How 2 assets with negative returns and negative correlations can make money

[blackomen]

So the PP carries Stocks, LT Treasuries, ST Treasuries, and Gold?  And only Stocks produce real returns over the long run?  Then why does it generate a return that's competitive to the 100% Equities allocation?  And why does the 60/40 Stock/Bond portfolio also generate a similar long-term return as well?

I don't know if there's a simple term for this phenomenon.  I don't know what words to use to define it.  But I can do the following: 1) Give you the circumstances when it occurs and 2) Give an example of it happening.

So here's when it occurs:

When you have 2 negatively correlated assets, holding those 2 assets in equal-weighted proportions and rebalancing them periodically will generally lead to higher returns than simply buying and holding them without rebalancing.

An example:

You have 2 assets that had these returns during these 5 years:

Asset 1: +15%, +15%, +15%, +15%, -50%.
Asset 2: -10%, -10%, -10%, -10%, +50%.

The gross compound return of Asset 1 is: (1.15^4)*(1-0.5) - 1 = -12.5%
The gross compound return of Asset 2 is: (0.9^4)*1.5 - 1 = -1.5%.

If you bought these 2 assets in equal weights and just held them without doing anything for 5 years, you would have made a -7% return.

But if you bought these 2 in equal weights and rebalanced them back to 50/50 every year, here's what your returns would look like:

2.5%, 2.5%, 2.5%, 2.5%, 0%

Your gross return is: 1.025^4 -1 = 10%.

Now I don't know if this phenomenon contributes significantly to the PP returns and even if it did, I wouldn't know how to measure it and communicate the results in a way that the average person can understand.  But I'm just pointing it out here.

[Cortopassi]

Buy Low Sell High, I think is the best layman's term.  Obviously without rebalancing, your overall is negative.  But every year you are selling some of that 15% winner to buy the 10% loser, and in that last year, you've bulked up the loser at a lower price and lightened the winner at a higher price, so when the reverse occurs, you are able to take advantage of it.

Everyone talks about buying low and selling high, but does it really happen unless you are in a PP or a managed fund who's purpose is to rebalance on a schedule?  I think mostly not.

For example, I owned DODGX for years.  Basically up every year, always beating SP500, until 2008.  Did I have a non correlated asset to go along with it?  No.  I simply kept on plowing more money into one fund, which I *thought* was diversified, just because it held a wide variety of stuff.  Well, I was wrong.  If I even had a basic 50/50 split with long term bonds, and rebalanced occasionally, I would have been so much better off.

Mike

[Kshartle]

Ahhhh.....the rebalance return bonus. This is perhaps my favorite investing myth.

Blackomen....first off you have a great handle, truly one of my favorites here.

Let's try with slightly different numbers:

You have 2 assets that had these returns during these 5 years:

Asset 1: +15%, +15%, +15%, +15%, +50%.
Asset 2: -10%, -10%, -10%, -10%, -50%.

The gross compound return of Asset 1 is: (1.15^4)*(1+0.5) - 1 = +162.4%
The gross compound return of Asset 2 is: (0.9^4)*(1-0.5) - 1 = -67.2%

If you bought these 2 assets in equal weights and just held them without doing anything for 5 years, you would have made a +47.6% return.

But if you bought these 2 in equal weights and rebalanced them back to 50/50 every year, here's what your returns would look like:

2.5%, 2.5%, 2.5%, 2.5%, 0%

Your gross return is: 1.025^4 -1 = 10%.

PLEASE check my math so I don't look more foolish than usual.

Your only choice is to rebalance or not to rebalance. For any given set of data it's either advantages to rebalance or not (from an absolute return perspective only). You cannot know ahead of time whether rebalancing will help or hurt returns over time.

but but but.......assets don't just go up year after year without a big crash wiping out the gains right? Ohhhhh I beg to differ......ST bonds had positive returns for 22 years from '72 - '93. Stocks had positive returns for 8 years from '82 - '90. LTBs had positive returns for 9 years from 2000 - '08 and Gold had positive returns for 12 years from 2001-'12.

You just can't know what will be best for returns. Rebalance to maintain acceptable diversification for risk purposes. That's the free lunch. There is no free lunch for returns that also reduces risk, sadly. If I find one I promise I'll let everyone know. 

[Kshartle]

PP of 10k started Jan 1, 1981 with NO rebalance is now 143k
PP of 10k started Jan 1, 1981 with annual rebalance is now 117k
PP of 10k started Jan 1, 1981 with 35/15 rebalance is now 133k
Stock only of 10k started Jan 1, 1981 is now 278k

Please double-check me, but that’s 33 years and the PP ain’t even close to stocks and not rebalancing has been better than either popular rebalance strategy (from a return perspective).

