## Stocks and bonds move in opposite directions and improve results? Really?

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Topic Author
Frans
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### Stocks and bonds move in opposite directions and improve results? Really?

It is often said that stocks and bonds have a tendency to move in opposite directions and that this behavior noticeably improves returns and lowers risk of combinations of stocks and bonds. When stocks underperform, the rationale goes, bonds have the tendency to compensate for this by doing better, resulting in better overall returns and less variation. Equally, when stocks do better, bonds have the tendency to underperform, with similar results. Really?

Let's look at the combination of 50% Large Company Stocks and 50% Intermediate-Term Government Bonds for the years 1928 through 2013 with yearly rebalancing and using the yearly returns data in the 2014 Ibbotson Stocks, Bonds, Bills and Inflation Classic Yearbook.

It turns out that from 1928 through 2013, Large Company Stocks and Intermediate-Term Government Bonds moved in opposite directions in only 51 of the 86 years, or 59% of the time. If there were no correlation between the directions of movement between these asset classes and we had a large sample size (and 86 years is not a large sample size) then we would expect that number to be close to 50%. It's unclear whether this deviation from 50% is caused by the alleged correlation or statistical variation due to a small sample size.

Let's calculate the Compound Annual Return (CAR) and risk expressed as Standard Deviation (STDEV) of the 50/50 mix.
Let's then randomized the sequence of the years of the bond data to undo the alleged correlation of stocks and bonds having the tendency to move in opposite directions for any given year and recalculate CAR and STDEV. When this randomization process is repeated, the resulting CAR and STDEV vary a bit from one try to the next, so let's run this process several times and look at the lowest and highest values of CAR and STDEV and "averaged" the CAR and STDEV by calculating the geometric means.

The results:
When using 50 sets of randomized data, both the CAR and STDEV of the original, non-randomized combination were right smack in the middle of the sets of results of those 50 randomized sets and were extremely close to the geometric means of the CAR and STDEV of the randomized set. Here are the numbers:
CAR of original set and geometric mean of CAR of random set: 8.09% and 8.08%.
Minimum and maximum CAR of random set: 8.00% and 8.20%.
STDEV of original set and geometric mean of STDEV of random set: 10.44% and 10.48%.
Minimum and maximum STDEV of random set: 9.32% and 11.33%.

Conclusions:
1. Both CAR and STDEV of the original set are extremely close to the geometric mean of the randomized set (with deltas of 0.01% and 0.04% respectively) and almost dead center of the CAR and STDEV populations of the randomized set
2. While it is true that the original set had an ever-so-slightly better return of 0.01% and an ever-so-slightly better STDEV of 0.04%, it's open to debate whether those minute deltas are caused by an alleged correlation between stocks and bonds in the sense that they move in opposite directions, or pure statistical variation.
3. The claim that stocks and bonds move in opposite directions and noticeably improve results is false.

Note: I repeated the calculations for 50/50 combinations of Large Company Stocks & Long-Term Government Bonds, Large Company Stocks & Long-Term Corporate Bonds, and Small Value Stocks & Intermediate Term Government Bonds and the results were very similar.

edge
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

So, uh, you could have just calculated (or looked up) correlation and come to this conclusion much quicker.

The correlation is low, but not highly negative. The portfolio with the best long term result is 100% stocks. Adding bonds improves sharpe ratio but not returns.
Last edited by edge on Fri Dec 04, 2015 7:59 pm, edited 1 time in total.
nisiprius
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Frans, my comment is simply: you are right.

The idea of a negative correlation between stocks and bonds is either a) an urban legend, or b) recency, or c) both, and I've commented on it any number of times.

You didn't even need to need to do that much work; Ibbotson has done it for you. The correlation between stocks and bonds is not negative, it's zero. It's zero over the full period of the SBBI time series, 1926-2014, and it's zero over a second, shorter-term chart, 1970-2014 that they included in order to show international stocks.

What's the explanation of the urban legend? Well, first of all, it's easy to understand how negative correlation helps, so it's what people like to explain. But I think negative correlation is the investing equivalent of perpetual motion or Maxwell's demon. It would work incredibly powerful magic if it existed in the wild, between actual assets, because it would imply that you could cancel out risk without canceling out return. (You can of course get negative correlation between artificial derivatives, but the short positions that give you the negative correlation cancel out return at the same time as they are canceling out risk; the true believers think that it might not cancel out perfectly so there's potentially a small win).

The other issue is that, seemingly, financial people don't understand sampling variation, and assume that any period of observed negative correlation must be a real phenomenon, not just the luck of the sample.

Zero correlation is, in fact, quite helpful, but it's hard to explain and nowhere near as exciting as negative correlation would be. And it only helps if both of the assets both have reasonably similar return, and reasonably high volatility. If all those conditions are met, then, when asset A zigs, asset B zigs or zag, and when asset A zags, asset B zigs or zags. The result is that the combination of the two does have less than double the volatility, and risk-adjust return is improved.

1926-2014

1970-2014
Last edited by nisiprius on Fri Dec 04, 2015 7:49 pm, edited 3 times in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
xjz
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

My understanding is that we invest in stocks and bonds not because they move in opposite directions (negative correlation), but in independent directions (near-zero correlation, or at least far from 1 or -1), which is useful primarily because it lowers variance/standard deviation (risk) without too heavy of an impact on the mean (return).

