Can't Prune a Target Fund

[sgeeeee]

The rebalance premium is discussed in the financial literature.  Mathematical derivations for the functional description of the premium have been published.  Qualitatively, the argument is made that rebalancing is inherently a “buy low, sell high” strategy.  You are a net buyer when an asset has underperformed and a net seller when a market outperforms.  History tells a different story.  You can analyze this for yourself using FIRECalc.  Make three runs: 1) $500,000 entirely in bonds for 30 years, 2) $500,000 entirely in equities for 30 years, 3) $1,000,000 in a 50/50 portfolio for 30 years.  Look at the detailed results for all three cases.  Add the results from 1) and 2) to look at the case without rebalancing.  Compare to case 3) for annual rebalancing.  Historically, the unbalanced portfolio would have achieved greater returns than the balanced portfolio in 60% of the 102 different 30 year sequences.  The average terminal value achieved by the unbalanced portfolio is more than 10% higher than that achieved using a rebalancing scheme.  Rebalancing does not generally provide a return premium, but it does reduce volatility and risk.  The standard deviation in the terminal values of the 102 thirty year sequences is reduced by more than 25% using rebalancing.  At the end of the 30 year sequences, the average unbalanced portfolio is comprised of more than 78% stock – significantly more risky than the 50% stock allocation of the balanced portfolio.
Results of historical simulations of a 30 year investment.  In one case equal amounts are placed into an S&P500 fund and in a short-term treasury fund, and then left untouched for 30 years.  In the second case, the identical initial investments are made, but the portfolio is rebalanced to achieve a 50/50 allocation at the end of each year.  The average terminal value and standard deviation are given in multiples of the original investment.

.......................................................Unbalanced ...Annually.........Rebalance
........................................................Portfolio .......Rebalanced.....Premium
Average terminal value after 30 yrs.........9.57............8.45...............-10.10%
Standard Deviation of terminal value.......5.11............3.83.................25.13%

 

[Rich_by_the_Bay]

The rebalance premium is discussed in the financial literature

Can't vouch for the validity of your analysis, but you appear to be leaving all the money in the nest egg under your rebalancing scenario. The money lives to fight another day in the asset class to which it was reassigned for rebalancing purposes.

I am not sure that this is the same during the post-FIRE scenario: you rebalance by removing the funds altogether to meet your expenses. Those gains have declared themselves as relative "winners" at the time you withdraw them; not day to day, but net for that year (or whatever period you choose).

I emailed Gummy in the hopes he would take a look at this, but so far no reply.

 

[cute fuzzy bunny]

Gummy said he was 'retiring' from this board a couple of years ago. I saw that he still regularly posts on other boards and recently commented about not caring much for this board since someone told a couple of canadian jokes in his presence and he didnt think it was humorous.

So your email may not get replied to...

He still posts on the financialwebring web site, so maybe if you ask your question there and dont bring up anything about hockey players, you'll get an answer.

For the morbidly curious, this is the thread:

http://early-retirement.org/forums/index.php?topic=667.msg8573#msg8573

Apparently in some cases intelligence comes with a pretty thin skin.

Back to the topic at hand...

Seems to me there might be something interesting in looking at 3 or 5 year rebalancing instead of 1-2 year. Bull markets seem to run a lot longer than a year, so rebalancing will most certainly curtail some of your returns while giving you the longer term volatility reduction. But the volatility reduction in these cases works both ways.

Taking a little longer to get to the rebalancing might produce lower volatility AND a comparable or better return. Hitting the cycle wrong would screw you up though.

HEY! This is market timing!

Imagine doing a 4-5 year rebalance and moving some money into equities in 1995 and then slushing your huge equity gains back into bonds in 1999, then all that bond money back into stocks in 2003. Pretty good stuff.

Now pick a less optimum window...

 

[sgeeeee]

Can't vouch for the validity of your analysis . . .

Nor can you vouch for Bernstein's or Gummy's. But you can do the analysis yourself, and you can include regular withdrawals or leave them out. You can change the asset allocation and look at various bond types.