[Cortopassi]

Just wondering, can you cherry pick starting times, with no rebalancing that show stocks only doing significantly worse?  I bet you can.

And of course, don't forget, one of the selling points of a PP is the lowered volatility and drawdowns.  How hard would it have been for stock only holders to sit tight during the 1987, 2001 and 2008 timeframes?

Mike

[Kshartle]

Just wondering, can you cherry pick starting times, with no rebalancing that show stocks only doing significantly worse?  I bet you can.

And of course, don't forget, one of the selling points of a PP is the lowered volatility and drawdowns.  How hard would it have been for stock only holders to sit tight during the 1987, 2001 and 2008 timeframes?

Mike

Yes you can cherry pick any start and end times you want. That's my entire point. We can't trade the past, only the future, and there is no certainty that rebalancing going forward will return more than not. If you believe there is, then how can I cherry pick a 33 year period where it didn't work? My cherry picking proves at least over 33 years, that there is no return bonus for rebalancing. It either will work or it won't, but you have no way of knowing beforehand.

If rebalancing provides a bonus to returns.....how many more years do we have to wait for it? After it occurs it must also persist forever, otherwise it never really worked.

Regarding your second point.........that's why I said "Rebalance to maintain acceptable diversification for risk purposes. That's the free lunch."

[blackomen]

Just wondering, can you cherry pick starting times, with no rebalancing that show stocks only doing significantly worse?  I bet you can.

And of course, don't forget, one of the selling points of a PP is the lowered volatility and drawdowns.  How hard would it have been for stock only holders to sit tight during the 1987, 2001 and 2008 timeframes?

Mike

Yes you can cherry pick any start and end times you want. That's my entire point. We can't trade the past, only the future, and there is no certainty that rebalancing going forward will return more than not. If you believe there is, then how can I cherry pick a 33 year period where it didn't work? My cherry picking proves at least over 33 years, that there is no return bonus for rebalancing. It either will work or it won't, but you have no way of knowing beforehand.

If rebalancing provides a bonus to returns.....how many more years do we have to wait for it? After it occurs it must also persist forever, otherwise it never really worked.

Regarding your second point.........that's why I said "Rebalance to maintain acceptable diversification for risk purposes. That's the free lunch."

If disproving anything is as simple as cherrypicking a single period where something doesn't work, then we can disprove virtually anything.  A more meaningful approach to this is, given historical data, which has a higher probability of success, rebalancing or no rebalancing?

[Kshartle]

Just wondering, can you cherry pick starting times, with no rebalancing that show stocks only doing significantly worse?  I bet you can.

And of course, don't forget, one of the selling points of a PP is the lowered volatility and drawdowns.  How hard would it have been for stock only holders to sit tight during the 1987, 2001 and 2008 timeframes?

Mike

Yes you can cherry pick any start and end times you want. That's my entire point. We can't trade the past, only the future, and there is no certainty that rebalancing going forward will return more than not. If you believe there is, then how can I cherry pick a 33 year period where it didn't work? My cherry picking proves at least over 33 years, that there is no return bonus for rebalancing. It either will work or it won't, but you have no way of knowing beforehand.

If rebalancing provides a bonus to returns.....how many more years do we have to wait for it? After it occurs it must also persist forever, otherwise it never really worked.

Regarding your second point.........that's why I said "Rebalance to maintain acceptable diversification for risk purposes. That's the free lunch."

If disproving anything is as simple as cherrypicking a single period where something doesn't work, then we can disprove virtually anything.  A more meaningful approach to this is, given historical data, which has a higher probability of success, rebalancing or no rebalancing?

If it can be proven that rebalancing does not provide a return bonus (which it clearly does not for at least a period of 33.5 years or less)...........why would you think there's a higher probability of success with it? What rationale is there for such a belief? How can you determine the probability of such a thing? You literally have to estimate the length and strength of the trends of the four assets for as long as you intend to follow the strategy?

Good luck, that's impossible. You have no way to know or estimate if rebalancing will work over the next year, 5 years, ten years, 33.5 years etc.

That's why I'm just trying to point out.....don't rebalance because you think your returns will be better. Do it for the right reasons so you're not dissapointed when it costs you money. Do what's right for you but also in accordance with reality (of which a return bonus to rebalancing is not a part of).

I suppose you first have to agree that the past 33.5 years of data proves there is no return bonus for rebalancing.