Most of your post seems to be pointing out symptoms that the correlation is low: they move in different directions nearly half the time (this measurement is biased because both stocks and bonds have long-term returns above 0, so they both move up more often than down), and the risk and return of a blended portfolio is about the same even when you scramble the order of the returns.

To evaluate whether or not a blended portfolio is favorable, why not try comparing the risk/return characteristics of the blended portfolio against the characteristics of pure-stock and pure-bond portfolios?
FiveK
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Saying that the returns of two asset classes are not highly correlated is somewhat short of saying they move in opposite directions.
Assume in one year stocks go up 10% and bonds 1%, while swapping those returns in the next year. Although moving in the same direction, they would not be highly correlated. Due to the low correlation rebalancing would be advantageous.

viewtopic.php?t=170003
viewtopic.php?t=131803
viewtopic.php?t=113258

P.S. Pretty much what xjz also said.
Topic Author
Frans
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Thanks for the feedback. I don't know what kind of assumptions go into calculation correlations, e.g. if the assumption is that distributions are normal, impact of sample size, etc. So that's why are used the actual data and make zero assumptions.

So, why is this claim of correlation so widespread?

I didn't look at gain vs. loss, but under- or over-performance as compared to the asset's CAGR over the period I looked at.
Phineas J. Whoopee
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

No, with respect to moving in opposite directions.

No. Not really. Really not. Really no.

Whoever gave that impression was, at best, misinformed. I won't speculate about at worst.

US stocks and US Treasury bonds have a correlation of approximately zero. That means their market movements are unrelated. They could both go up. They could both go down. They could go in opposite directions. One could move and the other remain unchanged.

Somebody will say I'm wrong and bring up the flight to quality. Too late. I mentioned it myself. Flights to quality are already part of the statistical measure of past correlations of stocks and Treasury bonds.

Past performance does not guarantee future results.

It is absolutely not the case that stocks and bonds are negatively correlated, which would mean they tend to move in opposite directions, no matter how often certain members of the press and commissioned salespeople assert "bonds zig while stocks zag."

Whether mixing them improves results depends on your own personal investment policy statement's definition of improvement.
Will Rogers wrote:It isn't what we don't know that gives us trouble, it's what we know that ain't so.
PJW
Last edited by Phineas J. Whoopee on Fri Dec 04, 2015 8:12 pm, edited 4 times in total.
edge
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Calculating covariance and correlation uses the actual sequence of returns and does not assume any particular distribution.

It is widespread for the same reason why any simple/directional/convenient but wrong concept is widespread.

The over/under cagr is not a good approach for understanding portfolio behavior. It mixes too many things together.
Frans wrote:Thanks for the feedback. I don't know what kind of assumptions go into calculation correlations, e.g. if the assumption is that distributions are normal, impact of sample size, etc. So that's why are used the actual data and make zero assumptions.

So, why is this claim of correlation so widespread?

I didn't look at gain vs. loss, but under- or over-performance as compared to the asset's CAGR over the period I looked at.
lee1026
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

I agree that there isn't that much annual data. But then again, why do you need annual data? Use daily data instead. There have been an awful lot of days, and we have a large data set of those.

Using daily data for S&P 500, (SPY) and the Vanguard Long-Term Treasury fund (VUSTX), we find a correlation of -0.24 from 1993 to today. But then again, the correlation have been a lot more negative recently then it have been in the past, so it may not continue into the future.

https://www.portfoliovisualizer.com/ass ... Y%2C+VUSTX
john94549
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

"It is often said" (the passive voice) gets a 5 out of 5 (5 being the worst) from the grammar police. Who said it? How often? And where?

I have a stand-alone bond fund (active voice). I have a stock fund (active voice). I have watched each go up and down (active voice). Based on my personal observations, (fill in the blank).
MindBogler
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

lee1026 wrote:I agree that there isn't that much annual data. But then again, why do you need annual data? Use daily data instead. There have been an awful lot of days, and we have a large data set of those.

Using daily data for S&P 500, (SPY) and the Vanguard Long-Term Treasury fund (VUSTX), we find a correlation of -0.24 from 1993 to today. But then again, the correlation have been a lot more negative recently then it have been in the past, so it may not continue into the future.

https://www.portfoliovisualizer.com/ass ... Y%2C+VUSTX
And the correlation is -0.38 if you use VUSUX...

Great post...but get ready for an onslaught of glib remarks.
dangerous
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Equities by their very nature must at all times be expected to outperform debt.

Debt (ok, aside from consumer debt like credit cards) is always created to finance the ownership (i.e, purchase or creation) of something. Equity is owning that thing. If the expected return of ownership (i.e, equity) was less than the expected return of the debt (how much the borrower has to pay) nobody would ever borrow.

The purpose of bonds isn't to outperform equity, its to provide some protection for a portfolio. If you need ANY of your invested money for more than 30 years, I'd say you don't really need bonds in your portfolio. But most people need some of their money within that 30 year time span.
Topic Author
Frans
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Dangerous, I don't think you understand the issue. The issue is not stocks outperforming bonds, but if stocks under-perform compared to what they on average do, do bonds over-perform to what they on average do, and vice versa.
Last edited by Frans on Fri Dec 04, 2015 8:51 pm, edited 1 time in total.
Topic Author
Frans
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Never mind, I edited my previous post.
Last edited by Frans on Fri Dec 04, 2015 8:52 pm, edited 1 time in total.
MindBogler
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

This is one of my favorite charts. No additional commentary required:

Phineas J. Whoopee
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

I agree, mostly, with dangerous, and would like to add that if one doesn't need their resources for thirty years, and therefore can take on lots of risk, one year later they won't need their resources for twenty nine years. What's one year of lots of risk going to do for anybody? And if twenty nine years is enough, then why specify thirty? How much time isn't enough?

