Correlation Cycles

In the CMT courses we teach on the correlation between different securities. The reason is that when we are constructing a portfolio, we don’t want to invest in too many securities that have high correlation —unless they all go straight up of course—then we’ll take ‘em all! The reality is we cannot know that in advance and the prudent thing to do is to have diversification in our portfolio to minimize risk. The way we do this is to look for uncorrelated securities. In plain english, we look for securities that will not all fall and rise together.

This is a really clever way to manage risk, but there are some dangers with correlations that I want to explain. One of these I was not even aware of until I started writing this post.

Let’s first take a step back and explain correlation. If you’re a stats geek, you can skip this part.

Here’s the interpretation as plainly as I can state it. “Correlation is a value that describes the linear relationship between two variables”. Now let’s break that down.

• “Variables” are our datasets. In statistics they can be anything, but in our case they are the two securities we want to explore to see if there is a relationship in how they move. We line up the two datasets and measure the percentage gains for each over a rolling period.
• “Linear Relationship” is how we would describe the line if we plotted all the data on a chart. Imagine that for every week we measured the percentage change for the two securities. We then plot that point on a XY plot. If we do this with enough data, we can see if there is a relationship. We can show this in Optuma using a Regression Chart.

We can see in the first image below that SPX and DJI move in almost complete unison because a change in one seems to always have the same proportional change in the other. (NOTE: The slope of the line is “Beta” a beta of 1 would be the same percentage change. “High Beta” are values greater than 1 and means that for a 1% change in SPX, there is a bigger change in that stock).

In the second image, the XJO and DJI still have a positive relationship, but the spread of the points shows us the relationship is not as strong. In the final image we show the relationship between the US$ (DXY) and the DJI. The relationship is slightly negative and there is a wide dispersion around the line.

Weekly Regression Charts

The important thing right now is to understand that Correlation tells us how closely related these two data sets are.

• “Value” is a single result that is going to reveal if there is a strong linear relationship between the variables. It ranges from +1 for strongly positive to -1 for strongly negative. A Value of 0 means there is no relationship at all between the securities. Now here’s the part that confuses a lot of people. In correlation, the direction is indicated by the positive or negative, while the magnitude of the value represents the strength of the linear relationship. So a +0.95 value tells us there is a very strong positive correlation. It does not tell us the slope of the line in the Regression Chart (that’s Beta), only that the spread of the points around the line is really tight (like the first chart above).

Ok, now that we have dealt with that, let’s look at how we actually present Correlations. Below is a Correlation Chart from Optuma. Every security we add gets posted on the rows and columns. To find the correlation value between two securities, you simply find the intersection point and read the value.

Correlation Grid

I know these are all Indices and you may not be adding these to a portfolio, but they are suitable for the purpose of illustration.

If you were holding HSI and you wanted to diversify, you would search along the HSI row and find the indice with the lowest correlation value. That would be the one that is closest to 0, which in this case would be DAXX. Remember that it is closest to 0, not the lowest number.

There are a number of things that jump out at me when I look at this chart:

1. TSX (Canada) and XJO (Australia) are highly correlated. That makes sense to me as both their economies are heavily dependant on natural resources. In fact, I have written before how the Aussie Dollar is a good proxy for a commodities trade—although that no longer seems to be the case—more on that soon.
2. There are two zones of high correlation. The SPX, DJI, RUT & NDY (all US-based indices) are obviously highly correlated. Although there is a small disconnect between the small caps and the large caps highlighted by the lower correlation of RUT (Russell 2000) to the others. The second zone seems to be mainly European (and Japan’s Nikkei). That really got me thinking about whether this grid is showing me a correlation between the indices or if the currency fluctuations were getting involved. Again, this is going to be an area that we need to do more research, but is important to consider.
3. The fact that this chart is mostly green, and there is no red, tells me that all these indices are all positively correlated. I know there are some negative numbers, but nothing strongly negative that it would be painted red by the software.
4. These values did not look like the correlations that were presented in the text books that I had previously read. For instance this is a similar grid that was presented in a 2007 text on market correlations by Markos Katsanos.

Market Correlations by Markos Katsanos

That chart is a weekly grid made up from 52-weeks of data. To compare, I need to update my chart to be the same time-frame (see below).

Correlation Grid

There are a few different securities in there but for the pairs that overlap, you can see that the values are nothing alike. This did not make sense to me as we had always talked about correlations as constants. If they were there, they were there always. There are many texts/articles that talk about market correlations as absolutes, and this is telling me that that is not the case.

This led me to look for historical values of correlation. I could open up a Script Chart, add the same securities and set the script to reveal to me the weekly correlation to the SPX. Here is that chart:

Correlation Grid Script Chart

Immediately you can see that the correlation is not consistent, there is an oscillation that is happening. Correlations are in no way constant over time. This is only the last five years, but these oscillations seem to go on for many years. In fact, in 1995 Japan’s Nikkei was at -0.90 correlation. Even the Dow and the SPX deviate slightly. Note: there is a currency component to this that needs to be considered - I’ll save that for another post.

The only time that all indices are correlated are in times of major bear markets. Then everything is correlated to 1! You can see the 2007-2009 period near the start of this longer-term chart here.

All Indices Correlated

Bottom line is that correlations are not static, we can clearly see there is a cycling in correlations. We could try some Fourier analysis on the cycles, but I’ll save that for the next post as well!

For now, what are the correlation dangers that we have discovered? These are the four things that you need to be aware of if you are using correlations:

1. Correlations are not static. All securities cycle between being highly correlated and no correlation. The Aussie dollar spent years being highly correlated to the Thomson Reuters Commodity Index (see below). I wrote a post about that relationship a couple of years ago — but no more. It could be the correlation is a function of the market phase that we are in —it appears that the AUDUSD is in an accumulation phase. It would be interesting to see how correlations change during different market phases, sigh —but that again needs more research.

Cycle Between Being Highly Correlated and No Correlation

1. Correlations are not Causation. This is an observed relationship between securities but does not make a good concrete trading signal. Please do not take this as a signal to trade from. These types of inputs are great as a component of a “weight of the evidence” approach, but should not be used in isolation.
2. You must work with the same currency. Otherwise you can’t know if you are observing a correlation between the security or the currency.
3. Correlations lag. Like many indicators, the Correlation is telling us what has happened, not what is going to happen (comes back to point 2 above).

Correlations are a powerful technique that we can use, but as with everything, we need to be sure that we understand what it is that we are working with and what the limitations are. Nothing is 100% perfect 100% of the time.

Of course adding too many uncorrelated securities to a portfolio can also have the effect of diversifying away all risk and, by extension, the opportunity for gain. Our rewards are compensation for the risk we bear.