Don't Confuse Correlation with Causality

One of the first things that I learned as a quant is “don’t confuse correlation with causality”. Unless there is a direct relationship (e.g. interest rates go up, bond prices go down), statistical correlations don’t necessarily hold up.

Correlations move around
The folks at Bespoke have an interesting study showing the correlations of different asset classes and sectors over two time frames, one longer and one shorter. In the short term, S&P 500 sectors have become slightly more correlated with each other. The Yen has become more correlated with virtually all assets while Treasuries have become less correlated.

The lesson of this study is: Asset correlations move around. In this case, U.S. Treasuries have become a much better diversifier to U.S. equities in the short run. Which correlations should an investor rely on when building a portfolio?

Understand the fundamental case
My inner quant tells me to ignore the short term figures as the time frame is too short to matter. My inner fundamental investor tells me to figure out why the correlations are moving around. In fact, there may be a perverse causal relationship at work with asset classes that show negative correlations. Here are some examples:

• EAFE (1980s) – International equities were sold as diversifiers as they exhibited low correlation to US equities. Money moved in and eventually correlations rose.
• Emerging markets (1990s) – Emerging markets were sold as diversifiers to US and international equities. Even during periods of stress, their correlations were historically low. Money moved in and correlations rose.
• Hedge funds (starting about 2000) – Hedge fund returns were uncorrelated to equities, especially during the post-Tech Bubble bear market. Money moved in…

Comments

[User 232539]

Naming the error

A strong correlation between two variables does not mean that action by one variable causes another variable to perform in some way. The error is referred to as post hoc ergo propter hoc, a Latin phrase which means; after this; therefore, because of this (Carroll). Carroll further argues that causation can be estimated in a controlled experiment in which all of the plausible causes are known and accounted for. Carroll also calls this error post hoc reasoning and cites a few examples. A golfer always wears a red shirt on the last day of a tournament because of a belief that this shirt brings him luck. Actually, the golfer performed many other actions that also have some effect on his game. The use of a dousing stick to locate water when walking in a dry river bed that has an underground spring is another example. Further, although there appears to be a correlation between per capita beer consumption and teachers’ salary increases, a rise in per capita beer consumption has many variables associated with it, disposable income, advertizing, per capita salary increases as a result of rises in the cost of living, etc., etc. Teachers’ salaries are a smaller set of the capita source of income; and could also be influenced by cost of living raises and show up as a correlation but hardly a cause. Another name for the error is non causa pro causa, a Latin phrase meaning, non-cause for cause (Fischer, 1970).

Classification of relationships

According to Lethen (1996), there are 3 relationships that are commonly used to classify a realtionship as having causation or not. The first relationship is causation. Changes in X cause changes in Y. When there is a Soccer tournament in Muscatine, local hotel weekend sales increase - definitely a correlation and probably a cuase. Common response is another relationship that may reveal correlation but not causation. Here are a few examples: During summer months, more people walk in the park, people wear tee shirts, temperature is hot in Alaska, and there are more shark attacks in California. All of these actions correlate with summer ber are hardly causes for each other. Finally, there is a relationship described as confounding. Confounding is when X is intertwined with Y and many other variables. Lethen (1996) cites an example of testing the effects on a headache pain reliever without managing many other variables including the effect of a placebo. In this case, a controlled experiment should be done to study the causation.

Alternative thoughts
A spoof on correlation and causation is contained in a humorous article in which the respondents to a new poll have determined that correlation is causation, after all. Here is a quote from the article, “Now, with the results of the latest poll, we are able to determine that people’s lack of belief in correlation not being causal has caused correlation to now become causal. It’s a real advance in the field of meta-epistemology (New Poll Shows Correlation is Causation).” Please read for a real laugh.

References

Carroll, R., Post hoc fallacy, The Skeptics Dictionary. Retrieved June 13, 2008 from skepdic.com/posthoc.ht....

Fischer, D. (1970). Historians' Fallacies: Toward a Logic of Historical Thought . Fallacies of Causation (ch 4.). New York: Harper & Row.

Lethen, J. (November 13, 1996). Correlation and Causation. Retrieved June 13, 2008 from www.stat.tamu.edu/stat...

New Poll Shows Correlation is Causation. Retrieved on June 13, 2008 from obereed.net/hh/correla....

[notsosmart]

all this caused me to have a headache.

[CharlieStromeyer Jr]

hmm, now frontier markets are being sold as diversifiers

[sbenard]

I recently wrote about the correlation of various global stock indexes on my blog. The whole idea of different stock indexes being non-correlated is largely a myth. Check out the charts on this posting. Two of the charts are Emerging Markets and the EAFE.

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