One could, I suppose, use a declining proportion of more-risky to less-risky assets. That might work.

PJW
Topic Author
Frans
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Can we go back to the original issue?
dangerous
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Frans wrote:Dangerous, I don't think you understand the issue. The issue is not stocks outperforming bonds, but if stocks underperform compared to what they on average do, do bonds underperform to what they on average do, and vice versa.
My point was that if you want the highest expected return over a VERY long time frame without caring about short term fluctuations, you should buy 100% stocks, and 0% bonds, which is effectively the point of the OP. But I'm also pointing out that bonds do have a purpose, but the purpose isn't to enhance returns, it is to reduce risk.

The OP is a bit misleading, it implies that bonds don't "improve results." It depends on the result you seek. If you're seeking returns adjusted for short term risks, they will improve results. If its absolute long-term expected returns, then they won't improve results.

By the way, some people will claim that bonds contribute a "rebalancing bonus". There is no such thing as a rebalancing bonus. Rebalancing is to maintain equal amounts of risk over time by maintaining a constant AA. Rebalancing to get some kind of return "bonus" is just market timing - buying dips and selling spikes.
dangerous
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Phineas J. Whoopee wrote:I agree, mostly, with dangerous, and would like to add that if one doesn't need their resources for thirty years, and therefore can take on lots of risk, one year later they won't need their resources for twenty nine years. What's one year of lots of risk going to do for anybody? And if twenty nine years is enough, then why specify thirty? How much time isn't enough?

One could, I suppose, use a declining proportion of more-risky to less-risky assets. That might work.

PJW
The reason why I picked 30 was because treasuries maxed out in duration at 30 years. The longer term bonds have a higher expected return. So if you're investing in bonds for a duration longer than 30 years, you are not getting compensated at all for the extra risk you could take on. Indicating you shouldn't invest in bonds at all, you should invest in an asset class that does compensate you, i.e, equities.
Topic Author
Frans
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Dangerous, you still don't get it, if I may be so blunt. The question is, do stocks out-perform when bonds under-perform and vice versa and does this improve returns/lower risk as compared to there being no such correlation. Hint: my answer is - not in any significant way.
nisiprius
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Stocks and bonds don't move in opposition, but they do move independently, and this does improve return and lower risk for a mixture compare to using either one individually. But, as you say, maybe not significantly. It's a small effect, not very reliable, and the importance is exaggerated.

For Portfolio Visualizer, I am going to compare two portfolios, and I am going to use three asset classes: Total Stock, Total Bond, and cash. I am going to assume we want to compare portfolios with the same risk, as measured by standard deviation. I am also going to assume that we want to choose a period of time over which stocks and bonds had the same risk-adjusted return, and with a little tinkering I've picked 1975-2012. Total Stock had a Sharpe ratio of 0.47, Total Bond 0.46. Not as equal as I'd like, but given that the only tool I have is picking year ranges, it's about as close as I can get.

First, using the asset classes in isolation. 100% Total Bond gives me a standard deviation of 6.70%. In order to cut down the risk of Total Stock I'm going to mix it with Cash/Money Market until I get as close as possible to the same standard deviation. That turns out to be 35.3% stocks, 64.7% cash.

Got that? I've got two portfolios, with almost equal Sharpe ratios, almost equal standard deviations, and almost equal CAGRs: 7.83% for stocks and cash, 8.06% for all bonds.

Now for the moment of truth. Let's try equal amounts of stocks and bonds, and adjust cash to get the same standard deviation as close as we can. That turns out to be 31.7% Total Stock, 31.7% Total Bond, and 36.6% cash.

The result is that standard deviation is 6.68%, just a smidge lower than the other portfolios, but CAGR is 8.50%, or about 0.50% higher than the others, and the Sharpe ratio is boosted from 0.47 to 0.56.

That's the "improvement" from mixing stocks and bonds instead of using either in isolation. It's not huge, but it's there, and it's because of imperfect correlation between stocks and bonds.

Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Johno
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

dangerous wrote:
Frans wrote:Dangerous, I don't think you understand the issue. The issue is not stocks outperforming bonds, but if stocks underperform compared to what they on average do, do bonds underperform to what they on average do, and vice versa.
My point was that if you want the highest expected return over a VERY long time frame without caring about short term fluctuations, you should buy 100% stocks, and 0% bonds, which is effectively the point of the OP. But I'm also pointing out that bonds do have a purpose, but the purpose isn't to enhance returns, it is to reduce risk.

The OP is a bit misleading, it implies that bonds don't "improve results." It depends on the result you seek. If you're seeking returns adjusted for short term risks, they will improve results. If its absolute long-term expected returns, then they won't improve results.

By the way, some people will claim that bonds contribute a "rebalancing bonus". There is no such thing as a rebalancing bonus. Rebalancing is to maintain equal amounts of risk over time by maintaining a constant AA. Rebalancing to get some kind of return "bonus" is just market timing - buying dips and selling spikes.
As noted, 'rebalancing bonus' is properly defined as being merely the advantage in compound annual return of an annually rebalanced portfolio with a given weight of components as compared to the (same) weighted sum of the individual component returns. That does tend to exist in stock/bond combinations because the returns of the two aren't correlated closely, they don't have to be negatively correlated. You're right that in most (not all, especially if not limiting it to just the US in just last century) long past periods 100% stock portfolio returned more than stock/bond portfolio with any significant % of bonds.

