Three assets all with negative correlations?
Three assets all with negative correlations?
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/nonexistent?
 arcticpineapplecorp.
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Re: Three assets all with negative correlations?
I think most want "noncorrelated 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?
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?
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Re: Three assets all with negative correlations?
A statistical requirement is that a correlation matrix must be positive semidefinite. 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.
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.

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Re: Three assets all with negative correlations?
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.
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.
Re: Three assets all with negative correlations?
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?
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?
Re: Three assets all with negative correlations?
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
https://www.portfoliovisualizer.com/ass ... ingDays=60
Re: Three assets all with negative correlations?
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 uncorrelated, 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
Re: Three assets all with negative correlations?
The correlation coefficients are all 0.5 and the determinant of the correlation matrix is 0, thus positive semidefinite 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 anticorrelations 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.DDog wrote: ↑Sat May 25, 2019 7:51 pmIt 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?
 House Blend
 Posts: 4569
 Joined: Fri May 04, 2007 1:02 pm
Re: Three assets all with negative correlations?
+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/(n1) to 1.
Re: Three assets all with negative correlations?
Thanks for the generalization to n.House Blend wrote: ↑Sun May 26, 2019 8:40 am+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/(n1) to 1.
Re: Three assets all with negative correlations?
Seems to me that cash would not be correlated to either of them.
Re: Three assets all with negative correlations?
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 nonzero correlation with things that are affected by interest rates, which is everything really.
Re: Three assets all with negative correlations?
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
 Aptenodytes
 Posts: 3758
 Joined: Tue Feb 08, 2011 8:39 pm
Re: Three assets all with negative correlations?
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.
Re: Three assets all with negative correlations?
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?Aptenodytes wrote: ↑Sun May 26, 2019 9:12 amYou 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.
Re: Three assets all with negative correlations?
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...DDog wrote: ↑Sun May 26, 2019 11:17 amI’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?Aptenodytes wrote: ↑Sun May 26, 2019 9:12 amYou 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.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks."  Benjamin Graham
Re: Three assets all with negative correlations?
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.Aptenodytes wrote: ↑Sun May 26, 2019 9:12 amYou 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.
Re: Three assets all with negative correlations?
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.JoMoney wrote: ↑Sun May 26, 2019 11:29 amEven 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...
VFVA = a + 1.19 (MKTRf) + 0.46 SMB + 0.86 HML + error

 Posts: 91
 Joined: Tue Mar 02, 2010 6:44 pm
Re: Three assets all with negative correlations?
What about the Permanent Portfolio or Bridgewater's all weather portfolio?