing strategy is maximizing expected log of wealth, which is the same as maximizing expected continuously compounded return....but, it is not the same thing as maximizing expected wealth. In many scenarios, rebalancing reduces the right tail of the distribution of final wealth, and raises the median value. In the case where two assets have the same expected return, the average wealth is the same, but average log of wealth is greater for the rebalanced portfolio.

I think this makes sense, and maximizing log of wealth is probably the best objective in many situations. The problem is that in most realistic situations, the expected benefit in terms of CAGR from the effect is extremely small (as in a few basis points...not the 0.5 to 1.5% mentioned in the title of a related thread).


Would it be correct, then, to say that any additional bonus above those few basis points is due to mean reversion in the market?

On a different, note, can mean reversion be expected to continue?
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Re: "There is a rebalancing bonus ... false"

Postby nedsaid » Fri Jun 28, 2013 12:57 am

My thoughts on rebalancing is that is mainly is done to control risks. I am not convinced that there is a rebalancing bonus but it does make sense in that it forces one to buy low and sell high.

My attitude towards rebalancing is pretty relaxed. I don't do it very often. The key thing is not to let your asset allocation get out of whack.
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Re: "There is a rebalancing bonus ... false"

Postby Dandy » Fri Jun 28, 2013 4:37 pm

I think of rebalancing as controlling risk. If I wanted to go for greater returns (and risk) I would have a minimal allocation to fixed income and never rebalance. Equities over time outperform fixed income - if you sell equities and buy fixed income I think you are making a trade off which is I will settle for more stability/capital preservation/less risk and give up better long term gains/volitility and accept higher risk.

Reblancing forces you to take current profits but doesn't insure greater profits over the longer term??
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Re: "THERE IS A REBALANCING BONUS ... FALSE"

Postby Retireyoung » Wed Nov 06, 2013 8:35 pm

[THREAD RESTARTED - CHECK POST DATES BEFORE RESPONDING TO OLDER REPLIES - admin alex]

MindBogler wrote:
In total over the 51 years there has been a 0.37% annualized benefit - assuming zero costs for rebalancing.

Well, I guess I can get well more than 2x my annual ER by rebalancing. That sounds like a bonus to me? :wink:

Also, this article doesn't seem to get into rebalancing via bands, which I do, at any rate.

And..I love this link at the bottom of the page: http://www.retailinvestor.org/why/timing.html

That page needs more than a few grains of salt.


I did not understand what you mean by : "this article doesn't seem to get into rebalancing via bands, which I do, at any rate."
what is rebalancing via bands ?

Thanks
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Re: "THERE IS A REBALANCING BONUS ... FALSE"

Postby LadyGeek » Wed Nov 06, 2013 9:01 pm

Retireyoung wrote:I did not understand what you mean by : "this article doesn't seem to get into rebalancing via bands, which I do, at any rate."
what is rebalancing via bands ?

Welcome! Good question. It's just another word for "threshold". Here's a tutorial by forum member tfb: +/- 5% Rebalancing Bands

The wiki has some background info: Rebalancing (if this thread is confusing, follow the guidance here)

A Vanguard publication which deep-dives on the topic: Portfolio Rebalancing in Theory and Practice
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Re: "There is a rebalancing bonus ... false"

Postby Bradley » Wed Nov 06, 2013 9:05 pm

The most comprehensive and educational discussions on rebalancing were posted by Gummy on his website. One such discussion which discusses Bernstein's Rebalancing opinion can be found here: http://www.gummy-stuff.org/rebalancing-bonus.htm
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Re: "There is a rebalancing bonus ... false"

Postby Rick Ferri » Wed Nov 06, 2013 10:20 pm

gummy wrote:So, the rebalancing bonus is 11.3% - 11.0% = 0.3%, right? Right!


Sounds right to me also. I estimated about a 0.25% rebalancing benefit between US stocks and bonds net of cost in the very long-term.

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Re: "There is a rebalancing bonus ... false"

Postby Retireyoung » Thu Nov 07, 2013 6:19 am

Thanks for the explanation.
I see the bonus for re-balancing is very small < 1% , i wonder if it is still positive after tax deductions and trading commissions ?
The other thought i have is what if we use this bands in a different way , rebalance only when a security is +/-2 * standart deviation from its 200 day moving average
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Re: "There is a rebalancing bonus ... false"

Postby Rick Ferri » Thu Nov 07, 2013 12:27 pm

Rebalancing is primarily done to keep the risk of a portfolio in line with your investment objectives. Any MTP benefit (excess return benefit) is just that, a benefit.

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Re: "There is a rebalancing bonus ... false"

Postby JW Nearly Retired » Thu Nov 07, 2013 12:31 pm

Retireyoung wrote:Thanks for the explanation.
I see the bonus for re-balancing is very small < 1% , i wonder if it is still positive after tax deductions and trading commissions ?
The other thought i have is what if we use this bands in a different way, rebalance only when a security is +/-2 * standart deviation from its 200 day moving average

bump
I've done a lot of 50/200 moving average type simulations, including rebalance only. I'll post something as soon as I can dig them up.
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ps: They are disappointing.
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Re: "There is a rebalancing bonus ... false"

Postby Clearly_Irrational » Thu Nov 07, 2013 1:28 pm

JW Nearly Retired wrote:I've done a lot of 50/200 moving average type simulations, including rebalance only. I'll post something as soon as I can dig them up.
JW
ps: They are disappointing.


My experience was that A) They're too slow to changeover or B) They whipsaw too much. In and of themselves 50/200 SMA cross systems are not that great.
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Re: "There is a rebalancing bonus ... false"

Postby JW Nearly Retired » Thu Nov 07, 2013 2:52 pm

JW Nearly Retired wrote:
Retireyoung wrote:Thanks for the explanation.
I see the bonus for re-balancing is very small < 1% , i wonder if it is still positive after tax deductions and trading commissions ?
The other thought i have is what if we use this bands in a different way, rebalance only when a security is +/-2 * standart deviation from its 200 day moving average

bump
I've done a lot of 50/200 moving average type simulations, including rebalance only. I'll post something as soon as I can dig them up.
JW
ps: They are disappointing.