The historical record is what it is. The case I provided is not the only simulation I've run. So far, they've all shown the same thing. Rebalancing does not guarantee improved performance and, in fact, would have resulted in lower returns more often than it resulted in higher. I've only looked at cases I could examine using the historical record (ie. S&P 500/bond allocations). I have not examined a vast number of stock/bond ratios, etc. There may be asset allocations that make rebalancing more attractive than the range I've looked at.

In order to develop an analytical expression for the "rebalance premium", the derivations I've seen make a lot of assumptions that do not really hold up. You end up with an expression that illustrates how rebalancing could provide a premium, but not an expression that describes the historical reality.

 

[Rich_by_the_Bay]

Nor can you vouch for Bernstein's or Gummy's. But you can do the analysis yourself...

True - I wasn't trying to discount your analysis, just admitting that I wasn't savvy enough to validate it for myself .

If you saved a link to any of your analyses in FIRECALC (or get a chance to do so), I'd enjoy taking a look at it (in the results tab, "Link for recreating this scenario" checkbox). Thanks.

 

[sgeeeee]

True - I wasn't trying to discount your analysis, just admitting that I wasn't savvy enough to validate it for myself  .

If you saved a link to any of your analyses in FIRECALC (or get a chance to do so), I'd enjoy taking a look at it (in the results tab, "Link for recreating this scenario" checkbox). Thanks.

Rich,

Unfortunately, the FIRECALC simulations are just the starting point for this analysis. You have to cut and paste the detailed results from the simulations into a spreadsheet and then program the columns to do your dirty work. You start with 3 columns of 102 rows of numbers (corresponding to an all bond portfolio, an all stock portfolio and a 50/50 portfolio) Then, you create some addition and subtraction columns, a column of comparison and finally some statistical analysis of two of the columns.

Posting spreadsheets in the forum is kind of awkward. I do have an excel workbook that includes all the data and analysis mentioned in my first post in a form that is documented well enough that someone familiar with this kind of analysis could probably follow. I would be happy to share that if you have some way for me to send you the worksheet. Additional analysis workbooks I have that examined withdrawals and other stock/bond ratios would be difficult to decifer if you weren't the person who did the work.

 

[setab]

This may show my ignorance, but I thought one of the reasons to have a Target fund was so you didn't have to think that hard about rebalancing, etc. So, why would you want to prune it?

setab

 

[Rich_by_the_Bay]

This may show my ignorance, but I thought one of the reasons to have a Target fund was so you didn't have to think that hard about rebalancing, etc. So, why would you want to prune it?

That's really the point. Pruning implies that when you sell holdings to meet expenses, you sell off the asset class(es) that have done well over the past year, and rebalance mostly by selling the winners (then tweaking what you have left). So for simplicity if an intended 50:50 stock to bond portfolio after a year moved to 45:55, you would sell some bonds to get back to 50:50.

With a target fund, you can only withdraw stocks and bonds in whatever proportion the fund is mapped to. You can't "prune" a target fund, you can only withdraw from all "branches" in a fixed proportion. Hope that helps.

 

[ats5g]

That's really the point. Pruning implies that when you sell holdings to meet expenses, you sell off the asset class(es) that have done well over the past year, and rebalance mostly by selling the winners (then tweaking what you have left). So for simplicity if an intended 50:50 stock to bond portfolio after a year moved to 45:55, you would sell some bonds to get back to 50:50.

With a target fund, you can only withdraw stocks and bonds in whatever proportion the fund is mapped to. You can't "prune" a target fund, you can only withdraw from all "branches" in a fixed proportion. Hope that helps.

Hey Rich,

The target fund is constantly pruning for you [as I alluded to here].

So, with the balanced/target funds, you're still "pruning the winners" in your withdrawal.

- Alec

 

[justin]

Here's a brief analysis I did after seeing SG's summary of his analysis:

I started with $1,000,000 and used the advanced firecalc so that I could use the 8 asset classes under the "How is it invested?" tab. I chose an all stock portfolio consisting of 20% each of the five available stock asset classes:
microcap
small
small cap value
SP500
Large cap value

With annual rebalancing, the average terminal portfolio value after 30 years is $20,167,569. When each of the five asset classes are purchased initially and allowed to grow for 30 years with NO rebalancing, the average terminal portfolio value is $21,397,815. Great, I just proved what SG was saying before: rebalancing results in a lower terminal portfolio value, therefore there is no rebalancing bonus.

