The Detriments of Rebalancing

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
AllYouNeedIsLove
Posts: 66
Joined: Sat Feb 14, 2015 4:30 pm

Re: The Detriments of Rebalancing

Post by AllYouNeedIsLove » Fri Apr 03, 2015 1:02 pm

tadamsmar wrote:
AllYouNeedIsLove wrote: A 50/50 portfolio of two components with expected returns of 7% and 3% would have a combined expected return of 5% -- WITHOUT REBALANCING. Rebalancing over time will move assets out of the higher returning portion of the portfolio and thereby lower the overall expected return below 5%. I do not see much discussion on this " decreased expected return cost" of rebalancing.
You math is a little wrong. If you start at 50/50 then drift of the ratio toward the higher returning asset will cause the combined return to go above 5%. Never rebalancing will increase your expected returns.

But if you are just interested in return, the the obvious thing to to is just put 100% of your nest egg in the higher returning asset.

The fact that you are at 50/50 means you are interested more than the highest possible expected returns, you are trying to limit risk. That's the main reason for rebalancing.

There may be a small rebalancing bonus if the market don't act like a random walk, but it depends on how the correlations match up with your rebalancing frequency, whether you are losing to momentum or gaining from reversion.

Tadamsmar,

My post was an attempt to gauge the expected returns between a rebalanced portfolio and a non-rebalanced portfolio with the following facts. The portfolio is currently 55/45 AA, will have no contributions or withdrawals for the next 15 years, and then will be spent down from the over weighted portion of the portfolio to a 50/50 AA.

Before posting I tried to do my own analysis. I began by looking for an empirical result by analyzing the past performance of the Life Strategy Target fund (rebalanced cohort) and the returns of Total Stock and Total Bond (non-rebalanced cohort). I gave up on this exercise due to the trap of making a generalized conclusion on limited past data. Life Strategy only goes back to 1994 and markets in the past 20 years have been unique in certain regards.

The goal of this analysis is to decide if I am comfortable with my current risk (as measured by expected return rather than AA), and to determine if I can lessen my time investment into the management of my portfolio by not rebalancing over the next 15 years.

A good suggestion in this thread was to use a financial advisor, but that is something I do not want to consider as I truly am a DIY (although admittedly a DIY with a desire to decrease my effort on this aspect of my life). Not rebalancing would also simplify the tax issues as I am mostly in taxable accounts.

Thanks for your reply.

-AllYouNeedIsLove
I don't care too much for money, money can't buy me love

YDNAL
Posts: 13774
Joined: Tue Apr 10, 2007 4:04 pm
Location: Biscayne Bay

Re: The Detriments of Rebalancing

Post by YDNAL » Fri Apr 03, 2015 2:32 pm

AllYouNeedIsLove wrote:My [original] post was an attempt to gauge the expected returns between a rebalanced portfolio and a non-rebalanced portfolio with the following facts. The portfolio is currently 55/45 AA, will have no contributions or withdrawals for the next 15 years, and then will be spent down from the over weighted portion of the portfolio to a 50/50 AA.....

The goal of this analysis is to decide if I am comfortable with my current risk (as measured by expected return rather than AA), and to determine if I can lessen my time investment into the management of my portfolio by not rebalancing over the next 15 years.
1. For illustration, take S&P 500 returns in the TWO preceding 15 calendar years. No data-mining here, just the way it went down.