It's not like I just picked a single random day, week, month or year. I am talking about the entire time from Jan 1, 1981 through today. That is longer than some people here have been alive. A 10k investment not rebalanced has returned more than rebalancing. If that doesn't prove there is no return bonus from rebalancing, how many more years will it take?

[blackomen]

Yes you can cherry pick any start and end times you want. That's my entire point. We can't trade the past, only the future, and there is no certainty that rebalancing going forward will return more than not. If you believe there is, then how can I cherry pick a 33 year period where it didn't work? My cherry picking proves at least over 33 years, that there is no return bonus for rebalancing. It either will work or it won't, but you have no way of knowing beforehand.

If rebalancing provides a bonus to returns.....how many more years do we have to wait for it? After it occurs it must also persist forever, otherwise it never really worked.

Regarding your second point.........that's why I said "Rebalance to maintain acceptable diversification for risk purposes. That's the free lunch."

If disproving anything is as simple as cherrypicking a single period where something doesn't work, then we can disprove virtually anything.  A more meaningful approach to this is, given historical data, which has a higher probability of success, rebalancing or no rebalancing?

If it can be proven that rebalancing does not provide a return bonus (which it clearly does not for at least a period of 33.5 years or less)...........why would you think there's a higher probability of success with it? What rationale is there for such a belief?

I suppose you first have to agree that the past 33.5 years of data proves there is no return bonus for rebalancing.

I don't have the need or patience to prove or disprove anything..  the purpose here is just to point something out.

Since when did this turn into a full fledged debate?  I was merely pointing something out and there's no claim whether rebalancing is advantageous or disadvantageous, it's up to you and other readers to draw your own conclusions.

[Kshartle]

I don't have the need or patience to prove or disprove anything..  the purpose here is just to point something out.

Since when did this turn into a full fledged debate?  I was merely pointing something out and there's no claim whether rebalancing is advantageous or disadvantageous, it's up to you and other readers to draw your own conclusions.

Ohhh Np. There are so many threads and so many people who think there's some kind of free lunch bonus to returns from rebalancing I just didn't want people drawing the wrong conclusion. They even have a term for it called "volatility capture".

It is interesting that you can have two assets that are neg correlated and both have a losing period but by rebalancing annually you can squeak out a positive return. Math sometimes works out in ways that seem counterintuitive.

If you ask 50 fund managers if a simple thing like rebalancing annualy can net a portfolio return when the 2 assets are both losers over 5 years.......I doubt the majority would say yes.

[Cortopassi]

KS,

I assume you used peak to trough to calculate those?

100% different assets, no rebalance:

Stock only is 278k, max DD 55%
Bond only is 230k, max DD 32%
Gold only is 21k (yikes!), max DD 57%
Cash only is 48k no DD

My God, why did I ever buy gold? 

Max DD with annual or 35/15 rebalance is 14.5%.  For me, this is the free lunch and reason to rebalance.  I know I would not have survived the stock and gold drawdowns without way too much stress and likely capitulation.

Mike

[Kshartle]

KS,

I assume you used peak to trough to calculate those?

100% different assets, no rebalance:

Stock only is 278k, max DD 55%
Bond only is 230k, max DD 32%
Gold only is 21k (yikes!), max DD 57%
Cash only is 48k no DD

My God, why did I ever buy gold? 

Max DD with annual or 35/15 rebalance is 14.5%.  For me, this is the free lunch and reason to rebalance.  I know I would not have survived the stock and gold drawdowns without way too much stress and likely capitulation.

Mike

Completely agree with the underlined.

[Kshartle]

Blackomen....first off you have a great handle, truly one of my favorites here.

Ok, since you brought it up....I have always wondered: What exactly is a "Kshartle"?

I'll not bother with any jokes.

It's the username my college assigned back in 2002. That's when I really started getting online with everything and needing a username. It's a play on my first, middle and last names with letters from each. I started using it or slight variations for everything so I don't have to remember much.

[Kshartle]

How boring. I was hoping it was more of the joke oriented name. 

I was hasty when I signed up. I didn't know it would keep me signed in for life. I didn't want to have to remember.

[Kshartle]

It is certainly possible to get higher returns by rebalancing, so I don't really understand the dogmatic assertions otherwise. 

Who has dogmatically asserted otherwise? As far as I can tell, I'm pretty much the only one who's said definitively there is no such thing as a bonus, though others now agree.

I don't think anyone has said it's not possible to get higher returns by rebalancing. That's obviously false as your time period study demonstrates.