That is true. However, the non-rebalanced portfolio only had 6% greater returns in exchange for a much riskier unbalanced portfolio. By the end of the 30 year period, the portfolio looked like this:
24.0% microcap
16.0% small
35.0% small cap value
8.0% SP500
17.0% Large cap value

The higher-return (but higher risk?) microcap and small cap value asset classes comprise 59% of the average terminal portfolio, instead of 40% at the portfolio starting point. That is a significant amount of additional risk only to obtain a cumulative 6% performance boost after 30 years.

 

[sgeeeee]

Here's a brief analysis I did after seeing SG's summary of his analysis:

I started with $1,000,000 and used the advanced firecalc so that I could use the 8 asset classes under the "How is it invested?" tab.  I chose an all stock portfolio consisting of 20% each of the five available stock asset classes:
microcap
small
small cap value
SP500
Large cap value

With annual rebalancing, the average terminal portfolio value after 30 years is $20,167,569.  When each of the five asset classes are purchased initially and allowed to grow for 30 years with NO rebalancing, the average terminal portfolio value is $21,397,815.  Great, I just proved what SG was saying before: rebalancing results in a lower terminal portfolio value, therefore there is no rebalancing bonus.

That is true.  However, the non-rebalanced portfolio only had 6% greater returns in exchange for a much riskier unbalanced portfolio.  By the end of the 30 year period, the portfolio looked like this:
24.0% microcap
16.0% small
35.0% small cap value
8.0% SP500
17.0% Large cap value

The higher-return (but higher risk?) microcap and small cap value asset classes comprise 59% of the average terminal portfolio, instead of 40% at the portfolio starting point.  That is a significant amount of additional risk only to obtain a cumulative 6% performance boost after 30 years. 

Very interesting. I appreciate your efforts. I ran a series of rebalancing studies several months ago before FIRECALC provided these other asset classes. No matter how I looked at it, rebalancing did not generally provide a premium, but it did provide risk reduction. I've wanted to go back and do the more detailed study to see if the results were the same for more asset classes. But fortunately, my lazy retirement attitude has allowed me to put it off until someone else did the work for me.

Thanks, Justin.

 

[justin]

Very interesting. I appreciate your efforts. I ran a series of rebalancing studies several months ago before FIRECALC provided these other asset classes. No matter how I looked at it, rebalancing did not generally provide a premium, but it did provide risk reduction. I've wanted to go back and do the more detailed study to see if the results were the same for more asset classes. But fortunately, my lazy retirement attitude has allowed me to put it off until someone else did the work for me.

Thanks, Justin.

My little mini-research efforts confirmed what I had suspected before - rebalancing will significantly reduce volatility while marginally reducing expected returns.

For my personal portfolio, I have decided to get a little riskier with the individual asset classes (lots of "smalls" and "values" of some sort or another, and a big chunk of emerging markets). Hopefully portfolio theory will make me rich in a low-volatility way.

A number of the asset classes, considered separately, are pretty high on the risk scale. However when the (hopefully uncorrelated) assets are rebalanced annually, the overall portfolio volatility will be less than the sum of the volatility of the parts.

 

[wabmester]

My little mini-research efforts confirmed what I had suspected before - rebalancing will significantly reduce volatility while marginally reducing expected returns.

You mean to tell me that you never believed in the mythical rebalancing bonus?

To me, the results you and SG are seeing are intuitively obvious.   The long-term returns will be dominated by the asset classes with the highest expected returns if you buy and hold.

To be fair to Bernstein, he does recognize this.  And he recognizes that the weighted sum of expected returns is a bogus metric.

What he really says is that if you have multiple asset classes that all have high expected returns, high volatility, and low correlation, then you should see a genuine return bonus from rebalancing.   I think.