Code: Select all

                            $10K investment				    $10K investment	
Year 1		 1985	31.24%	  13,124 		2000	-9.03%	  9,097 	
Year 2		 1986	18.49%	  15,551 		2001	-11.85%	 8,019 	
Year 3		 1987	5.81%	   16,454 		2002	-21.97%	 6,257 	
Year 4		 1988	16.54%	  19,176 		2003	28.36%	  8,032 	
Year 5		 1989	31.48%	  25,212 		2004	10.74%	  8,894 	
Year 6		 1990	-3.06%	  24,441 		2005	4.83%	   9,324 	
Year 7		 1991	30.23%	  31,829 		2006	15.61%	 10,779 	
Year 8		 1992	7.49%	   34,213 		2007	5.48%	  11,370 	
Year 9		 1993	9.97%	   37,624 		2008	-36.55%	 7,214 	
Year 10		1994	1.33%	   38,124 		2009	25.94%	  9,086 	
Year 11		1995	37.20%	  52,307 		2010	14.82%	 10,432 	
Year 12		1996	22.68%	  64,170 		2011	2.10%	  10,651 	
Year 13		1997	33.10%	  85,410 		2012	15.89%	 12,344 	
Year 14		1998	28.34%	 109,615 		2013	32.15%	 16,312 	
Year 15		1999	20.89%	 132,514 		2014	13.48%	 18,511
2. So, without the services of a clear crystal ball to "expect" anything in the future, I rebalance to mitigate Stock Market risk -- especially negative sequence of returns-- a fitting example being 2000-2002 (or worse -- think Japan).

Regards.
Landy | Be yourself, everyone else is already taken -- Oscar Wilde

inbox788
Posts: 5693
Joined: Thu Mar 15, 2012 5:24 pm

Re: The Detriments of Rebalancing

Post by inbox788 » Fri Apr 03, 2015 2:47 pm

If the minimum return is 5% then the average will clearly be higher. Only using less than 5% market returns and even negative returns can you compare adequately. Even more importantly, WHEN the lagging returns happen matter greatly.

User avatar
ogd
Posts: 4854
Joined: Thu Jun 14, 2012 11:43 pm

Re: The Detriments of Rebalancing

Post by ogd » Fri Apr 03, 2015 2:52 pm

AllYouNeedIsLove wrote:Before posting I tried to do my own analysis. I began by looking for an empirical result by analyzing the past performance of the Life Strategy Target fund (rebalanced cohort) and the returns of Total Stock and Total Bond (non-rebalanced cohort). I gave up on this exercise due to the trap of making a generalized conclusion on limited past data. Life Strategy only goes back to 1994 and markets in the past 20 years have been unique in certain regards.
The usual caveat: LifeStrategy was a bad fund before 2011, because it included a market-timing fund which (like seems to be the norm) excelled at bad timing. See http://www.reuters.com/article/2011/09/ ... GC20110930 .

This is unfortunate, and it's unfortunate that Vanguard continues to make little tweaks such as recently with higher % of international. The LifeStrategy funds can't be used for longer-term 3-fund portfolio benchmarks. The best for your comparison above would be the simple, boring, domestic balanced fund VBIAX.

User avatar
Kevin M
Posts: 10304
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: The Detriments of Rebalancing

Post by Kevin M » Fri Apr 03, 2015 7:45 pm

evarrr wrote:Whether or not higher return is achieved through rebalancing depends on the correlation between asset classes (low correlation = higher expected return when rebalancing).
We would like this to be true, and intuitively it seems that it should be, but according to portfolio theory math, I don't think it's true. The expected return of a portfolio is simply the weighted sum of the expected returns of the components, and has nothing to do with the expected correlations.

Portfolio math shows that for any two assets with a correlation of less than 1 (perfectly correlated), the variance, and thus standard deviation, will be less than if the correlation were 1. So the typical interpretation is that combining assets with less than perfect correlation lowers portfolio risk, but has no impact on expected return.

So if we combine assets x and y into portfolio 1, and combine assets w and z into portfolio 2 with the same weights, and if E(x) = E(w) and E(y) = E(z), but the correlation of w and z is less than the correlation of x and y, then the expected returns will be the same, E(1) = E(2), but the standard deviation of portfolio 2 will be lower, SD(2) < SD(1), so portfolio 2 is considered more efficient.

Assuming constant expected returns, variances and covariances, rebalancing at the end of the holding period simply resets the portfolio weights to the original values for the next holding period.

Of course all of this is dealing with expected values, not realized values, and expected values are not directly observable, so all of this is guesstimating anyway.