Sorry, I wasn't doing 200 day moving average rebalancing bands like you were thinking about. I was doing simulations of going in and out of SP500 equities based on the 50/200 moving average like crossing events. (Actually settled on 36 days for the short average based on unimportant reasons.) Finally, my rebalance on the crossing signal stuff did not survive my last operating system upgrade. :oops:

So this won't add much to the rebalancing discussion but for what it's worth, this picture below shows going all-in/all-out on the cross compared to SP500 buy & hold from 1951, which is the start of the daily SP500 data I was able to get. When out of the stock market the money was assumed to earn the T-bill rate. The bottom line is the timed versus B&H portfolio are still so close together after 62 years the difference is trivial. Comes to 0.2% compounded in favor of market timing, which I call noise level. If you go back and count the number of signals that got you out and back in with much profit, you find it's a really small number and IMO that makes the results depend a whole lot on pure luck....i.e., the cross happens just before or just after some big move in the market. Given all-in/all-out trades yield such a trivial benefits, if you were just rebalancing on the signals it produced, that will amount to an even more trivial difference.
JW
ps: (I know in/out timing back then would have been nuts to do because of taxes and trading costs. This was just an exercise to get an idea of any possible benefit in the future)

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Re: "There is a rebalancing bonus ... false"

Postby LadyGeek » Fri Nov 08, 2013 12:28 am

Bradley wrote:The most comprehensive and educational discussions on rebalancing were posted by Gummy on his website. One such discussion which discusses Bernstein's Rebalancing opinion can be found here: http://www.gummy-stuff.org/rebalancing-bonus.htm

We've just added a link to Gummy's site in the wiki: Gummy-stuff
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Re: "There is a rebalancing bonus ... false"

Postby LH » Fri Nov 08, 2013 3:57 am

There is a rebalancing bonus, trouble is it could be positive or negative : p
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Re: "There is a rebalancing bonus ... false"

Postby YDNAL » Fri Nov 08, 2013 6:21 am

boggler wrote:This article seems to rail against the notion that there is a bonus by rebalancing.
http://www.retailinvestor.org/why/bonus.html

Rebalancing to your target asset allocation to maintain constant risk exposure is completely valid. However, this is separate from the idea of a "bonus."

Then, rebalance to maintain risk and if you get a "bonus" the Holiday Season is upon us !
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Re: "There is a rebalancing bonus ... false"

Postby Retireyoung » Sat Nov 09, 2013 8:48 pm

I found some nice articles about equal weight and volatility based allocations :
http://gestaltu.blogspot.co.il/2012/02/ ... ce-of.html
http://www.parametricportfolio.com/wp-c ... eb.CA_.pdf
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Re: "There is a rebalancing bonus ... false"

Postby Retireyoung » Sat Nov 09, 2013 8:49 pm

JW Nearly Retired wrote:
Retireyoung wrote:Thanks for the explanation.
I see the bonus for re-balancing is very small < 1% , i wonder if it is still positive after tax deductions and trading commissions ?
The other thought i have is what if we use this bands in a different way, rebalance only when a security is +/-2 * standart deviation from its 200 day moving average

bump
I've done a lot of 50/200 moving average type simulations, including rebalance only. I'll post something as soon as I can dig them up.
JW
ps: They are disappointing.

Thanks for the graphs!
50/200 moving average clearly reduce risk but return is almost the same!!
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Re: "There is a rebalancing bonus ... false"

Postby JustinR » Sat Nov 09, 2013 10:38 pm

So...what's the consensus?

Is or isn't there a rebalancing bonus?
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Re: "There is a rebalancing bonus ... false"

Postby umfundi » Sun Nov 10, 2013 4:44 am

JustinR wrote:So...what's the consensus?

Is or isn't there a rebalancing bonus?


It depends. If investments fluctuate with no real trend, there is a bonus. If investments move with a trend, there may even be a penalty.

Suppose you have two investments, A and B. Here are their prices:

Code: Select all
Case 1:
   Start    Mid     End
A  $1.00   $1.10   $1.00
B  $1.00   $0.90   $1.00

Case 2:
   Start    Mid     End
A  $1.00   $1.10   $1.20
B  $1.00   $0.90   $0.80

In Case 1 you will have a bonus if you rebalance at the Mid value, in Case 2 you will have a penalty. (I leave the arithmetic to you.)

I ran a simulation of a 50/50 portfolio over the decade 2001 - 2010 (including regular monthly investments, and rebalancing monthly) and the rebalancing bonus was about 0.3% per year. I suspect that if we run the numbers for 2010 - present, there might be a rebalancing penalty.

The purpose of rebalancing is to maintain your AA and thus to manage risk. The fact that it yields a bonus in uncertain times is a nice little side benefit.

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Re: "There is a rebalancing bonus ... false"

Postby JustinR » Sun Nov 10, 2013 5:06 am

umfundi wrote:
JustinR wrote:So...what's the consensus?

Is or isn't there a rebalancing bonus?


It depends. If investments fluctuate with no real trend, there is a bonus. If investments move with a trend, there may even be a penalty.

Suppose you have two investments, A and B. Here are their prices:

Code: Select all
Case 1:
   Start    Mid     End
A  $1.00   $1.10   $1.00
B  $1.00   $0.90   $1.00

Case 2:
   Start    Mid     End
A  $1.00   $1.10   $1.20
B  $1.00   $0.90   $0.80

In Case 1 you will have a bonus if you rebalance at the Mid value, in Case 2 you will have a penalty. (I leave the arithmetic to you.)

