Extreme Example of Correlation For Some Perspective

Dec 23, 2011 in Correlation

Quick, what is the correlation between a stock-bond balanced portfolio and a portfolio that holds the S&P 500 but is leveraged to 2x its daily moves?

This is an extreme example of correlation which shows how it can often be meaningless in investment analysis. Below is the historical correlation of the plain vanilla Vanguard 60-40 Stock-Bond index mutual fund vs the +2x Leveraged S&P 500 ETF (SSO).

The correlation is 0.99 meaning they both have big moves relative to their own historical movement on the same days.But what does this tell you about ‘risk’? Not much. What does it indicate about return? Not much. The volatility characteristics of these two products are completely different despite correlation of ~1.00. Below is the total return comparison

Another example: Pharmaceuticals vs Financials. The 120-day correlation here is 0.88, which is high --- though there is a 29 percentage point difference in YTD returns (2,900 basis pts).

So when you hear people talk about how high correlations means you can’t differentiate yourself ---- this is not because of correlation. Everyone has times when they are out of sync with the market but that doesn’t mean it wasn’t possible to add material value vs an index. To say so is disingenuous.

While we have a correlation chart on ETFreplay.com, we use it only as peripheral information. In an appreciating market, you WANT high correlation to the appreciating asset. But let's be clear, it is possible to differentiate your portfolio no matter what happens with correlation.

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High Correlations? And what?

Sep 15, 2011 in Correlation

This is getting silly.  Portfolio managers around the world are complaining about high correlations.   The truth is that things that are somewhat correlated to start with (stocks) will see their correlations go higher when volatility rises -- it's not a mystery, its mathematical.   This has happened many times and while people are now saying ‘all-time high correlations’ – this misses the much more important point.

Crises cause securities to have larger than normal moves --- and correlation is a measure of how far one security moves in relation to the movement in another. Essentially, when one security has a big move vs its history, does the other also have a large move relative to its historical movement?   

Correlation is somewhat of a tricky topic.   Something may move very little but still be highly correlated to something that drops a lot.   Look at the utility sector (XLU) vs the S&P 500 (SPY).   XLU has a 0.89 correlation to SPY over the past 60 days.   But XLU is slightly positive so far in Q3 while SPY is currently -9.5% QTD.

Let's do a portfolio example just to see how better to think about this.  If I take 85% ultra-short term bonds (t-bills), but blend it with 15% KBE (bank industry etf) and I compare this to 100% bank index, the result is like this:


You can see how the cash has diluted the loss to just -3% this quarter.   (KBE is -21.1% during the same period).   The correlation has been 0.99 - 1.00.   From this standpoint, a correlation of 1.00 has told you nothing about the true risk in this case.   The correlation is so high obviously because the combination of KBE and t-bills moves a lot whenever KBE moves a lot.  It doesn’t move a lot on an absolute basis --- but it does move a lot relative to its historical range of movement.    Easy enough.


So back to using different securities --  utilities high correlation with the S&P 500 hasn't prevented it from going up recently (slightly).   Utilities have gone up despite the correlation between these two rising.  Thus, when portfolio managers are complaining about high correlations – they are just really complaining of the natural result of high volatility.

Earlier this year we created a simple – but what we think is more useful --- application than your standard correlation matrix.   The ‘Down Day Stats’ module measures how much various ETFs move on just the days a benchmark drops more than X%.


Let’s use the industry ETFs (equities only).  We can use SPY to show all down days this year.   You find that defensives like Pharmaceuticals, Food & Beverage and Telecom outperform on down days.   Energy and mining do the worst.


But then flip it around, use the inverse S&P 500 (SH) to show what happens on up days.   Energy and mining are best and defensives are worst.   They are all highly correlated – so you must consider volatility #1 --- and then think about correlation #2.   It would be nice if lots of equity securities were not correlated.  But the fact is they are and it gets worse whenever there is a crisis. If you want a market that is less correlated, then you need to have an extended period without any volatility storms.


Summary:  If the market goes down, volatility will rise and this will push correlations up.  If the market goes up, the reverse will occur.   How many times have we seen this over the past 15 years? Many.


Why would it stop in 2011?


See also 2010 Posts On Correlation



Volatility Storms, Crises and ETF Correlation

May 16, 2010 in Correlation

First, a chart of GLD vs the FXE Euro Currency ETF is a simple yet powerful way to show the primary issue in the world right now:  

This EC (Euro currency) crisis has brought on a volatility storm (sharply rising volatility/VIX).   It is common to hear analysts and portfolio managers say --- what does a Greek default have to do with my US domestic small cap stock??   Well, a lot actually if the Greek problems lead to a crisis – as a crisis will cause overall market volatility to rise.

Correlations RISE in times of crisis.  This is not just a random statement, it can be viewed mathematically using the Capital Asset Pricing Model (CAPM) framework.

In CAPM, the correlation between two assets can be expressed as a function of their Betas and the variance of the market.  If we assume that both assets have a beta of 1.0 and identical residual risk, then it becomes mathematically true that correlations rise as variance rises.  Thus, some type of crisis causes overall variance to rise (in this case it’s the escalating debt problems in Europe)--- and then this rising variance will cause correlations to rise.  

Note the serious divergence of small cap US stocks and the MSCI ETF Europe (correlation at first drops on the lower chart) -- and then the subsequent increase in ETF correlation when VIX/volatility increased sharply.




see also:

Correlations Rise In Times of Crisis

for a more complete technical explanation of this topic see "Active Portfolio Management"  (Grinold & Kahn, 2000).  This book is extremely technical and really only for professional investors with mathematical orientation. 

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Correlations During Crisis

Feb 24, 2010 in Commodities | Correlation

I know that this may be implied by others --- but its not enough that something simply be non-correlated to be included in a portfolio. It also needs to have positive expected return. 

Structurally speaking, commodities markets are both 1) quite volatile and 2) generally quite sensitive to the overall economy -- which is what the stock market is sensitive to. In times of crisis, its been shown over and over again that correlations generally rise, so that you thought you were getting non-correlation, but instead you just get a more volatile asset that delivers an even larger drawdown for your portfolio. An excellent example is what just happened with crude oil in 2008, see images:


Classic Example of Mixing Non-Correlating Assets

Jan 06, 2010 in Correlation



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