The misleading nature of correlations

In this note we explain certain subtle features of calculating correlations between time-series. Correlation is a measure of linear co-movement, to be contrasted with the quadratic nature of risk. This can lead to misleading impressions arising from correlating two time-series. We show that the correlation of a manager with a benchmark leads to an estimate of the square root of how much exposure the manager has to the benchmark. We also show that an estimate of correlation with monthly data over five years has an associated error of 0.13, and therefore only a correlation of greater than 0.26 should be considered significantly greater than zero.