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

AllYouNeedIsLove
Posts: 66
Joined: Sat Feb 14, 2015 4:30 pm

Re: The Detriments of Rebalancing

Post by AllYouNeedIsLove » Fri Apr 03, 2015 8:53 pm

ogd wrote:
AllYouNeedIsLove wrote:Before posting I tried to do my own analysis. I began by looking for an empirical result by analyzing the past performance of the Life Strategy Target fund (rebalanced cohort) and the returns of Total Stock and Total Bond (non-rebalanced cohort). I gave up on this exercise due to the trap of making a generalized conclusion on limited past data. Life Strategy only goes back to 1994 and markets in the past 20 years have been unique in certain regards.
The usual caveat: LifeStrategy was a bad fund before 2011, because it included a market-timing fund which (like seems to be the norm) excelled at bad timing. See http://www.reuters.com/article/2011/09/ ... GC20110930 .

This is unfortunate, and it's unfortunate that Vanguard continues to make little tweaks such as recently with higher % of international. The LifeStrategy funds can't be used for longer-term 3-fund portfolio benchmarks. The best for your comparison above would be the simple, boring, domestic balanced fund VBIAX.
Thanks ogd. I was unaware of the LifeStrategy composition prior to 2011.

-AllYouNeedIsLove
I don't care too much for money, money can't buy me love

AllYouNeedIsLove
Posts: 66
Joined: Sat Feb 14, 2015 4:30 pm

Re: The Detriments of Rebalancing

Post by AllYouNeedIsLove » Fri Apr 03, 2015 9:03 pm

Kevin M wrote:
evarrr wrote:Whether or not higher return is achieved through rebalancing depends on the correlation between asset classes (low correlation = higher expected return when rebalancing).
We would like this to be true, and intuitively it seems that it should be, but according to portfolio theory math, I don't think it's true. The expected return of a portfolio is simply the weighted sum of the expected returns of the components, and has nothing to do with the expected correlations.

Portfolio math shows that for any two assets with a correlation of less than 1 (perfectly correlated), the variance, and thus standard deviation, will be less than if the correlation were 1. So the typical interpretation is that combining assets with less than perfect correlation lowers portfolio risk, but has no impact on expected return.

So if we combine assets x and y into portfolio 1, and combine assets w and z into portfolio 2 with the same weights, and if E(x) = E(w) and E(y) = E(z), but the correlation of w and z is less than the correlation of x and y, then the expected returns will be the same, E(1) = E(2), but the standard deviation of portfolio 2 will be lower, SD(2) < SD(1), so portfolio 2 is considered more efficient.

Assuming constant expected returns, variances and covariances, rebalancing at the end of the holding period simply resets the portfolio weights to the original values for the next holding period.

Of course all of this is dealing with expected values, not realized values, and expected values are not directly observable, so all of this is guesstimating anyway.

Kevin
Kevin,

I appreciate your knowledge, expertise, and detailed mathematical treatment of these issues. I understand that "expected returns" are guesstimates. However, I do feel that educated guesstimates are an important tool in my planning. I am going to continue this analysis and deal with the imprecision through confidence intervals and attention to significant figures rules.

Thanks for your replies.

-AllYouNeedIsLove
I don't care too much for money, money can't buy me love

AllYouNeedIsLove
Posts: 66
Joined: Sat Feb 14, 2015 4:30 pm

Re: The Detriments of Rebalancing

Post by AllYouNeedIsLove » Fri Apr 03, 2015 9:20 pm

Kevin M wrote:
evarrr wrote:Whether or not higher return is achieved through rebalancing depends on the correlation between asset classes (low correlation = higher expected return when rebalancing).
We would like this to be true, and intuitively it seems that it should be, but according to portfolio theory math, I don't think it's true. The expected return of a portfolio is simply the weighted sum of the expected returns of the components, and has nothing to do with the expected correlations.

Portfolio math shows that for any two assets with a correlation of less than 1 (perfectly correlated), the variance, and thus standard deviation, will be less than if the correlation were 1. So the typical interpretation is that combining assets with less than perfect correlation lowers portfolio risk, but has no impact on expected return.

So if we combine assets x and y into portfolio 1, and combine assets w and z into portfolio 2 with the same weights, and if E(x) = E(w) and E(y) = E(z), but the correlation of w and z is less than the correlation of x and y, then the expected returns will be the same, E(1) = E(2), but the standard deviation of portfolio 2 will be lower, SD(2) < SD(1), so portfolio 2 is considered more efficient.

