Three assets all with negative correlations?

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D-Dog
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Three assets all with negative correlations?

Post by D-Dog » Sat May 25, 2019 7:06 pm

It’s relatively easy to find two different assets that have historically had negative correlations. For example, VTSAX (total stock market) and EDV (long term treasuries). But I haven’t been able to find an example of three assets that have had mutually negative correlations. I’ve been using portfolio visualizer and haven’t found anything. Does anyone have an example of three assets A, B, and C where each of the three correlations (A vs B, B vs C, and A vs C) have all been negative? Is there some fundamental reason why this is rare/non-existent?

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arcticpineapplecorp.
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Re: Three assets all with negative correlations?

Post by arcticpineapplecorp. » Sat May 25, 2019 7:10 pm

I think most want "non-correlated assets", not necessarily "negative correlated assets". Noncorrelating assets can move in different directions or the same but usually by different amounts in either event.

If you have a negative correlation doesn't that mean when one goes up the other goes down?

If negative correlation means things move in the opposite directions, then how do you have three negative correlating assets when there's only two directions (up and down)? What's the third direction that would be different from the other two?

Do you mean to ask what three assets will have one go up, one go down and one sideways??

Is there a reason you want that? Is there something you're trying to achieve by looking for three assets with negative correlations?
"May you live as long as you want and never want as long as you live" -- Irish Blessing | "Invest we must" -- Jack Bogle

dbr
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Re: Three assets all with negative correlations?

Post by dbr » Sat May 25, 2019 7:34 pm

A statistical requirement is that a correlation matrix must be positive semi-definite. This article describes some of the considerations that apply to that:

https://blogs.sas.com/content/iml/2012/ ... atrix.html

It looks like it is statistically possible to have three negative correlations such as -.5, -.5, -.5 or less, but not if they equal and are more negative. There is a formula in the paper for testing this.
Last edited by dbr on Sat May 25, 2019 8:14 pm, edited 1 time in total.

NotTooDeepLearning
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Re: Three assets all with negative correlations?

Post by NotTooDeepLearning » Sat May 25, 2019 7:40 pm

If A is the opposite sign of B, and B is the opposite sign of C, then it is necessarily true that A has the same sign as C. Transitivity I think?

Edit: I guess it is possible to have three things that are pairwise negatively correlated.
Last edited by NotTooDeepLearning on Sat May 25, 2019 8:28 pm, edited 2 times in total.

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D-Dog
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Re: Three assets all with negative correlations?

Post by D-Dog » Sat May 25, 2019 7:51 pm

It seems like it should be theoretically possible to have three negatively correlated assets.

Asset A returns: 1, -1, 0
Asset B returns: 0, 1, -1
Asset C returns: -1, 0, 1

I haven’t calculated it, but I think these would all be negatively correlated.

Three negatively correlated assets just doesn’t seem to occur in practice. Or maybe it does, I don’t know. I’d love to see an example if there is one. Could it be that there are stocks and there are bonds, and everything else is more or less a combination of the two? Is there a third fundamental different asset?

stlutz
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Re: Three assets all with negative correlations?

Post by stlutz » Sat May 25, 2019 8:12 pm

IRL, the best additional asset I could come up with was UUP, the US Dollar Bullish fund. It has had negative correlation with stocks and 0 correlation with EDV.

https://www.portfoliovisualizer.com/ass ... ingDays=60

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JoMoney
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Re: Three assets all with negative correlations?

Post by JoMoney » Sat May 25, 2019 8:23 pm

D-Dog wrote:
Sat May 25, 2019 7:06 pm
...Is there some fundamental reason why this is rare/non-existent?
Because investment worthy securities are all heavily impacted by similar systemic economic variables like broad economic growth, inflation, interest rates, and time duration. Marketable securities that easily available for people to trade are also reliant on the same money & banking system - when an event occurs that impacts one, it impacts the money flows/availability in the others.

There are highly illiquid "assets" that would be uncorrelated, but that feature is more of a function of stale prices and there being no market from which to get an immediate price.

There are things that I would not consider an "asset" that are reliably un-correlated, certain types of options and contracts that can be structured specifically to act in an inverse way. You could also go to the casino and whatever results you had would likely be uncorrelated with the stock or bond markets, but these are not assets - they have a negative expected value. You can find casino games that have great "negative correlations", like betting on red and black concurrently at a roulette wheel - but again that wouldn't result in any positive expected value, even worse, on the rare occasion where the result becomes correlated you lose everything wagered on that expected "negative correlation" :(
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

dbr
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Re: Three assets all with negative correlations?

Post by dbr » Sun May 26, 2019 8:12 am

D-Dog wrote:
Sat May 25, 2019 7:51 pm
It seems like it should be theoretically possible to have three negatively correlated assets.

Asset A returns: 1, -1, 0
Asset B returns: 0, 1, -1
Asset C returns: -1, 0, 1

I haven’t calculated it, but I think these would all be negatively correlated.

Three negatively correlated assets just doesn’t seem to occur in practice. Or maybe it does, I don’t know. I’d love to see an example if there is one. Could it be that there are stocks and there are bonds, and everything else is more or less a combination of the two? Is there a third fundamental different asset?
The correlation coefficients are all -0.5 and the determinant of the correlation matrix is 0, thus positive semi-definite and hence allowed. There is not a mathematical reason why three variables cannot have mutually negative correlations. Note that if the correlations were all perfect anti-correlations with coefficients -1, then the matrix has a determinant of -4, and that is not allowed. So the negative correlations if all equal cannot be more negative than -0.5.