I ran a simulation of a 50/50 portfolio over the decade 2001 - 2010 (including regular monthly investments, and rebalancing monthly) and the rebalancing bonus was about 0.3% per year. I suspect that if we run the numbers for 2010 - present, there might be a rebalancing penalty.

The purpose of rebalancing is to maintain your AA and thus to manage risk. The fact that it yields a bonus in uncertain times is a nice little side benefit.

Keith

Thanks for summarizing this in such an simple way to understand.

I wonder if the answer then is to look at longer periods or bigger bands between rebalancings to reduce the effect of trends.

What rebalancing periods did you use to backtest?

What if you increased it to half a year, or a year, or 1.5, or 2 years, etc.? Does the rebalancing bonus increase (or chance of a penalty decrease)?
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Re: "There is a rebalancing bonus ... false"

Postby umfundi » Sun Nov 10, 2013 5:44 am

JustinR wrote:Thanks for summarizing this in such an simple way to understand.

I wonder if the answer then is to look at longer periods or bigger bands between rebalancings to reduce the effect of trends.

What rebalancing periods did you use to backtest?

What if you increased it to half a year, or a year, or 1.5, or 2 years, etc.? Does the rebalancing bonus increase (or chance of a penalty decrease)?

Justin,

In my simulation I rebalanced monthly. I ran two simulations:

1. A 50/50 portfolio with no new investments.
2. Constant dollar monthly investments with no starting balance.

You can blend these two as you wish.

I was satisfied enough with the results that I simply put all my money in Vanguard LifeStrategy Moderate, where they do the continuous rebalancing and I don't have to worry about it.

That said:

I think that anything other than robotic rebalancing on a fixed schedule is market timing. Think about it: The market fluctuates, and you want to sell high and buy low. You want to catch the wave. The question is, what is the wavelength? If you know that, you should rebalance each half wave period.

Let's say the market is set to go up for six months, and then drop back. Well, then if you rebalance monthly, you will miss some of the rise by selling too early. Better to wait and rebalance after six months.

The fact is, this underlying rhythm in the market does not exist. For the data of a decade like 2001-2010 it may be that rebalancing twice yearly earned more of a bonus than rebalancing monthly. That means nothing, it is an artifact of the data.

Yes, I know, there are things called momentum (the cycle is longer than you thought) and reversion to the mean (the cycle is shorter than you thought), but I don't buy any of it.

So, what's practical? Rebalance by directing new contributions to under-performing investments. That's easy. Rebalance by directing distributions and dividends to a sweep account, and reinvest them yourself. That is also easy. Beyond that, I think a yearly checkup is fine. But, do take a peek if the market reaches a new high or low.

Edit: This previous post by nisiprius in this thread makes the same points as I do.

Keith
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Re: "There is a rebalancing bonus ... false"

Postby umfundi » Sun Nov 10, 2013 6:20 am

rmelvey wrote:How come every time I try to explain this on the forum everyone treats me like a crazy person :confused

Well, I don't think I have ever done that!

In the old days you had to buy round lots of shares. So, let's say you bought 10 shares per month. The price fluctuated, but let's say that at the end your average price was $10 per share.

In this day, people invest a fixed amount per period. So, let's say you invest $100 per month. Guess what: Your average price will be less than $10 per share!

This is not magic. It is not an investment strategy. It is an artifact of the arithmetic: If you buy a constant number of shares, you will pay the average price. If you invest a constant dollar amount, your average price per share is the harmonic mean of the prices, which is always lower than the simple average of the prices.

http://economistatlarge.com/finance/app ... onic-means

Yes, if rebalancing is sell high, buy low, it reduces your basis cost per share. That has nothing to do with the how the appropriate means and averages are calculated.

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Re: "There is a rebalancing bonus ... false"

Postby ClosetIndexer » Sun Nov 10, 2013 7:18 am

umfundi wrote:In this day, people invest a fixed amount per period. So, let's say you invest $100 per month. Guess what: Your average price will be less than $10 per share!

This is not magic. It is not an investment strategy. It is an artifact of the arithmetic


True, but it is a great way to get people excited about the idea of making regular contributions to retirement savings. :)

Also just wanted to pop in and say I'm glad this thread got bumped. Camontgo's posts especially showed me some things that I thought I had a complete understanding of, but actually didn't!
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Re: "There is a rebalancing bonus ... false"

Postby JoMoney » Sun Nov 10, 2013 8:33 am

I can find lots of periods over the past 20 years where the result of a 60/40 rebalanced portfolio achieved more than just a buy and hold of the same proportion of each (and in rare instance more than either alone).
I can also find periods where rebalancing produced less than the un-rebalanced proportionate buy and hold.
I can find periods with the same starting point that the investor could have quit while ahead, but if they kept rebalancing, the bonus is lost.
I'm convinced the bonus does exist, it can also be negative, it's fleeting and completely period dependent.

Rebalance to maintain risk profile, if bonus occurs at the point you quit - Happy Days :happy
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Re: "There is a rebalancing bonus ... false"

Postby JW Nearly Retired » Sun Nov 10, 2013 12:46 pm

umfundi wrote:
Yes, if rebalancing is sell high, buy low, it reduces your basis cost per share. That has nothing to do with the how the appropriate means and averages are calculated.

I want to point out that rebalancing is not just sell high/buy low..... half the period of a full market cycle it is selling low & buying high. That might be why nobody can seem to show more than a tiny speck of a rebalancing "bonus".

