Correlation: Are these things opposites?

Dec 16, 2006 by Adam C. Powell, Ph.D.

Definition:

Correlation: The strength and direction of a linear relationship between two random variables (historical prices of two assets).

For a longer definition, and a good illustration of the concept, see Wikipedia.

When building a diversified portfolio, it is important to know how the performance of the assets within the portfolio correlate. Often you will hear that historical prices are not an indicator of future prices. This is true, however, sometimes the change in expectations for one type of asset will change the expectations for another asset.

For instance, when the price of petroleum rises, the shipping industry becomes less profitable, as petroleum is one of its major expenses, and the increase in the price of petroleum increases the cost of shipping. This form of correlation, called inverse correlation (one thing goes up while the other goes down) is indicated by negative correlation coefficients.

The opposite of inverse correlation is direct correlation. Two assets are directly correlated when their prices tend to move in the same direction (either both go up at once, or both go down at once). For instance, the performance of EEM, the iShares Emerging Markets Index, is directly correlated with the performance of ADRE, the BLDRS Emerging Markets 50 ADR Index. This should make intuitive sense, as both funds are designed to track the same thing (emerging markets). They are simply run by different companies. Buying two assets that are highly directly correlated does little to diversify a portfolio, just as drinking both Coca-Cola and Pepsi each day does little to diversify a diet. Directly correlated assets have positive correlation coefficients.

Finally, there are also uncorrelated assets. The price of pork bellies is probably relatively uncorrelated to the price of copper. The variables affecting agricultural production (rain, disease, etc.) are very different from those affecting mining.

How can you determine the correlation between two assets?

1. Feed the historical prices of both assets into a computer and have it determine their correlation
2. Use the calculations on http://www.spdrindex.com/correlation/ 
3. Eyeball it from a graph

Calculating correlations is beyond the of this blog entry. However, I will talk about how to use graphs.

1. Go to Yahoo! Finance
2. Enter a ticker (like EEM) in the “Get Quotes” box and click “Go”
3. Look at the graph, and click “1y” for a one year view
4. Enter another ticker (like ADRE) in the “Compare:” box and click “Compare”

 As you can see, EEM is highly directly correlated with ADRE, as the changes are practically overlapping.

The iPath Goldman Sachs Crude Oil Index (OIL) is highly inversely correlated with the iShares Dow Jones Transportation Average (IYT).

Two stocks are relatively uncorrelated when from a comparison graph, it is not clear whether the upwards movement of one stock will cause another to move up or down. Sony and Altria (formerly Phillip Morris) are rather uncorrelated, as they are both based in different industries and in different parts of the world.