So since stock/bond return correlation has typically been ~zero over the long haul, ie the annual returns of stocks and bonds are on average noise relative to one another, you wouldn't expect a dramatic effect by pairing up the stock and bond returns of different years randomly as OP did.

The issues with negative stock/bond correlation are two as I see it. First if one believes the recent 'mode of oscillation' of the two markets, which does tend more to negative correlation, is here to stay. It would be impossible to prove upfront one was right about that, but it could be so. Secondly correlation might be more negative historically in 'times of turmoil' than it is overall, and that could also relate to the first point, if you feel the story of markets from now will be more about big crises which travel faster from where ever in the world they originate to affect virtually all national markets, compared to the past. However, one has to consider how much it matters if bond/stock correlation is negative for short periods. For the relatively small % of money in bonds which would be shifted to stocks when the stock market dives, it matters. For the rest, besides cheering you up when you check your account, it's less clear it matters. This frequently comes up in the treasury fund v CD debate: the visible though perhaps temporary bump in treasury fund price assuming yields fall in a crisis, whereas an old CD gains just as much advantage by having a now (more) above market rate, but there's no market to market price change. For the portion of fixed income you *don't* sell to rebalance it's hard to see why you'd care about such a form over substance difference, but some people seem to.
Topic Author
Frans
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Nisiprius, What you are describing and calculating is the well-known (one would hope) interaction between different asset classes that allow you to select allocations to maximize return at a given risk or minimize risk at a given return; the Efficient Frontier in other words. That's not what I tried to address. I observed that, with a given allocation between certain stock and bond asset classes, there is no or a very small negative correlation and it's impact, if any, is extremely small. Your first reply correctly referred to the lack of a strong correlation. Since I don't really understand how correlation is calculated and what its limitations are in terms of accuracy and the accuracy of the resulting CAR and STDEV numbers, I chose to do some calculations of the final results, CAR and STDEV, using the actual numbers. I don't think that using correlation coefficients will tell you what differences you can expect, if any, if you randomize the years as I did.
jwillis77373
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

What is said about stocks and bonds really being two sides of the same coin is very interesting.

\$1 of company stock
or
\$1 of company bond

At the end of the term for the bond I get \$1 plus fixed interest
At the end of the term for the stock I get \$1 plus the increase in value of the company

Each is a "bet"

A Bond holder is taking a "short position" in a company and the issuer is trying to make sure they loose

A Stock holder is taking a "long position" in a company and the issuer is trying to make sure they win

The issuer holds more cards than a Bond holder (they know more about their company and how they intend to spend the proceeds) and a Bond holder often knows less about a publically traded company.. so they are more likely to "loose" the bet.. rating agencies can attempt to "grade" a Bond independently.. but its really a way for a holder to "outsource the research" and pay someone else to manage their decisions.. the dotcom stock bubble.. the real estate derivatives bubble.. offer convincing proof that paying someone else to make your decisions.. especially if they make more money than you.. usually doesn't lead to an increase in personal portfolio value
lee1026
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

First if one believes the recent 'mode of oscillation' of the two markets, which does tend more to negative correlation, is here to stay. It would be impossible to prove upfront one was right about that, but it could be so.
One way to figure out if the market expect for the correlation to stay is by finding a stock/bond ETF that have an active options market and see how its implied volatility compares with stock and bond volatility. Unfortunately, I have not been able to find one.
A Bond holder is taking a "short position" in a company and the issuer is trying to make sure they loose
Huh? Bondholders want the company to do well. Badly ran companies are the ones that default.
jwillis77373
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Perhaps its less inflammatory to say,

a Bond holder is a short-term investor to a company with a planned exit strategy whose goal is to extract maximum profit from the company over that short-term.

a Stock holder is a long-term investor to a company without an exit strategy whose goal is to maximize profits for a company over an indefinite long-term.
Last edited by jwillis77373 on Sat Dec 05, 2015 6:52 am, edited 1 time in total.
Quark
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

dangerous wrote:[]My point was that if you want the highest expected return over a VERY long time frame without caring about short term fluctuations, you should buy 100% stocks, and 0% bonds, which is effectively the point of the OP. But I'm also pointing out that bonds do have a purpose, but the purpose isn't to enhance returns, it is to reduce risk.[]
Beware of the fallacy of time diversification. Stocks have higher expected returns because they are riskier, but risk mean they may have lower actual returns, over any given time frame, long or short.

As you write, the purpose of bonds is to reduce risk. A less risky portfolio may have higher actual returns than a more risky portfolio.
Maynard F. Speer
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Frans wrote:Nisiprius, What you are describing and calculating is the well-known (one would hope) interaction between different asset classes that allow you to select allocations to maximize return at a given risk or minimize risk at a given return; the Efficient Frontier in other words. That's not what I tried to address. I observed that, with a given allocation between certain stock and bond asset classes, there is no or a very small negative correlation and it's impact, if any, is extremely small. Your first reply correctly referred to the lack of a strong correlation. Since I don't really understand how correlation is calculated and what its limitations are in terms of accuracy and the accuracy of the resulting CAR and STDEV numbers, I chose to do some calculations of the final results, CAR and STDEV, using the actual numbers. I don't think that using correlation coefficients will tell you what differences you can expect, if any, if you randomize the years as I did.
The basic idea with stocks, bonds and commodities/gold is that when money flees one asset class, it's usually going to find its way into one of the others (it has to go somewhere) ... So at least when there's short-term pain - like the 2008 crash - there's usually something being bid up ... And that's your improved risk-adjusted return (which you could then leverage up to a better return than 100% stocks, with lower risk)