If you define high and low stock prices based on an average over long bull/bear market cycle like periods of time, you get just about equal amounts of sell low/buy high rebalancing as you do the kind we wish we were doing. Per the graph, ignoring all the small oscillations, the full cyclic 2006 - 2011 rebalancing story went: sell high -> buy high -> buy low -> sell low, if you were keeping your AA constant. You would expect the net effect to be nothing.
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Re: "There is a rebalancing bonus ... false"

Postby Retireyoung » Mon Nov 11, 2013 11:47 am

Can anybody back-test buying low selling high with long term moving average (maybe even using Bolinger-bands) ? It will give more accurate answer about the Bonus .
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Re: "There is a rebalancing bonus ... false"

Postby Akiva » Mon Nov 11, 2013 2:14 pm

Retireyoung wrote:Can anybody back-test buying low selling high with long term moving average (maybe even using Bolinger-bands) ? It will give more accurate answer about the Bonus .

boggler wrote:Basically, the "bonus" relies upon the assumption that the markets are mean-reverting. If they are, then buying low and selling high works, otherwise, it doesn't.


The rebalancing bonus has nothing to do with "mean reversion" (which no one in this thread is using correctly) or with momentum effects.

The reason you rebalance is because rebalancing causes your geometric returns (i.e. what you get) to be closer to the arithmetic returns of the portfolio components. Depending on volatility, there is some "drag" that pulls the returns you see down from the arithmetic average. So you get a bonus from rebalancing by eliminating this drag.

As was explained:
rmelvey wrote:Its kind of ironic that people keep saying that rebalancing reduces risk, but does not increase return. Holding arithmetic returns constant, decreasing risk increases the geometric return.

In summary, rebalancing increases returns because it decreases risk. Buying low and selling high has absolutely nothing to do with the bonus I am talking about.


Put another way, your allocation has some arithmetic return. Rebalancing will bring your geometric return closer to this arithmetic average because it reduces your risk and therefore the drag on your returns.

Re: this, from earlier in the thread:
nisiprius wrote:Look, someone had better state clearly and unambiguously what the proposition is, because what tends to happen these discussions is that different advocates of rebalancing put forward different claims for what it is supposed to be doing, never quite clearly stated.


(I'm not quoting the whole thing to save space)

You are overlooking the fact that for any risky asset there is a maximum safe allocation. Going beyond this allocation will reduce your geometric returns and increase your risk. Going too far beyond will make your risk of ruin approach certainty. (This is a really subtle point that very few people seem to understand fully.) The reason for this is because gains and losses are asymetric. To get back what you lost, you need gain = ((1/(1-loss%))-1. I.e. A 50% loss requires and offsetting 100% gain. So if you over-allocate to a particular risk, then you hurt your geometric returns because the higher arithmetic gains don't offset the volatility the additional allocation added.

In the case of a single coin-flipping game,

p = the probability of winning on a given bet.
B = the ratio of the amount won to the amount lost
f = the percent of your assets risked on each flip

So the growth rate will be:

G(f) = p * ln(1+B*f) + (1-p)*ln(1-f)

The maximium safe allocation is:

f = mathematical expectation / B = ((B+1)*p-1)/B

So for example, a 50/50 flip with a B of 1.25, has a maximum f = .1

For f = .1, G(f) = .6% per flip.

G(.05) = .46% per flip.
G(.15) = .46% per flip
G(.2) = 0% per flip

So if you invested more than 20% in this scheme, you'd lose money even though it has positive expectancy.

Did this help?

nisiprius wrote:The thing about arithmetic and geometric means is really simple: for any unit time period, the right thing to do is to take the arithmetic means of the returns of the assets in the portfolio; for periods spanning more than one unit, you take the geometric mean of those arithmetic means.

Now, all this stuff, like the Monty Hall problem and so many things in probability, is tricky enough to think about that it is genuinely hard to be sure you've got it right, particularly if it's offered up in some new guise, hence the endless debate.

There are a fair number of people, though, who really believe that rebalancing magically ratchets up returns because it is an automatic mechanical way of buying low and selling high, and that the effect depends simply on the fact that it is rebalancing, and doesn't depend on mean reversion. As opposed to saying that if you rebalance at periodic intervals, you may actually catch a small benefit if the rebalancing interval happens to resonate with the mean reversion period.

No mean reversion, no rebalancing bonus. You always have the opportunity to shape the distribution of outcomes and remold it nearer to the heart's desire, but which shape is best depends on one's personal heart's desire--that is to say, one's appetite for risk and which direction one prefers to have the outcomes skewed.


There are two related things going on here:

First off, there's the point that you can actually take too much risk. Up to a point, more risk increases your returns. Beyond that point, you may have higher arithmetic returns, but the growth rate of your capital will decline or go negative.

Second off, there's the mathematically true point that rebalancing makes a given portfolio's growth rate better track the arithmetic returns of the underlying assets. This has nothing to do with mean reversion (either actual mean reversion or the sort of thing people in this thread have in mind when they use that expression).

swaption wrote:You know, this hypothetical example seemingly ends up in a dead end when applied ot the real world. Or does it? On the surface, this geometric 100% gain and 50% loss does not really exist, at least in the world of coin flips. Even if one flip, it's a bad bet for the house and no such thing exists in Vegas or anywhere. Vegas is a world with no expected return. But of course Kelly and Shannon were dealing with a different kind of world. They were dealing in a world where there was some sort of advantage, something that gave an expectation of a return. The Kelly Criteria was essentially an approach to sizing bets so that the advantage could be realized without going bust.


Well, the calculations tell you how much to risk at a given time to optimize your growth rate for a given draw-down risk. The coin flipping example is just a really simple, easy-to-understand model of what is going on. You can do the calculations with actual investments, but it involves solving some nasty calculus problems, and the math would obscure the point the example is intended to prove.

For example:
camontgo wrote:Over longer horizons, the result remains the same. The likelihood of the average returns being close increases with a longer horizon..but the "realized return difference" window where you get a bonus shrinks....so the average bonus over many trials is still zero.

Where have I gone wrong with this analysis?


If you increase the volatility of your assets to make the bonus more extreme, it will show up more obviously. Similarly, you could add a cash component and rebalance between all three at the optimal f to make it as apparent as possible. (It may even be that your simulation is having problems because it is over-leveraged without a "cash" component. In which case the rebalancing can't help you since you are taking too much risk to begin with.)
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Re: "There is a rebalancing bonus ... false"

Postby umfundi » Mon Nov 11, 2013 4:12 pm

Please define (with references and a simple example) "Arithmetic Return" and "Geometric Return".