Assuming constant expected returns, variances and covariances, rebalancing at the end of the holding period simply resets the portfolio weights to the original values for the next holding period.

Of course all of this is dealing with expected values, not realized values, and expected values are not directly observable, so all of this is guesstimating anyway.

Kevin
Kevin,

I believe your treatment above deals with the expected return and risk of a portfolio as a function of the correlation of its two components. However, I believe evarrr's assertion is about the effect of rebalancing on the expected return as a function of the correlation of the two components.

I believe there is a difference there.

I am particularly interested in the effect of rebalancing on expected return. I realize there exists a lot of literature and sophisticated analysis on this topic. I was hoping to simplify things a little bit by getting input from the forum on a specific case: a specific time frame, a specific AA, a specific spend down methodology, and application of Rick Ferri's expected return guesstimates.

-AllYouNeedIsLove
I don't care too much for money, money can't buy me love

User avatar
Kevin M
Posts: 10304
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: The Detriments of Rebalancing

Post by Kevin M » Fri Apr 03, 2015 10:32 pm

AllYouNeedIsLove wrote: I am particularly interested in the effect of rebalancing on expected return. I realize there exists a lot of literature and sophisticated analysis on this topic. I was hoping to simplify things a little bit by getting input from the forum on a specific case: a specific time frame, a specific AA, a specific spend down methodology, and application of Rick Ferri's expected return guesstimates.
I think you'll find that the most common view is that rebalancing is to manage risk, not to enhance expected return. As I think we've shown, you generally get the highest expected return by holding the asset with the highest expected return. Holding assets with correlation of less than 1 improves efficiency (e.g., Sharpe ratio; i.e., ratio of expected return minus risk-free rate to standard deviation), but unless you're going to leverage what you believe to be a more efficient portfolio, you achieve higher expected return by simply holding the asset with higher expected return.

As I said, rebalancing simply resets the portfolio weights to the original values; it does not change the expected return of the portfolio according to standard portfolio theory, but resets it to the initial value (again, assuming constant risk premiums, constant expected values, etc.).

Empirical evidence may show higher realized returns from certain rebalanced portfolios, but that is different than the portfolio theory math. You may find this article interesting: The Rebalancing Bonus. It challenges the standard portfolio math of Markowitz.

I think some of us hope for a rebalancing bonus (I know I do), but don't count on it.

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

pascalwager
Posts: 1278
Joined: Mon Oct 31, 2011 8:36 pm

Re: The Detriments of Rebalancing

Post by pascalwager » Sat Apr 04, 2015 1:15 am

If you don't rebalance, how do you maintain the asset allocation required in your Investment Policy Statement?

heartandsoul
Posts: 82
Joined: Sat Jan 24, 2015 4:21 am

Re: The Detriments of Rebalancing

Post by heartandsoul » Sat Apr 04, 2015 2:11 am

Kevin M wrote: I think you'll find that the most common view is that rebalancing is to manage risk, not to enhance expected return.......
I think some of us hope for a rebalancing bonus (I know I do), but don't count on it.

Kevin
You will get your rebalancing bonus, also known as volatility capture, for as long as there is mean reversion and roughly parallel performance between asset classes. If there is a prolonged period of divergence between the assets then risk is increased. This increased risk is hard to understand or appreciate after the approximate performance equality between bonds and stocks that we have had for the last 40+ years.
'Life is a strange thing. Just when you think you learned how to use it. It's gone' SS

magneto
Posts: 962
Joined: Sun Dec 19, 2010 10:57 am
Location: On Chesil Beach

Re: The Detriments of Rebalancing

Post by magneto » Sat Apr 04, 2015 5:43 am

Firstly as stated frequently above, rebalancing is primarily about risk control, but if we move on to the rebalancing bonus or detriment :-