I believe stock/bond correlation tends to go down with interest rates ... So in a higher rate environment, bonds may be good hedges against stocks, while in a lower right environment, they can move more together - that might be one to look into in more detail?
"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
Doc
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Maynard F. Speer wrote:The basic idea with stocks, bonds and commodities/gold is that when money flees one asset class, it's usually going to find its way into one of the others (it has to go somewhere) ... So at least when there's short-term pain - like the 2008 crash - there's usually something being bid up ... And that's your improved risk-adjusted return (which you could then leverage up to a better return than 100% stocks, with lower risk)
Yep. When you try to do the statistics you need to decide whether your needs are based on short or longer term correlations. If you re-balance annually on your mother in laws birthday then annual correlations are meaningful. On the other hand if you balance using say 2% band then correlations based on weekly or even daily correlations are probably more appropriate.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.
edge
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Uh. This 'interaction' is correlation. You probably need to do some more reading on the subject and less posting. Randomizing the years, assuming done for both assets in the same way, does not do anything.
Frans wrote:Nisiprius, What you are describing and calculating is the well-known (one would hope) interaction between different asset classes that allow you to select allocations to maximize return at a given risk or minimize risk at a given return; the Efficient Frontier in other words. That's not what I tried to address. I observed that, with a given allocation between certain stock and bond asset classes, there is no or a very small negative correlation and it's impact, if any, is extremely small. Your first reply correctly referred to the lack of a strong correlation. Since I don't really understand how correlation is calculated and what its limitations are in terms of accuracy and the accuracy of the resulting CAR and STDEV numbers, I chose to do some calculations of the final results, CAR and STDEV, using the actual numbers. I don't think that using correlation coefficients will tell you what differences you can expect, if any, if you randomize the years as I did.
Angelus359
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

One question that I don't see answered here is what happens to returns if you keep an 80/20 stock bond ratio, precisely, and rebalance every quarter (when dividends are paid) using dividends if possible or sales if you must.

Annual might not be often enough to really take advantage of the concept

A sudden dip in stocks, where you then simply buy more stocks, or a spike in stocks where you buy more bonds might beat stocks over time?
Dude2
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

dangerous wrote:Equities by their very nature must at all times be expected to outperform debt.

Debt (ok, aside from consumer debt like credit cards) is always created to finance the ownership (i.e, purchase or creation) of something. Equity is owning that thing. If the expected return of ownership (i.e, equity) was less than the expected return of the debt (how much the borrower has to pay) nobody would ever borrow.
I think it is a vast oversimplification on the purpose for bonds. Stocks and bonds are both ways that companies raise capital. What they do with that money is literally their business. It isn't always about buying "things". Money fuels their business machine, and they must use it to generate more money than they have raised.
\$1 of company stock
or
\$1 of company bond

At the end of the term for the bond I get \$1 plus fixed interest
At the end of the term for the stock I get \$1 plus the increase in value of the company

Each is a "bet"
There is absolutely nothing about the bold above that must be true. No agreement is made that the stock will ever return \$1 or increase in value over any term. That's why it is a bet; whereas, the bond is an agreement.
Dude2
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Angelus359 wrote:One question that I don't see answered here is what happens to returns if you keep an 80/20 stock bond ratio, precisely, and rebalance every quarter (when dividends are paid) using dividends if possible or sales if you must.

Annual might not be often enough to really take advantage of the concept

A sudden dip in stocks, where you then simply buy more stocks, or a spike in stocks where you buy more bonds might beat stocks over time?
The invisible variable in the equation is the amount of risk. We have to make a leap of faith and say to ourselves that if we stay with 80/20 that we have maintained a constant risk level. Given that, when stocks tanked, we sold bonds high to buy stocks low. When bonds tanked, we sold stocks high to buy bonds low. I agree that we should come out ahead with that strategy when it is related to an associated risk factor. The Vanguard funds that offer a fixed asset allocation rebalance themselves smartly on a daily(ish) basis (taxes, fees are all considerations). We should be able to use those funds as role models, i.e. compare the total return of the combined TSM/TBM at some ratio to the total return of Balanced Index over some time period.

VBINX (Vanguard Balanced Index) start 1993 - present total return --> 10,000 becomes 58,346
TSM start 1993 - present 74,660
TBM start 1993 - present 23,700 --> 0.6 * 74,660 + 0.4 * 23,700 = 54,276

That is the time frame that was convenient. I'm sure we can argue endlessly about why the time frame biases the results.
dbr
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

I always thought that one adds bonds to a portfolio to reduce variability because bonds have much less variability than do stocks. A result is that expected return is also reduced. The difference in variability between stocks and bonds is huge, and that is about all there is to that story. If a person wants to somehow increase the "efficiency" of a portfolio by combining uncorrelated assets, then both assets should be highly variable.
longinvest
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

dbr wrote: If a person wants to somehow increase the "efficiency" of a portfolio by combining uncorrelated assets, then both assets should be highly variable.
Exactly.

Just for the theoretical fun of it (as I'm not into that kind of investing): What could be highly variable but uncorrelated with stocks? Maybe a long-term zero-coupon (strip) bond fund, or a long-term TIPS fund (TIPS having small coupons and thus higher duration than nominal bonds).