Thank you,

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Re: "There is a rebalancing bonus ... false"

Postby Akiva » Mon Nov 11, 2013 4:25 pm

umfundi wrote:Please define (with references and a simple example) "Arithmetic Return" and "Geometric Return".

Thank you,

Keith


See wikipedia (or anything else google pulls up for this):
Arithmetic
Geometric

See also, See Erb and Harvey, The strategic and tactical value of commodity futures. Financial Analysts Journal (2006).

This paper is available online and has a good section on how rebalancing works and why.
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Re: "There is a rebalancing bonus ... false"

Postby umfundi » Mon Nov 11, 2013 4:38 pm

Akiva wrote:
umfundi wrote:Please define (with references and a simple example) "Arithmetic Return" and "Geometric Return".

Thank you,

Keith


See wikipedia (or anything else google pulls up for this):
Arithmetic
Geometric

Akiva,

Thank you.

I already know how to do arithmetic.

You seem to imply there is an investment strategy associated with these?

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Re: "There is a rebalancing bonus ... false"

Postby Akiva » Mon Nov 11, 2013 4:43 pm

umfundi wrote:
Akiva wrote:
umfundi wrote:Please define (with references and a simple example) "Arithmetic Return" and "Geometric Return".

Thank you,

Keith


See wikipedia (or anything else google pulls up for this):
Arithmetic
Geometric

Akiva,

Thank you.

I already know how to do arithmetic.

You seem to imply there is an investment strategy associated with these?

Keith


See also the paper I added to the previous post. It explains why investors should care about this. Calling it a "strategy" is probably a bit far fetched. It's just mathematical truth. Rebalancing makes your portfolio's geometric returns closer to it's arithmetic one (because it reduces your risk and thereby eliminates volatility drag). So if you do a proper attribution analysis, the rebalancing returns will be positive for all practical situations. The people who are saying it costs you are coming up with their answer by not doing an apples to apples comparison.
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Re: "There is a rebalancing bonus ... false"

Postby camontgo » Mon Nov 11, 2013 5:30 pm

camontgo wrote:Over longer horizons, the result remains the same. The likelihood of the average returns being close increases with a longer horizon..but the "realized return difference" window where you get a bonus shrinks....so the average bonus over many trials is still zero.

Where have I gone wrong with this analysis?


If you increase the volatility of your assets to make the bonus more extreme, it will show up more obviously. Similarly, you could add a cash component and rebalance between all three at the optimal f to make it as apparent as possible. (It may even be that your simulation is having problems because it is over-leveraged without a "cash" component. In which case the rebalancing can't help you since you are taking too much risk to begin with.)


Yes, if you read my later posts, I did increase the volatility to extreme levels, and there did appear to be a bonus when I calculated the average CAGR across all trials in the simulation (rebalancing vs. non-rebalancing). My simulation used two uncorrelated assets with identical volatility and expected returns (random walk..no mean reversion).

However, the average final wealth for rebalancing vs. not rebalancing remained the same even with extreme parameters. On average, there was no expected "wealth bonus"...however CAGR is more closely related to the log of final wealth. So, the rebalanced portfolio (which had a less skewed distribution...i.e. the median of all outcomes was closer to the mean) had a higher mean of log wealth...and therefore a higher average CAGR. I think the less skewed distribution of outcomes is desirable, so, in that sense, I concluded there is a rebalancing bonus.

However, with realistic parameters (for broad asset classes) the effect was tiny (a small fraction of a percent for two assets with 20% annual standard deviation).
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Re: "There is a rebalancing bonus ... false"

Postby Akiva » Mon Nov 11, 2013 5:59 pm

camontgo wrote:
camontgo wrote:Over longer horizons, the result remains the same. The likelihood of the average returns being close increases with a longer horizon..but the "realized return difference" window where you get a bonus shrinks....so the average bonus over many trials is still zero.

Where have I gone wrong with this analysis?


If you increase the volatility of your assets to make the bonus more extreme, it will show up more obviously. Similarly, you could add a cash component and rebalance between all three at the optimal f to make it as apparent as possible. (It may even be that your simulation is having problems because it is over-leveraged without a "cash" component. In which case the rebalancing can't help you since you are taking too much risk to begin with.)


Yes, if you read my later posts, I did increase the volatility to extreme levels, and there did appear to be a bonus when I calculated the average CAGR across all trials in the simulation (rebalancing vs. non-rebalancing). My simulation used two uncorrelated assets with identical volatility and expected returns (random walk..no mean reversion).

However, the average final wealth for rebalancing vs. not rebalancing remained the same even with extreme parameters. On average, there was no expected "wealth bonus"...however CAGR is more closely related to the log of final wealth. So, the rebalanced portfolio (which had a less skewed distribution...i.e. the median of all outcomes was closer to the mean) had a higher mean of log wealth...and therefore a higher average CAGR. I think the less skewed distribution of outcomes is desirable, so, in that sense, I concluded there is a rebalancing bonus.

However, with realistic parameters (for broad asset classes) the effect was tiny (a small fraction of a percent for two assets with 20% annual standard deviation).


Well, it certainly ends up being significant in a diversified commodities portfolio. (See the paper I cited above.) That might be because the risk reduction is greater because there are more assets. Or it might be because there's something non-obvious with the way you are attributing this bonus in your simulation.

Using a back of the book calculation, the standard deviation of a 50/50 portfolio should be ~14% and with a 10% return, using the approximation that says that geo mean = arith mean - variance * .5, the CAGR of the combined portfolio should be 10%-14%^2*.5 = 9% (vs 8% for no rebalancing which in the limit gives you 20% variance). So your effect size seems to be an order of magnitude off.