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House Blend
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Re: Three assets all with negative correlations?

Post by House Blend » Sun May 26, 2019 8:40 am

dbr wrote:
Sat May 25, 2019 7:34 pm
A statistical requirement is that a correlation matrix must be positive semi-definite.
+1. Add the restriction that the diagonal entries are 1, and you have all of the requirements.

You can have n variables whose pairwise correlations are all equal to x as long as x is in the range from -1/(n-1) to 1.

dbr
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Re: Three assets all with negative correlations?

Post by dbr » Sun May 26, 2019 8:42 am

House Blend wrote:
Sun May 26, 2019 8:40 am
dbr wrote:
Sat May 25, 2019 7:34 pm
A statistical requirement is that a correlation matrix must be positive semi-definite.
+1. Add the restriction that the diagonal entries are 1, and you have all of the requirements.

You can have n variables whose pairwise correlations are all equal to x as long as x is in the range from -1/(n-1) to 1.
Thanks for the generalization to n.

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midareff
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Re: Three assets all with negative correlations?

Post by midareff » Sun May 26, 2019 8:47 am

Seems to me that cash would not be correlated to either of them.

dbr
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Re: Three assets all with negative correlations?

Post by dbr » Sun May 26, 2019 8:56 am

midareff wrote:
Sun May 26, 2019 8:47 am
Seems to me that cash would not be correlated to either of them.
If a variable is not variable, such as return on cash which is constantly zero, then a correlation does not exist rather than being zero.

If cash has a return, such as being in an interest bearing account and we allow the return to vary because interest rates vary, then there should be some non-zero correlation with things that are affected by interest rates, which is everything really.

columbia
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Re: Three assets all with negative correlations?

Post by columbia » Sun May 26, 2019 9:08 am

Since 1978. Not negative, of course.

Code: Select all

Monthly Correlations

Name	US Stock Market	Long Term Treasury	Gold	Portfolio 1	Portfolio 2	Portfolio 3
Correlations for the portfolio assets
US Stock Market	-	0.05	0.04	1.00	0.05	0.04
Long Term Treasury	0.05	-	0.06	0.05	1.00	0.06
Gold	0.04	0.06	-	0.04	0.06	1.00

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Aptenodytes
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Re: Three assets all with negative correlations?

Post by Aptenodytes » Sun May 26, 2019 9:12 am

You are searching for what are called factors. No need to do the search from scratch unless you have billions to invest and can justify the expense. Nobel prize winners have done it for you. And people like Larry Swedroe have synthesized the results in understandable, actionable ways.

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D-Dog
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Re: Three assets all with negative correlations?

Post by D-Dog » Sun May 26, 2019 11:17 am

Aptenodytes wrote:
Sun May 26, 2019 9:12 am
You are searching for what are called factors. No need to do the search from scratch unless you have billions to invest and can justify the expense. Nobel prize winners have done it for you. And people like Larry Swedroe have synthesized the results in understandable, actionable ways.
I’m aware of the work on factors, but don’t fully understand all of the details. Are there three factors with negative correlations? And are there ETFs that track these factors?

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JoMoney
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Re: Three assets all with negative correlations?

Post by JoMoney » Sun May 26, 2019 11:29 am

D-Dog wrote:
Sun May 26, 2019 11:17 am
Aptenodytes wrote:
Sun May 26, 2019 9:12 am
You are searching for what are called factors. No need to do the search from scratch unless you have billions to invest and can justify the expense. Nobel prize winners have done it for you. And people like Larry Swedroe have synthesized the results in understandable, actionable ways.
I’m aware of the work on factors, but don’t fully understand all of the details. Are there three factors with negative correlations? And are there ETFs that track these factors?
Even if you believe in "factors" as a distinct source of risk/return, and that they are uncorrelated (they're not negatively correlated) there isn't really a good way to invest in a "factor" by itself... you're typically just buying a group of stocks that are weighted more on some "factor", but still heavily correlated with the stock market in general...
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

acegolfer
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Re: Three assets all with negative correlations?

Post by acegolfer » Sun May 26, 2019 1:42 pm

Aptenodytes wrote:
Sun May 26, 2019 9:12 am
You are searching for what are called factors. No need to do the search from scratch unless you have billions to invest and can justify the expense. Nobel prize winners have done it for you. And people like Larry Swedroe have synthesized the results in understandable, actionable ways.
I just downloaded F/F 3 factor monthly returns and calculated 3 pairwise correlations. They are all positive ranging from 0.125 to 0.320. Never seen 3 negatively correlated factors.

acegolfer
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Re: Three assets all with negative correlations?

Post by acegolfer » Sun May 26, 2019 1:47 pm

JoMoney wrote:
Sun May 26, 2019 11:29 am
Even if you believe in "factors" as a distinct source of risk/return, and that they are uncorrelated (they're not negatively correlated) there isn't really a good way to invest in a "factor" by itself... you're typically just buying a group of stocks that are weighted more on some "factor", but still heavily correlated with the stock market in general...
This is an excellent observation. Ppl may think factor funds are factors and thus efficient. But the reality is far from it. Even value factors have higher market beta than HML loading.

VFVA = a + 1.19 (MKT-Rf) + 0.46 SMB + 0.86 HML + error

happytrades
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Re: Three assets all with negative correlations?

Post by happytrades » Sun May 26, 2019 6:15 pm

What about the Permanent Portfolio or Bridgewater's all weather portfolio?

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