Can't Prune a Target Fund

[rmark]

Efficientfrontier.com from 1996

ABSTRACT
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."

[Rich_by_the_Bay]

Quote:

Originally Posted by rmark Efficientfrontier.com from 1996

Nice find, rmark. Here's the full link.

Bernstein thinks the rebalancing bonus is real. I am not equipped to critique it technically.

[wabmester]

Quote:

Originally Posted by rmark 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."

Gummy's paper references Bernstein's paper and makes clear the distinction between getting an actual return bonus and getting a bonus vs the weighted sum of the component expected returns. It's a subtle difference, but one of them puts money in your pocket, and the other one (Bernstein's) doesn't necessarily.

[justin]

weighted sum of the component expected returns -

The fact that rebalancing allows one to beat the weighted sum of the component expected returns is significant. Let's say you have a portfolio consisting of a mix of US and intl stock index funds, and a short term bond fund. Further assume that these three asset classes are loosely correlated (r^2 of 0.6 or so). The weighted sum of the component expected returns might be 8%, but with annual rebalancing, you might expect your return to be 8.2% or so. That 0.2% is your rebalancing bonus (alpha). A little more return for the same amount of risk.

[wabmester]

Quote:

Originally Posted by justin The fact that rebalancing allows one to beat the weighted sum of the component expected returns is significant.*

I may need to reread Gummy's articles again, but I believe he is basically making two points:

1) The weighted sum of annualized returns is not the same as the annualized return of a mixed portfolio.

2) The expected bonus is dependent upon the covariance being fixed (and of course, it changes all the time).

I'd be thrilled to learn that I'm wrong about this.* *But basically, Bernstein is not comparing rebalancing with buy-and-hold.

[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.................2 5.13%

[Rich_by_the_Bay]

Quote:

Originally Posted by sgeeeee 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/i...sg8573#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... :P

[sgeeeee]

Quote:

Originally Posted by Rich_in_Tampa 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]

Quote:

Originally Posted by sgeeeee 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]

Quote:

Originally Posted by Rich_in_Tampa 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]

Quote:

Originally Posted by 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?

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]

Quote:

Originally Posted by Rich_in_Tampa 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]

Quote:

Originally Posted by 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.*

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]

Quote:

Originally Posted by sgeeeee 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]

Quote:

Originally Posted by justin 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]

Quote:

Originally Posted by wab 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.