The point is it's all just data mining. You have absolutely no idea whether or not it will boost returns, therefore there is no bonus, just a theoretical one that may in fact turn out to be a loss. You can't trade the past, only the future and you don't which strategy will provide the highest returns. Therefore, base your rebalancing strategy on the one thing it's certain to help with, maximum drawdown/volitility.

Remember last year how many were depressed about the PP's return while stocks were surging? People were regretting being diversified or rebalancing out of stocks while the S&P was breaking out. They were lamenting diversification and re-balancing. Some people were talking about dropping the strategy. They didn't get that the entire point is not maximizing returns which the 15/35 PP is almost certain to NOT do.

It's ironic that a portofolio designed to be checked once a year is very popular with the type of investor who checks balances everyday (or hour )

[barrett]

It's ironic that a portofolio designed to be checked once a year is very popular with the type of investor who checks balances everyday (or hour).

KS, you are correct about that but some on here seem to have mastered not caring about their day-to-day fluctuations. Maybe people just stop posting when they get to that point. Jedi masters they are.

[Kshartle]

It's ironic that a portofolio designed to be checked once a year is very popular with the type of investor who checks balances everyday (or hour).

KS, you are correct about that but some on here seem to have mastered not caring about their day-to-day fluctuations. Maybe people just stop posting when they get to that point. Jedi masters they are.

Very good point B.

The negative year and several years of well below average performance brought out vocal naysayers to the strategy. They seemed completely surprised that they weren't getting their 9-10% smooth annual returns and their rebalance bonus / volitility capture. I got the impression that the majority of people attracted to the PP were people with a very short term focus who check all their balances weekly or daily.

I didn't think this might just be a vocal minority. 

[blackomen]

I don't have the need or patience to prove or disprove anything..  the purpose here is just to point something out.

Since when did this turn into a full fledged debate?  I was merely pointing something out and there's no claim whether rebalancing is advantageous or disadvantageous, it's up to you and other readers to draw your own conclusions.

Ohhh Np. There are so many threads and so many people who think there's some kind of free lunch bonus to returns from rebalancing I just didn't want people drawing the wrong conclusion. They even have a term for it called "volatility capture".

It is interesting that you can have two assets that are neg correlated and both have a losing period but by rebalancing annually you can squeak out a positive return. Math sometimes works out in ways that seem counterintuitive.

If you ask 50 fund managers if a simple thing like rebalancing annualy can net a portfolio return when the 2 assets are both losers over 5 years.......I doubt the majority would say yes.

Ya, I purposely picked 2 negative assets that produced a positive return when equal weighted and rebalanced to exaggerate the idea I'm trying to investigate.  In reality, I don't think I've ever encountered such a phenomenon using real data, both on short or long time frames.  Basically, if it's possible for 2 negative assets to make 1 positive using this so-called "volatility capture" then it's also possible for a negatively correlated assets with flat or slightly positive returns to produce even higher positive returns.  It CAN happen, but it doesn't mean it will always happen or even more than 50% of the time.

I get that the main benefit from rebalancing is hopefully lower volatility and higher sharpe ratios but even those are not guaranteed especially if the future correlations between the assets differ drastically from those observed in the past.

Haven't had a chance to read in detail but this article explores various approaches towards rebalancing a 60/40 portfolio and concluded that there are no significant differences between different strategies (except that frequent ones may obviously drive up transaction costs): http://www.vanguard.com/pdf/icrpr.pdf

[Stewardship]

Excellent posts, Kshartle.  Thank you.

blackomen, this thread seems similar to the last one you started.

[Kshartle]

I get that the main benefit from rebalancing is hopefully lower volatility and higher sharpe ratios but even those are not guaranteed especially if the future correlations between the assets differ drastically from those observed in the past.

This is a really good point. Many have the opinion that LTBs are negatively correlated with stocks like it's a law of the universe. When you look at the 42 years of PP history from '72-'13 you've got 26 years where LTBs and stocks ended the year in the same direction. So that's 62% movement in tandem (on an annual basis). That's a closer correlation than stocks and gold which only moved together 24/42 years.

If you look at stocks and bonds lately the correlations have been in lock step. If you read some of Browne's earlier works he considered these correlated assets with gold being negatively correlated to stocks.

So with any attempt to determine if asset rebalancing will boost returns over a given time period going forward, you have to assume correlations as well as length and depth of trends (longer and deeper favoring not rebalancing). I think it's impossible to do personally and the raw historical data by iteself is useless. Now making comparisons to historical periods and examining prior price action might prove useful.

