Limitations of Correlation Measurement

What are the limitations of correlation in regards to its consistency and causation?

Correlations are not constant, they change over time and in fact they can change very suddenly especially in times of market stress. You might have heard the saying, “in times of stress all correlations go to one”. Changes to correlations will clearly affect future performance of any portfolio.

Statisticians are very careful in describing relationships between assets as a move in one ‘explains’ a move in the other. That’s because ‘explains’ is not the same as causes. Correlation does not imply a causal relationship. For example, there might be a positive correlation between height and the size of feet. In general, the taller you are, the larger feet you have. But being tall doesn’t make you grow large feet or having large feet doesn’t make you grow tall. Sometimes however, there is a causal relationship. For example, the relationship between the spot or current price of an asset and its forward, or futures price. These are connected by the principle of no arbitrage. All things remaining equal, because there’s a mathematical connection between the two, a change in the price of one will be mirrored almost exactly by a change in the price of the other, a plus one or hundred percent positive correlation.

What is a spurious correlation?

Using a fairly simple formula, a correlation number can be produced for any set of data. We could pick two sets of data randomly and run the numbers. The resulting correlation though won’t necessarily make any rational sense. We call those spurious correlations. Say, for example, a steel producer wants to hedge against a fall in steel prices. They’re looking to offset that risk with something that has a positive correlation. It just so happens that steel prices correlate perfectly with the price of oranges. Theoretically, the producer could hedge the value of the steel production by selling oranges. But, would you bet your job on that being a rational hedge.

What needs to be considered when comparing correlation numbers?

Another thing to consider is when comparing correlation numbers. If one is 0.80 and the other 0.40, the only thing you can say is that one has a stronger positive correlation than the other. What you cannot say is that one is twice as strong as the other. What it implies is that the asset with the lower correlation has a greater variability of return compared to the asset with the higher correlation.  Or that it moves in an opposite direction to the benchmark more often than the one with the higher number. The question of how high the correlation number needs to be to use it confidently is a matter of judgment and further research.