Some funds using daily rebalancing rang alarm bells recently, so ran a spreadsheet on basis of 60/40 portfolio and stocks falling 50% (=% daily) over 12 months, then comparing daily rebalancing versus annual rebalancing, with bonds assumed stable. If spreadsheet correct (yet to be re-checked); daily rebalancing frittered circa 6%, versus annual rebalancing.
Is that enough to be of concern?
We don't see 50% stock declines that frequently, but those who worry about 0.01% fund fees might take note.
On the hypothetical return journey of a rising stock market over the subsequent 12 months, without any benefit from a delayed rebalancing bonus, a further underperformance of circa 6% is observed.
So on our two year hypothetical round trip, our investor seems to have frittered away a total of circa 12% by daily rebalancing?
All this assumes the most unlikely circumstance of annual rebalancing dates falling propitiously.

Looking at the issue from another angle, the investor would maximise the rebalancing bonus, by say buying stocks at troughs and selling stocks at peaks. But we don’t know in advance when these will occur. A daily rebalancing fund would outperform with a stock ripple wavelength of two days, assuming in sync at half wavelength (1 day), and assuming a generally sideways moving market. As soon as we introduce steadily rising or falling markets, then the wavelengths of those trends will dominate. So then for the chartists who see repeating cycles, the Four-Year or 42 month Kitchin Business Cycle, would suggest rebalancing every two years or 21 months. That would not have worked well recently!
'There is a tide in the affairs of men ...', Brutus (Market Timer)

AllYouNeedIsLove
Posts: 66
Joined: Sat Feb 14, 2015 4:30 pm

Re: The Detriments of Rebalancing

Post by AllYouNeedIsLove » Sat Apr 04, 2015 8:28 am

Kevin M wrote:I think you'll find that the most common view is that rebalancing is to manage risk, not to enhance expected return. As I think we've shown, you generally get the highest expected return by holding the asset with the highest expected return. Holding assets with correlation of less than 1 improves efficiency (e.g., Sharpe ratio; i.e., ratio of expected return minus risk-free rate to standard deviation), but unless you're going to leverage what you believe to be a more efficient portfolio, you achieve higher expected return by simply holding the asset with higher expected return.

As I said, rebalancing simply resets the portfolio weights to the original values; it does not change the expected return of the portfolio according to standard portfolio theory, but resets it to the initial value (again, assuming constant risk premiums, constant expected values, etc.).

Empirical evidence may show higher realized returns from certain rebalanced portfolios, but that is different than the portfolio theory math. You may find this article interesting: The Rebalancing Bonus. It challenges the standard portfolio math of Markowitz.

I think some of us hope for a rebalancing bonus (I know I do), but don't count on it.

Kevin
Kevin,

I've always been impressed when reading your posts. I think you have gotten down to the essence (as usual). Thank you very much for the link. I will read it today.

-AllYouNeedIsLove
I don't care too much for money, money can't buy me love

AllYouNeedIsLove
Posts: 66
Joined: Sat Feb 14, 2015 4:30 pm

Re: The Detriments of Rebalancing

Post by AllYouNeedIsLove » Sat Apr 04, 2015 8:30 am

pascalwager wrote:If you don't rebalance, how do you maintain the asset allocation required in your Investment Policy Statement?
To my knowledge there are many experts who believe in allowing the AA to drift with the course of the markets. I am sure there are some with this strategy specified in their IPS.
I don't care too much for money, money can't buy me love

AllYouNeedIsLove
Posts: 66
Joined: Sat Feb 14, 2015 4:30 pm

Re: The Detriments of Rebalancing

Post by AllYouNeedIsLove » Sat Apr 04, 2015 8:40 am

magneto wrote:Firstly as stated frequently above, rebalancing is primarily about risk control, but if we move on to the rebalancing bonus or detriment :-

Some funds using daily rebalancing rang alarm bells recently, so ran a spreadsheet on basis of 60/40 portfolio and stocks falling 50% (=% daily) over 12 months, then comparing daily rebalancing versus annual rebalancing, with bonds assumed stable. If spreadsheet correct (yet to be re-checked); daily rebalancing frittered circa 6%, versus annual rebalancing.
Is that enough to be of concern?
We don't see 50% stock declines that frequently, but those who worry about 0.01% fund fees might take note.
On the hypothetical return journey of a rising stock market over the subsequent 12 months, without any benefit from a delayed rebalancing bonus, a further underperformance of circa 6% is observed.
So on our two year hypothetical round trip, our investor seems to have frittered away a total of circa 12% by daily rebalancing?
All this assumes the most unlikely circumstance of annual rebalancing dates falling propitiously.