Anyone wants to backtests a combination of TSM and such a fund?
Last edited by longinvest on Sat Dec 05, 2015 11:45 am, edited 1 time in total.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW
Rx 4 investing
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

How does an allocation of 10 year treasury bonds serve a portfolio? Here are the Top 30 draw downs of the S&P 500 from 1927 to 2013. Next to the S&P 500 return is the corresponding total return on the 10-Year (LTR). As noted by Wes Gray:

"The resilience of this finding is remarkable. In the context of a traditional asset pricing model, such as the Capital Asset Pricing Model (CAPM), an asset that actually delivers returns when the rest of the world is blowing up (I.e., negative beta during treacherous times), should have a negative expected return because of the diversification benefits. But with US Treasury Bonds, we actually earn a positive expected return AND get the insurance benefit. One might even consider the US Treasury bond “anomalous.”

“Everyone is a disciplined, long-term investor until the market goes down.” – Steve Forbes
Quark
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Dude2 wrote:[]The invisible variable in the equation is the amount of risk. We have to make a leap of faith and say to ourselves that if we stay with 80/20 that we have maintained a constant risk level.[]
Why do we have to make that leap of faith? There does not appear to be any good reason to believe a constant allocation means a constant level of risk, although it may be the best we can do for operational purposes.
Dude2
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Quark wrote:
Dude2 wrote:[]The invisible variable in the equation is the amount of risk. We have to make a leap of faith and say to ourselves that if we stay with 80/20 that we have maintained a constant risk level.[]
Why do we have to make that leap of faith? There does not appear to be any good reason to believe a constant allocation means a constant level of risk, although it may be the best we can do for operational purposes.
If we are going to prove/disprove the OP's question that a combination of stocks/bonds improves returns (rebalancing bonus), then the only way we can maintain some sort of reference frame is to assume that risk stayed constant. If not, we can't draw any conclusions. The bonus is pretty small, and it can be explained away if risk zigged and zagged along the way (with a constant AA).
Doc
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Rx 4 investing wrote:How does an allocation of 10 year treasury bonds serve a portfolio? Here are the Top 30 draw downs of the S&P 500 from 1927 to 2013. Next to the S&P 500 return is the corresponding total return on the 10-Year (LTR).
Yep, the other side of the coin.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.
longinvest
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

(Following up on my previous post viewtopic.php?f=10&t=178924&p=2709242#p2709014)

PIMCO has a long-term TIPS ETF. Throwing this into Portfolio Visualizer tells me:

Portfolio 1
VTI Vanguard Total Stock Market ETF 100.00%
Portfolio 2
LTPZ PIMCO 15+ Year U.S. TIPS Index Fund ETF 100.00%
Portfolio 3
VTI Vanguard Total Stock Market ETF 50.00%
LTPZ PIMCO 15+ Year U.S. TIPS Index Fund ETF 50.00%

Portfolio Returns (Jan 2010 - Nov 2015)

Code: Select all

#  CAGR    Std.Dev.  Max. Drawdown
1  13.60%  13.50%    -17.58%
2   5.38%  11.06%    -20.54%
3  10.15%   7.88%     -9.65%
OK. Over the near 6-year period, long-term TIPS were not exactly as volatile as stocks (11.06% vs 13.50%), but close, and much more volatile than Total Bond Market (BND) which had a 2.95% standard deviation.

As expected, the volatility of the combined portfolio (7.88%) was lower than both TSM and long TIPS, and the return higher than the average:
10.15% > (13.60% + 5.38%) / 2 .
Last edited by longinvest on Sat Dec 05, 2015 4:18 pm, edited 1 time in total.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW
Johno
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Dude2 wrote:
Quark wrote:
Dude2 wrote:[]The invisible variable in the equation is the amount of risk. We have to make a leap of faith and say to ourselves that if we stay with 80/20 that we have maintained a constant risk level.[]
Why do we have to make that leap of faith? There does not appear to be any good reason to believe a constant allocation means a constant level of risk, although it may be the best we can do for operational purposes.
If we are going to prove/disprove the OP's question that a combination of stocks/bonds improves returns (rebalancing bonus), then the only way we can maintain some sort of reference frame is to assume that risk stayed constant. If not, we can't draw any conclusions. The bonus is pretty small, and it can be explained away if risk zigged and zagged along the way (with a constant AA).
Again, all 'rebalancing bonus' means is if X% stock, (100-X%) bond portfolio, periodically rebalanced, returned more than X% the stock return plus (100-X%) the bond return in the same period. It basically compares something you can do, have 50% stocks and 50% bonds, rebalancing (at some point), with something you can't actually do 'just give me 50% the return of stocks and 50% the return of bonds', nor can you calculate the std dev of return historically for something you can't do. So 'rebalancing bonus' actually says nothing about risk, therefore no way to 'explain it away' with measures of risk.

OTOH never rebalancing while something obvious you can do, gives arbitrarily answers over long periods depending when you start. For example. 50/50 stock/bond starting in 1926 and never rebalanced would be meaningful different than just 100% stocks in first few decades, but eventually not. It's a path dependent, opaque and confusing way to illustrate returns over long past periods, no surprise it's seldom used to illustrate them.