I need to think more deeply about why that is...
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Re: "There is a rebalancing bonus ... false"

Postby camontgo » Mon Nov 11, 2013 6:10 pm

Akiva wrote:Using a back of the book calculation, the standard deviation of a 50/50 portfolio should be ~14% and with a 10% return, using the approximation that says that geo mean = arith mean - variance * .5, the CAGR of the combined portfolio should be 10%-14%^2*.5 = 9% (vs 8% for no rebalancing which in the limit gives you 20% variance). So your effect size seems to be an order of magnitude off.


This math only applies if the realized return of the two portfolios is the same.

If I rebalance between two uncorrelated assets that both have a realized return of 10% per year over ten years, then I agree with your math.

However, just because the mean of the process is 10% and the std is 20% doesn't that both assets will have the same realized return over a given period (my simulation uses 10 years). In many cases they will drift apart (one could be 6% and the other could be 12% for example)...and for those trials the rebalancing bonus is negative. The cases where the realized returns of the two assets are actually equal or nearly equal (whether they hit the mean of 10% or not is irrelevant they could both be 12% or 8% and the bonus is the same) is the best case scenario for rebalancing.

See the plot I posted here: viewtopic.php?f=1&t=60457&hilit=+rebalancing+bonus#p1523390

Note that when I posted that plot I thought all trials averaged to zero (they nearly do), but I later realized that the average is slightly positive since this is a CAGR comparison.
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Re: "There is a rebalancing bonus ... false"

Postby Akiva » Mon Nov 11, 2013 6:25 pm

camontgo wrote:
Akiva wrote:Using a back of the book calculation, the standard deviation of a 50/50 portfolio should be ~14% and with a 10% return, using the approximation that says that geo mean = arith mean - variance * .5, the CAGR of the combined portfolio should be 10%-14%^2*.5 = 9% (vs 8% for no rebalancing which in the limit gives you 20% variance). So your effect size seems to be an order of magnitude off.


This math only applies if the realized return of the two portfolios is the same.


The approximation doesn't require that. Nor does a more general formula that doesn't use this approximation (see the paper I cited).

If I rebalance between two uncorrelated assets that both have a realized return of 10% per year over ten years, then I agree with your math.

However, just because the mean of the process is 10% and the std is 20% doesn't that both assets will have the same realized return over a given period (my simulation uses 10 years). In many cases they will drift apart (one could be 6% and the other could be 12% for example)...and for those trials the rebalancing bonus is negative. The cases where the realized returns of the two assets are actually equal or nearly equal (whether they hit the mean of 10% or not is irrelevant they could both be 12% or 8% and the bonus is the same) is the best case scenario for rebalancing.


Now the problem is apparent. You are attributing losses that come from your allocation (having money invested in something that lost money) to rebalancing.

The question isn't whether your final returns are higher, it's whether the rebalancing made your geometric returns closer to the arithmetic ones *for the same allocation* (which we know it must do mathematically). Obviously if you change your allocation into an asset that turns out to return more than you end up better off. But that doesn't prove that rebalancing doesn't work, it just proves that your allocation was suboptimal.

If you break up the portfolios' returns into the returns of each assets and the returns you got from rebalancing, the losses should fall on the assets that are underperforming and the rebalancing effect should still be positive (and about 1% according to my back of the book calculations).
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Re: "There is a rebalancing bonus ... false"

Postby camontgo » Mon Nov 11, 2013 6:35 pm

Akiva wrote:Now the problem is apparent. You are attributing losses that come from your allocation (having money invested in something that lost money) to rebalancing.


I'm assuming I invest in two assets that have the same mean and expected return. The assets follow a random walk...so they aren't guaranteed to end up in the same place over a given period...even though the process mean is identical.

I compare rebalancing vs. no-rebalancing across many trials. In some cases rebalancing wins (when realized returns are nearly equal). In other cases it loses.

Of course the reason it loses is because one asset did relatively poorly and the other did relatively well...but I had no way of knowing which would do well in advance. The simulation draws both sets of returns from the same distribution.

In what way does this simulation not reflect the situation (simplified a bit) faced by investors in the real world? I don't know exactly what I'm going to get when I invest in a risky asset...that's why its risky!

You can show a "bonus" when the returns are not equal...if both assets have the same risk adjusted return...but again it depends on them realizing the expected return....they will only do that on average. In any given trial (even a fairly long one) the results can be different.
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Re: "There is a rebalancing bonus ... false"

Postby Akiva » Mon Nov 11, 2013 6:44 pm

camontgo wrote:
Akiva wrote:Now the problem is apparent. You are attributing losses that come from your allocation (having money invested in something that lost money) to rebalancing.


I'm assuming I invest in two assets that have the same mean and expected return. The assets follow a random walk...so they aren't guaranteed to end up in the same place over a given period...even though the process mean is identical.

I compare rebalancing vs. no-rebalancing across many trials. In some cases rebalancing wins (when realized returns are nearly equal). In other case it loses.

Of course the reason it loses is because one asset did relatively poorly and the other did relatively well...but I had no way of knowing which would do well in advance. The simulation draws the returns for both from the same distribution.

In what way does this simulation not reflect the situation faced by investors in the real world?

You can show a "bonus" when the returns are not equal...if both assets have the same risk adjusted return...but again it depends on them realizing the expected return....they will only do that on average. In any given trial (even a fairly long one) the results can be different.


The issue is that you aren't doing your attribution analysis right. When reblancing "doesn't win", it's because the allocation drifted and the thing that got overallocated to did really well relative to the one that didn't. But that extra performance isn't due to rebalancing but to the fact that your allocation changed. If you do a proper attribution analysis, it will show that this "manager" did well because he overweighted the thing that did well and underweighted the thing that did poorly. This has nothing to do with rebalancing and is interfering with your results. You have to take out the effect of shifting allocations (say by comparing the non-rebalanced portfolio to a rebalanced one with the dollar averaged allocation you ended up with) in order for the effect to not be obscured by things with much larger effect sizes.
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Re: "There is a rebalancing bonus ... false"

Postby ClosetIndexer » Mon Nov 11, 2013 7:04 pm

Akiva wrote:
camontgo wrote:
Akiva wrote:Now the problem is apparent. You are attributing losses that come from your allocation (having money invested in something that lost money) to rebalancing.