Looking at the issue from another angle, the investor would maximise the rebalancing bonus, by say buying stocks at troughs and selling stocks at peaks. But we don’t know in advance when these will occur. A daily rebalancing fund would outperform with a stock ripple wavelength of two days, assuming in sync at half wavelength (1 day), and assuming a generally sideways moving market. As soon as we introduce steadily rising or falling markets, then the wavelengths of those trends will dominate. So then for the chartists who see repeating cycles, the Four-Year or 42 month Kitchin Business Cycle, would suggest rebalancing every two years or 21 months. That would not have worked well recently!
Magneto,

Thank you very much for your post. This is EXACTLY the kind of analysis I was looking for. I am essentially trying to get a handle on the "delta" of different approaches to rebalancing. I realize that your post is about one particular scenario but nonetheless it is very enlightening for me. Are funds such as LifeStrategy essentially balanced on a daily basis? I think your analysis is very relevant and I appreciate it very much.

I am trying to gather analyses like yours, make some guesstimates about expected returns, about relative returns, about likely worst case scenarios, and put some bounds on the issue. I would like to repeat that I am not expecting anything. I am just trying to essentially stress test my portfolio with and without a rebalancing strategy.

You and Kevin M have really shed some light in the last couple of posts. Thanks.

-AllYouNeedIsLove
I don't care too much for money, money can't buy me love

IlliniDave
Posts: 2294
Joined: Fri May 17, 2013 7:09 am

Re: The Detriments of Rebalancing

Post by IlliniDave » Sat Apr 04, 2015 10:00 am

The way I see it, which has already been said, is that rebalancing is primarily about managing the variance/volatility of a portfolio. Most of the time I'm a passive, hesitant rebalancer, and just make new purchases in whichever asset class is falling behind. You can construct situations where getting a wonderfully uncorrelated mix of assets with similar potential for long term growth and some luck/prescient timing thrown in where there will be an advantage in long term returns for rebalancing, but I think it's pretty unlikely. When you're working with two asset classes like stocks and bonds with generally different long-term growth potential, your overall return will almost always fall in between and be lower than the highest performing asset. That's true with any diversification strategy.
Don't do something. Just stand there!

pascalwager
Posts: 1278
Joined: Mon Oct 31, 2011 8:36 pm

Re: The Detriments of Rebalancing

Post by pascalwager » Sat Apr 04, 2015 11:40 am

Postby AllYouNeedIsLove » Sat Apr 04, 2015 8:30 am

To my knowledge there are many experts who believe in allowing the AA to drift with the course of the markets. I am sure there are some with this strategy specified in their IPS.
I can't recall any passive-investing-type authors who recommend letting your AA drift. Any references? That would seem to mean that they don't advocate using fixed-income for risk control, or maybe don't even use fixed-income at all.

If an IPS allows for a drifting AA, then it should also include a clear statement indicating that the market shall be allowed to determine the risk level of the portfolio.

User avatar
Maynard F. Speer
Posts: 2139
Joined: Wed Mar 18, 2015 10:31 am

Re: The Detriments of Rebalancing

Post by Maynard F. Speer » Sat Apr 04, 2015 12:13 pm

I see rebalancing as a way of ameliorating market timing issues .. Portfolios designed with efficient frontiers models (such as Yale's) - where your target allocations are based on correlation, risk and expected returns - are very appealing for me, in that they can provide the best of both worlds: equity-like returns with bond-like stability

Simple example of rebalancing between two non-correlated asset classes (gold and US equities) returning more than either in isolation - (but most importantly with much improved volatility):

Image
"Economics is a method rather than a doctrine, an apparatus of the mind, a technique of thinking, which helps its possessor to draw correct conclusions." - John Maynard Keynes

Post Reply