It is true that stock (and bond) 'risk', if defined as std deviation of return over a given period, varies from period to period unless you just calculate one value for the whole available data set. And the latter doesn't mean of course that it's 'constant'. I agree some people tend to ignore this. And specifically we'd tend to to rebalance into stocks when short term stock risk is higher (high short term future volatility tends to correlate with previously short term negative return*) and out of them when it's lower. It could be that a rebalancing method based on constant risk given projected short term future volatility and correlation** could give 'better results' (return, std dev of return and/or some higher moment of return distribution, and/or involving individual risk preferences) than fixed %'s. But that still wouldn't 'explain away' the comparison called 'rebalancing bonus'.

*since std dev of return changes in stocks over short periods are strongly autocorrelated, even the backward looking fact that realized volatility *has* been recently high tells you are taking more short term risk to buy stocks then compared to when recent realized vol has been low.
**as pointed out by Lee1026, there's no window on that via active options market on stock/bond portfolio ETF's, though one could use similar statistical modeling used to predict vol or empirical RiskMetrics type estimate of future correlation based on exponentially weighted recent correlation.
Dude2
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

I wouldn't define risk as standard deviation. I'd use standard deviation as a measure of volatility. To me risk is that nebulous factor that we can never really quantify. Given efficient and sane markets, higher recognized risk demands higher returns, and hopefully the market keeps on top of that. If risk is changing, even as my AA is fixed, then what conclusions can I draw about anything? That is all I was trying to express. We may have some disagreements even in this thread about whether the rebalancing bonus exists, but those that believe it does exists believe it is small. Something small may be able to be explained by other factors, like varying risk, luck, timing.
roflwaffle
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

I think something like maximum deviation is probably closer to what most people view as minimizing risk. One good example I can think of off the top of my head is holding all stocks (S&P 500) versus 60% stocks/40% treasuries (with yearly rebalancing) from 1918 to 2010. There's only a 6% different in total returns (in favor of all stocks), but the maximum yearly drop from the ending value in the balanced portfolio is ~25+% while the max for the all stock portfolio is 40+%.
edge
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

I don't think you mean 6% total return.
roflwaffle wrote:I think something like maximum deviation is probably closer to what most people view as minimizing risk. One good example I can think of off the top of my head is holding all stocks (S&P 500) versus 60% stocks/40% treasuries (with yearly rebalancing) from 1918 to 2010. There's only a 6% different in total returns (in favor of all stocks), but the maximum yearly drop from the ending value in the balanced portfolio is ~25+% while the max for the all stock portfolio is 40+%.
roflwaffle
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Yeah, it's a 6% difference between the two (All stocks versus 60/40 stocks/treasuries rebalanced annually) after 90+ years. IIRC, average yearly real returns for stocks are something like 4.5% before taxes, and you still capture most of the by rebalancing every year.
edge
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Not exactly sure how you are coming to these conclusions. Let's just take 1972 to 2014.

Growth of 10k in nominal dollars

TSM: 10.4% CAGR, \$703k
60/40 stocks/bonds: 9.6% CAGR, \$511k

Looks like stocks had a total return nearly 40% higher from what I can tell...moving the time scale back to 1918 would only make this difference larger. Including taxes would make the difference larger still because of the bond income.

roflwaffle wrote:Yeah, it's a 6% difference between the two (All stocks versus 60/40 stocks/treasuries rebalanced annually) after 90+ years. IIRC, average yearly real returns for stocks are something like 4.5% before taxes, and you still capture most of the by rebalancing every year.
roflwaffle
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

They're accurate as far as I can tell. I'm thinking the difference is because I'm using real dollars instead of nominal dollars and stopping at 2011. The data is from Robert Schiller's long term stock, bond, interest rate and consumption data spreadsheet. When I compare my all stock results from 1971 to 2011 to the results from other sites (eg http://thume.ca/indexView/), they're within a percent of each other. In portfoliovisualizer, when I have both those portfolios compared to the S&P 500 from 1988 (I guess they don't have S&P 500 data from before then) to 2011, they all line up together, better than my results do actually, probably because PV isn't using the same data I am.

Code: Select all

Portfolio performance statistics
Portfolio	Initial Balance	Final Balance	CAGR	Std.Dev.	Best Year	Worst Year	Max. Drawdown	Sharpe Ratio	Sortino Ratio	US Mkt Correlation	Intl Mkt Correlation
Portfolio 1			\$2,000	\$17,443 	9.44% 	18.62%	35.79%	-37.04%	-37.07% 	0.40	0.69	1.00	0.76
Portfolio 2			\$2,000	\$17,236 	9.39% 	11.05%	30.87%	-14.18%	-14.18% 	0.57	1.28	0.95	0.63
S&P 500 Total Return	\$2,000	\$17,476 	9.45% 	18.61%	37.58%	-37.00%	-37.61% 	0.40	0.70	0.99	0.73
But yeah, I'm not seeing a big difference in 100% S&P and 60% S&P/40% 10-year treasury returns from 1918 to 2011. The market has grown substantially from 2011 to present, which would move total returns towards 100% stocks. But.... That's happened plenty of times in the past and sooner or later there's a correction and the two portfolios converge.
edge
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

I would really have to see exactly how you got to these numbers but they seem very very way off. From 1928 - 2014 the geomean of stocks was 9.7%. The geomean of 10 year treasuries was 5.3%. (http://pages.stern.nyu.edu/~adamodar/Ne ... retSP.html)

There is simply no way that you end up with the same number with a 60/40 portfolio over a long period of time (30-40+ years).

In portfolio visualizer from 1988 (could have used 1985) to 2011 (could have used 2015) a 100% VFINX portfolio starting at 10k has a final balance of 85k while a 60/40 VFINX/VBMFX rebalanced annually is 77k. A difference in total return of around 10%.