I'm assuming I invest in two assets that have the same mean and expected return. The assets follow a random walk...so they aren't guaranteed to end up in the same place over a given period...even though the process mean is identical.

I compare rebalancing vs. no-rebalancing across many trials. In some cases rebalancing wins (when realized returns are nearly equal). In other case it loses.

Of course the reason it loses is because one asset did relatively poorly and the other did relatively well...but I had no way of knowing which would do well in advance. The simulation draws the returns for both from the same distribution.

In what way does this simulation not reflect the situation faced by investors in the real world?

You can show a "bonus" when the returns are not equal...if both assets have the same risk adjusted return...but again it depends on them realizing the expected return....they will only do that on average. In any given trial (even a fairly long one) the results can be different.


The issue is that you aren't doing your attribution analysis right. When reblancing "doesn't win", it's because the allocation drifted and the thing that got overallocated to did really well relative to the one that didn't. But that extra performance isn't due to rebalancing but to the fact that your allocation changed. If you do a proper attribution analysis, it will show that this "manager" did well because he overweighted the thing that did well and underweighted the thing that did poorly. This has nothing to do with rebalancing and is interfering with your results. You have to take out the effect of shifting allocations (say by comparing the non-rebalanced portfolio to a rebalanced one with the dollar averaged allocation you ended up with) in order for the effect to not be obscured by things with much larger effect sizes.


But... in the real world you're not going to know in advance if the assets you're investing in will diverge, allowing you to avoid rebalancing in that scenario. So it seems like the simulation as described is a better measure for the overall "bonus" obtained by rebalancing.

That said, very few people are going to just buy some stuff and rebalance never. So maybe it would be more useful to look at the different "bonuses" achieved by various methods for rebalancing. Say continuous (ie via monthly contributions) vs annual vs every X years?
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Re: "There is a rebalancing bonus ... false"

Postby camontgo » Mon Nov 11, 2013 7:07 pm

Akiva wrote:You have to take out the effect of shifting allocations (say by comparing the non-rebalanced portfolio to a rebalanced one with the dollar averaged allocation you ended up with) in order for the effect to not be obscured by things with much larger effect sizes.


I'd need to work through it, but I can see how something like this method might consistently show a "bonus"....but I don't see how this applies to real world investing decisions.

If I have two real world assets with modest correlation and similar expected returns, then should I invest equal amounts and forget it? Or should I periodically re-balance between them? How might the outcomes of the two approaches differ? These are the questions that I'm trying to answer.

I find that, if I assume a random walk for both assets, the average returns of the two approaches over many trials are very close for realistic volatilities, and the average wealth outcome is the same. Do you disagree with that?

Or do you agree, but say that the cases where the re-balancing approach loses aren't actually caused by "re-balancing"? In that case, what investing approach can I use to capture the re-balancing benefit while avoiding this potential pitfall?
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Re: "There is a rebalancing bonus ... false"

Postby Akiva » Mon Nov 11, 2013 7:12 pm

ClosetIndexer wrote:
Akiva wrote:
camontgo wrote:
Akiva wrote:Now the problem is apparent. You are attributing losses that come from your allocation (having money invested in something that lost money) to rebalancing.


I'm assuming I invest in two assets that have the same mean and expected return. The assets follow a random walk...so they aren't guaranteed to end up in the same place over a given period...even though the process mean is identical.

I compare rebalancing vs. no-rebalancing across many trials. In some cases rebalancing wins (when realized returns are nearly equal). In other case it loses.

Of course the reason it loses is because one asset did relatively poorly and the other did relatively well...but I had no way of knowing which would do well in advance. The simulation draws the returns for both from the same distribution.

In what way does this simulation not reflect the situation faced by investors in the real world?

You can show a "bonus" when the returns are not equal...if both assets have the same risk adjusted return...but again it depends on them realizing the expected return....they will only do that on average. In any given trial (even a fairly long one) the results can be different.


The issue is that you aren't doing your attribution analysis right. When reblancing "doesn't win", it's because the allocation drifted and the thing that got overallocated to did really well relative to the one that didn't. But that extra performance isn't due to rebalancing but to the fact that your allocation changed. If you do a proper attribution analysis, it will show that this "manager" did well because he overweighted the thing that did well and underweighted the thing that did poorly. This has nothing to do with rebalancing and is interfering with your results. You have to take out the effect of shifting allocations (say by comparing the non-rebalanced portfolio to a rebalanced one with the dollar averaged allocation you ended up with) in order for the effect to not be obscured by things with much larger effect sizes.


But... in the real world you're not going to know in advance if the assets you're investing in will diverge, allowing you to avoid rebalancing in that scenario. So it seems like the simulation as described is a better measure for the overall "bonus" obtained by rebalancing.


You also aren't going to change you allocation this drastically either. The point is that your simulation isn't a measure of rebalancing *at all* because all it shows is that having a better allocation ex post is better than not.

That said, very few people are going to just buy some stuff and rebalance never. So maybe it would be more useful to look at the different "bonuses" achieved by various methods for rebalancing. Say continuous (ie via monthly contributions) vs annual vs every X years?


Look, rebalancing is a mathematical fact. It causes your geometric returns to be closer to your arithmetic ones. No one is arguing that math is wrong. The only point of these simulations is to illustrate the mathematics for people or to show them things that maybe weren't obvious implications.