 

[cute fuzzy bunny]

So going back to what I mentioned earlier...perhaps what you want to do is balance every 3 years, maybe 5. Then you might not dampen the returns as much but you will reduce these runaway out of whack distributions.

Maybe the best of both worlds?

 

[sgeeeee]

You mean to tell me that you never believed in the mythical rebalancing bonus?

To me, the results you and SG are seeing are intuitively obvious.   The long-term returns will be dominated by the asset classes with the highest expected returns if you buy and hold.

To be fair to Bernstein, he does recognize this.  And he recognizes that the weighted sum of expected returns is a bogus metric.

What he really says is that if you have multiple asset classes that all have high expected returns, high volatility, and low correlation, then you should see a genuine return bonus from rebalancing.   I think.

While I agree about the intuitively obvious part, I did not think that Bernstein sounded like he recognized that "rebalancing bonus" was bogus. See for example:

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

“The actual return of a rebalanced portfolio usually exceeds the expected return calculated from the weighted sum of the component expected returns. A formula for estimating this excess return is derived and tested. It is demonstrated that assets with high volatility and low correlation with the remainder of the portfolio provide considerable excess return, or "rebalancing bonus."

He also addresses rebalance timing in the above cited paper. His conclusion: no single rebalance timing strategy is best for all periods. Bernstein only considers monthly, quarterly and annual rebalancing periods. I have seen other literature that indicated that less frequent rebalancing is better (every 2 or 3 years as opposed to annual). Unfortunately, I can't put my fingers on that reference at the moment.

A short time after Bernstein published the report cited above, he published this one:

http://www.efficientfrontier.com/ef/197/rebal197.htm
"When Doesn't It Pay to Rebalance?"

So maybe Bernstein does really understand that the rebalance bonus is bogus, but by the time I read the second paper I had already run a check using historical data. I wanted to confirm what seemed obvious to me.

 

[wabmester]

While I agree about the intuitively obvious part, I did not think that Bernstein sounded like he recognized that "rebalancing bonus" was bogus.  See for example:

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

In this paper, Bernstein says:

Markowitz1 considers the return of a portfolio to be equal to the weighted sums of the individual component returns, but this formulation is valid only for nonrebalanced portfolios over single periods.

This tells me that he understands that weighted sums of annualized returns aren't comparable to multi-year multi-component returns.

He also says:

... the 69 year period studied the significantly higher stock return overwhelms the bond return; for the last 40 years of the period the unrebalanced portfolio consists of greater than 90% stock

and

They suggest that convex portfolio insurance strategies as well as buy and hold ("flat") strategies produce superior returns in markets with a prolonged upward (or downward) bias, and concave rebalancing strategies produce superior returns in stagnant markets.

So, he understands why buy-and-hold usually will have higher returns for stock/bond mixes.

But then he goes on to say:

The above theoretical model and backtested portfolios suggest that significant excess return is available from combinations of asset pairs which have both low correlation and high risk.

Both he and Gummy go on to estimate what this bonus is for high-variance assets with similar returns but low correlation, which seems to be the only time you get the bonus.

Neither the SG study nor the justin study addresses this directly. 

 

[sgeeeee]

. . .

Neither the SG study nor the justin study addresses this directly. 

The study doesn't address a lot of things directly. It wasn't intended to. The data shows that there are periods when rebalancing paid off (about 40% of the time in my study). Since you can't predict the correlation of assets in the future, knowing what the correlation coeficient needs to be to gain a rebalance bonus is hardly helpful.

You could address this issue by looking at the correlation coeficients of the individual sequences, ordering them and looking at how those results correlate to a rebalance bonus. But that seems rather pointless. I would be happy to send you my spreadsheets if you are interested in the mental masterbation, however.

 

[wabmester]

Since you can't predict the correlation of assets in the future, knowing what the correlation coeficient needs to be to gain a rebalance bonus is hardly helpful. 

I'm not sure we're talking about the same thing here.   I've already stated that the rebalancing bonus is obviously bogus due to a variety of factors, including covariance drift.   Your study shows this to be true for portfolios comprised of S&P 500 stocks and bonds.   Bernstein himself tells you why there is no bonus for this case.