Expanding to 1985-2015 VFINX goes to 159k and 60/40 VFINX/VBMFX goes to 117k, a difference of almost 36%. As time frames are elongated, this number gets larger and larger. The equity risk premium over 10 year treasuries from 1928 to 2014 was over 4.5%. This is not surmountable in a portfolio that held substantial amount of bonds.
roflwaffle wrote:They're accurate as far as I can tell. I'm thinking the difference is because I'm using real dollars instead of nominal dollars and stopping at 2011. The data is from Robert Schiller's long term stock, bond, interest rate and consumption data spreadsheet. When I compare my all stock results from 1971 to 2011 to the results from other sites (eg http://thume.ca/indexView/), they're within a percent of each other. In portfoliovisualizer, when I have both those portfolios compared to the S&P 500 from 1988 (I guess they don't have S&P 500 data from before then) to 2011, they all line up together, better than my results do actually, probably because PV isn't using the same data I am.

Code: Select all

Portfolio performance statistics
Portfolio	Initial Balance	Final Balance	CAGR	Std.Dev.	Best Year	Worst Year	Max. Drawdown	Sharpe Ratio	Sortino Ratio	US Mkt Correlation	Intl Mkt Correlation
Portfolio 1			\$2,000	\$17,443 	9.44% 	18.62%	35.79%	-37.04%	-37.07% 	0.40	0.69	1.00	0.76
Portfolio 2			\$2,000	\$17,236 	9.39% 	11.05%	30.87%	-14.18%	-14.18% 	0.57	1.28	0.95	0.63
S&P 500 Total Return	\$2,000	\$17,476 	9.45% 	18.61%	37.58%	-37.00%	-37.61% 	0.40	0.70	0.99	0.73
But yeah, I'm not seeing a big difference in 100% S&P and 60% S&P/40% 10-year treasury returns from 1918 to 2011. The market has grown substantially from 2011 to present, which would move total returns towards 100% stocks. But.... That's happened plenty of times in the past and sooner or later there's a correction and the two portfolios converge.
nisiprius
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Frans wrote:Nisiprius, What you are describing and calculating is the well-known (one would hope) interaction between different asset classes that allow you to select allocations to maximize return at a given risk or minimize risk at a given return; the Efficient Frontier in other words. That's not what I tried to address. I observed that, with a given allocation between certain stock and bond asset classes, there is no or a very small negative correlation and it's impact, if any, is extremely small. Your first reply correctly referred to the lack of a strong correlation. Since I don't really understand how correlation is calculated and what its limitations are in terms of accuracy and the accuracy of the resulting CAR and STDEV numbers, I chose to do some calculations of the final results, CAR and STDEV, using the actual numbers. I don't think that using correlation coefficients will tell you what differences you can expect, if any, if you randomize the years as I did.
The effect of randomizing the order of annual returns of one of the asset classes is, basically, to reduce the correlation to zero, without changing the standard deviation or the mean of either. If you do this with a pair of asset classes that have zero correlation to begin with, you would expect there to be no effect. If they had positive correlation, then randomizing the order of one ought to improve risk-adjusted return. If they had negative correlation--unlikely--then randomizing the order of one ought to reduce risk-adjusted return.

The big phonus-balonus about correlations is this: if asset A has good risk-adjusted return and asset B has poor risk-adjusted return, then obviously mixing in B will tend to drag down the risk-adjusted return of the mix. If, at the same time, B has low correlation, that will tend to improve the risk-adjusted return of the mix. It's a balance, and low correlation is both a weak and unreliable effect. Therefore you can't lean on it unless you are convinced that B has and will continue to have good risk-adjusted-return in at of itself.

Too often low correlation is mentioned as if it automatically, all by itself, means that B will improve the portfolio as a whole.

What I believe to be true is this--the genuinely low, near-zero correlation of stocks and bonds can be expected to persist, not simply because it has been true in the past, but because they really are fundamentally different asset classes. I don't think this is true of the alleged "negative correlation." And the correlation is low enough, and the risk-adjusted return of bonds is high enough, that for a given standard deviation X you probably will get slightly higher returns creating a portfolio with that standard deviation using stocks, bonds and near-"cash" than you would using stocks and near-"cash" alone.

And, finally, I don't believe there's any way to create a 100% stocks portfolio that has comparably low risk to, say, a 30/70 stock/bond retirement income portfolio. You can only get a low-risk portfolio by using low-risk assets in it, any fiddling with around with "dividend stocks" or "low-vol stocks" or "countercyclical stocks" is just tweaks and fine-tuning... maybe some all-stocks portfolios only fell 44% in 2008-2009 instead of 50%, but that's about the limit.
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Quark
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### Re: Stocks and bonds move in opposite directions and improve results? Really?

Dude2 wrote:
Quark wrote:
Dude2 wrote:[]The invisible variable in the equation is the amount of risk. We have to make a leap of faith and say to ourselves that if we stay with 80/20 that we have maintained a constant risk level.[]
Why do we have to make that leap of faith? There does not appear to be any good reason to believe a constant allocation means a constant level of risk, although it may be the best we can do for operational purposes.
If we are going to prove/disprove the OP's question that a combination of stocks/bonds improves returns (rebalancing bonus), then the only way we can maintain some sort of reference frame is to assume that risk stayed constant. If not, we can't draw any conclusions. The bonus is pretty small, and it can be explained away if risk zigged and zagged along the way (with a constant AA).