If you do a proper attribution analysis (which will ascribe the returns each portfolio gets to different things after the fact), you'll see that the returns attributed to rebalancing are always positive, but that other effects that happen at the same time in your simulation are making the overall result positive or negative.
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Re: "There is a rebalancing bonus ... false"

Postby LadyGeek » Mon Nov 11, 2013 8:36 pm

I agree on the math, but would the shape of the distribution function (Gaussian vs. something else) affect results? Maybe I'm opening a can of worms, but it's probably the best way to do an apples-to-apples comparison.

Maybe I'm wrong, but this is always in the back of my mind when simulations vs. real-world are involved.
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Re: "There is a rebalancing bonus ... false"

Postby Rodc » Mon Nov 11, 2013 9:43 pm

I think you guys are talking past each other because you are interested in different questions. Any given observer, such as myself simply has to decide which questions (one, or both or neither) they are interested in.

As an investor with no knowledge of the future I'm more interested in the general question (camontgo) of outcomes and less about the narrower question (Akiva), though it is of academic interest as well.

What I take away is that rebalancing is not likely to make a big difference in my retirement income years down the road.

Given that every 5 years or so I reassess my needs, how I am doing with progress towards meeting goals, etc, and reset my asset allocation a bit, it is especially unlikely that rebalancing is "all that" in the context of my personal investing. I rebalance with rebalancing bands anyway. :)
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Re: "There is a rebalancing bonus ... false"

Postby camontgo » Tue Nov 12, 2013 11:38 am

Rodc wrote:I think you guys are talking past each other because you are interested in different questions. Any given observer, such as myself simply has to decide which questions (one, or both or neither) they are interested in.


Yes, I think we are asking/answering different questions.

I still think my approach is the correct one for the questions I'm trying to answer about how rebalancing, as commonly implemented, can affect investment outcomes. I believe my definition of the "rebalancing bonus" matches what Bernstein uses in his analyses here:

http://www.efficientfrontier.com/ef/996/rebal.htm
http://www.efficientfrontier.com/ef/197/rebal197.htm

I think that Akiva is correct that my "rebalancing bonus" can be decomposed into a "rebalancing gain + return divergence penalty" (my terminology). I think the first term will always be positive, and the second term will always be negative for the scenarios I'm simulating. However, I don't (yet) understand how we can separate these two components in practice. I think we'd need uncorrelated assets which were guaranteed not to diverge. So, I still think my analysis is consistent with practical implementations of rebalancing.

Regardless, this discussion has got me thinking about different aspects of the problem, and I'm trying to work through the paper Akiva references. Particularly, the "Turning Water into Wine" section. If it convinces me my approach needs an update I'll post something.

https://faculty.fuqua.duke.edu/~charvey ... ic_and.pdf
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Re: "There is a rebalancing bonus ... false"

Postby Akiva » Tue Nov 12, 2013 12:05 pm

LadyGeek wrote:I agree on the math, but would the shape of the distribution function (Gaussian vs. something else) affect results? Maybe I'm opening a can of worms, but it's probably the best way to do an apples-to-apples comparison.

Maybe I'm wrong, but this is always in the back of my mind when simulations vs. real-world are involved.


The shape of the distribution would mess up my back-of-the-book calculations. But it doesn't change the actual math (though it would make calculating it harder to do in practice).

Rodc wrote:I think you guys are talking past each other because you are interested in different questions. Any given observer, such as myself simply has to decide which questions (one, or both or neither) they are interested in.

As an investor with no knowledge of the future I'm more interested in the general question (camontgo) of outcomes and less about the narrower question (Akiva), though it is of academic interest as well.


I don't see how you can call any of this "academic" and I'm fully aware that comontgo isn't getting my point. That's why I'm trying to explain it better.

Look, if someone invested in an active fund that was 100% stocks and then came here and said that they were outperforming a 60/40 passive fund and posted statistics showing that this strategy often beat out the 60/40 passive fund in practice, no one would say that this proves that active management is sometimes better. They'd say it proves that stocks return more than bonds.

The problem is that comontgo's "question" doesn't tell you anything actually useful about rebalancing. All his simulation shows is that if you could see the future and pick a better allocation, then you'd be better off. But you *can't* see the future. All you have are expected returns and risks. And given those expectations, rebalancing will give you a higher expected growth rate.

Furthermore, if you properly attribute your returns, you'll see that *even* in comontgo's situation, the rebalancing "helped", it's just that it helped less than his keeping a bad allocation hurt. I really don't understand why you guys are having so much trouble with this.

But you don't know ahead of time whether an allocation is better or not because you can't see the future.

camontgo wrote:Yes, I think we are asking/answering different questions.

I still think my approach is the correct one for the questions I'm trying to answer about how rebalancing, as commonly implemented, can affect investment outcomes.


What question do you think you are answering? Because it seems to me that you think you have an answer when you really don't.

I think that Akiva is correct that my "rebalancing bonus" can be decomposed into a "rebalancing gain + return divergence penalty" (my terminology).


Are you not familiar with performance attribution (sadly this is not one of wikipedia's better pages). If you actually do this, you'll see that the "active" allocation in the non-rebalanced case is the source of the return difference. You don't need to invent new terms for this. We all already know that the primary determinant of returns is your allocation.

I think the first term will always be positive, and the second term will always be negative for the scenarios I'm simulating. However, I don't (yet) understand how we can separate these two components in practice. I think we'd need uncorrelated assets which were guaranteed not to diverge.


We do this all the time when analyzing the performance of a portfolio. First you take the arithmetic returns in each time period and decompose them using an attribution analysis (which will account for all of the divergence in your simulation). Then you find the difference between the arithmetic and geometric returns for each portfolio. That difference should always be lower for the rebalanced one.

So, I still think my analysis is consistent with practical implementations of rebalancing.


You analysis doesn't say anything about rebalancing. It's a demonstration that better allocations are better than worse ones. And that seeing the future is better than not. I don't see how you expect to derive any useful conclusions from either of these points.
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