So, the question remains: are there cases in which you are much more likely to get a rebalancing bonus?

Bernstein says, "the intrinsic rebalancing potential of any asset pair is the difference between its mean variance and covariance."

In other words, you're most likely to see the bonus with highly volatile assets with low correlation.

Are you saying that your S&P 500 / bond mix is a good test case for his assertion?

 

[sgeeeee]

. . .
Are you saying that your S&P 500 / bond mix is a good test case for his assertion?

You are so tedious sometimes, wab. What I'm saying is that over different periods of time, the S&P 500 and bond returns would exhibit unique (higher or lower) volatility and correlation properties. Since the rebalance strategy paid a bonus 40% of the time, you could order the 102 simulated sequences by volatility or correlation and examine the corrleation between these properties and the existence of a bonus.

My guess is that you wouldn't because other factors would dominate. And that points to the reason I would refer to Bernstein's derivation as mental masterbation.

But you knew all this, wab. Didn't you?

 

[bpp]

While I agree about the intuitively obvious part, I did not think that Bernstein sounded like he recognized that "rebalancing bonus" was bogus. See for example:

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

[...]

A short time after Bernstein published the report cited above, he published this one:

http://www.efficientfrontier.com/ef/197/rebal197.htm
"When Doesn't It Pay to Rebalance?"

So maybe Bernstein does really understand that the rebalance bonus is bogus, but by the time I read the second paper I had already run a check using historical data. I wanted to confirm what seemed obvious to me.

He admitted that the first article was a mistake over on Diehards a few months ago: http://socialize.morningstar.com/Ne...0000015&convId=167631&minReplySeq=61#replyTop

 

[sgeeeee]

He admitted that the first article was a mistake over on Diehards a few months ago:  http://socialize.morningstar.com/Ne...0000015&convId=167631&minReplySeq=61#replyTop

Thanks, bpp. My impression was that he figured out his first article was misleading and decided to provide a more practical answer in the second.

 

[wabmester]

Cool.  If I had seen that M* bit, it would have saved me from much head scratching.

So, in the end he admits that the bit about the sum of the weighted returns is bogus, but he says the results still hold for cases in which two assets have similar returns with high volatility and low correlation.

That makes more sense to me.   So, here's where I think that leaves the bonus:

It makes sense to rebalance between two asset classes if you know they have similar expected returns, high volatility, fairly fixed covariance, and you know the period of their covariance and can time the peaks and valleys.

In other words, not very often.

 

[sgeeeee]

. . . It makes sense to rebalance between two asset classes if you know they have similar expected returns, high volatility, fairly fixed covariance, and you know the period of their covariance and can time the peaks and valleys.

In other words, not very often.

Yeah.

The real reason to rebalance is to maintain risk at your personal comfort level. Which indicates that you should rebalance based on your allocation varying significantly from your target allocation levels -- not based on a schedule.

 

[Rich_by_the_Bay]

Yeah.

The real reason to rebalance is to maintain risk at your personal comfort level. Which indicates that you should rebalance based on your allocation varying significantly from your target allocation levels -- not based on a schedule.

I'm convinced. Makes blended/target/strategic funds a bit more appealing to me.

 

[justin]

It makes sense to rebalance between two asset classes if you know they have similar expected returns, high volatility, fairly fixed covariance, and you know the period of their covariance and can time the peaks and valleys.

I'm just guessing when I invest. A few components of my portfolio are what I would call "risky" (ie high volatility) with expected returns greater than the S&P 500. However, I don't really know what the returns, volatility or covariance will be in 20 or 30 years. As a result, a large portion of my portfolio is in less volatile investments. I'm primarily afraid of the "fat tails" scenario where almost everything is down (with the risky stuff seeing MAJOR losses). It will happen more than the normal distribution would suggest. Hopefully periodic rebalancing will allow me to capture some upside from riskier asset classes and will allow me to limit my downside.

In other words, I want to limit my overall portfolio volatility while capturing a portion of the higher than average expected returns.