For instance I think given the current economic situation there is a much greater likelihood of strong and sustained inflation over the medium to long-term (5-10) years. That would imply it's probably better for returns if you don't reblance as stocks move up and gold shoots up (sometime ).  Better to just let them ride for a long time rather than rebalance into cash or bonds that will be losing value in real terms.

Of course we'll see. Should be interesting. 

[Kshartle]

I don't understand how the statement "there is no such thing as a [rebalancing] bonus" can be true when one can look at long time periods and measure a rebalancing bonus.  Maybe it is just a language barrier.
I certainly don't think there is always going to be a rebalancing bonus, just like I don't think a particular is always going to go up/down.  No one knows what the future holds.

Yes but since your only choice is to rebalance or not, and you can't know beforehand the length and depth or trends or correlations, a rebalance bonus for return purposes ONLY exists in the past. It would be just as accurate to call it a rebalance penalty going forward as a bonus. How can it exist as a bonus and a penalty at the same time? It can't because it doesn't exist.

The existance of single 33.5 year period where not rebalancing returned more proves that there is no bonus for any forward 33.5 year time period or under (or ever imo). If there really was such a thing as a rebalance return bonus that exists, in any reasonable time frame, there couldn't be a 33.5 year period where it didn't work. It either exists or it doesn't. It doesn't, we're just doing backtesting and data mining/curve fitting. Again, it's just as accurate to call it a penalty.

Like I always say though, this is all a discussion about maximizing returns. If you want to talk about sharpe ratios and max DD potential etc. there is no question that diversification is useful and that includes rebalancing. I'm concentrated and not rebalancing based on anhy rules because I expect we'll see some some big trends (at least in terms of price movement) in the near future. I'm ok with missing out on a little "volitility capture" in the meantime.

[blackomen]

I get that the main benefit from rebalancing is hopefully lower volatility and higher sharpe ratios but even those are not guaranteed especially if the future correlations between the assets differ drastically from those observed in the past.

This is a really good point. Many have the opinion that LTBs are negatively correlated with stocks like it's a law of the universe. When you look at the 42 years of PP history from '72-'13 you've got 26 years where LTBs and stocks ended the year in the same direction. So that's 62% movement in tandem (on an annual basis). That's a closer correlation than stocks and gold which only moved together 24/42 years.

If you look at stocks and bonds lately the correlations have been in lock step. If you read some of Browne's earlier works he considered these correlated assets with gold being negatively correlated to stocks.

So with any attempt to determine if asset rebalancing will boost returns over a given time period going forward, you have to assume correlations as well as length and depth of trends (longer and deeper favoring not rebalancing). I think it's impossible to do personally and the raw historical data by iteself is useless. Now making comparisons to historical periods and examining prior price action might prove useful.

For instance I think given the current economic situation there is a much greater likelihood of strong and sustained inflation over the medium to long-term (5-10) years. That would imply it's probably better for returns if you don't reblance as stocks move up and gold shoots up (sometime ).  Better to just let them ride for a long time rather than rebalance into cash or bonds that will be losing value in real terms.

Of course we'll see. Should be interesting.

http://media.pimco.com/Documents/PIMCO_ ... ct2013.pdf

Yep, correlations can be notoriously difficult to predict..  and the above is just a study of the Stock-Bond Correlation.  I can only imagine how messy a study incorporating a 3rd asset gold would be.  Plus, for a taxable account, the capital gains taxes will probably drag down any rebalancing bonus out there so your rebalanced return from 1981 is probably even more optimistic than in practice.

[Kshartle]

Plus, for a taxable account, the capital gains taxes will probably drag down any rebalancing bonus out there so your rebalanced return from 1981 is probably even more optimistic than in practice.

Another great point. Selling winning assets in a taxable account negates what is essentially tax deffered gains if you never sell until retirement drawdown.

I personally don't follow the PP at the moment because of interest rates but if I did I think I would still just buy lagging assets and never rebalance, for many of the reasons mentioned. To each their own.

[Roberto]

KShartle, if you don't mind my asking, what is your current allocation strategy?

[Kshartle]

KShartle, if you don't mind my asking, what is your current allocation strategy?

Roughly:

35% gold miners
15% gold/silver
50% stocks (mostly non US developed but includes some Russia and US Oil companies)

Some cash in the bank that's maybe 3% of the investments.

I've bought nothing but gold miners since the 2013 April (I think) decline. I already owned a substantial amount of the them but I just keep adding. Picked up 500 shares of GDX at $22.30 right before the close yesterday in fact. I hope that's my last buy of those and they just take off.

If Russia falls back a few percent more in the next couple weeks I'll double my stake there.

I buy what everyone else appears to have left for dead or is shorting.