Aug 18

Correlation

by David Harper, CFA, FRM, CIPM

FRM |

3D arrows 

Learning objectives

  • Define, calculate and interpret correlation.
  • List and discuss the properties of correlation

The (population) correlation is a standardized covariance; it is covariance (a measure of linear co-movement) translated into a unit-less number by division of the product of volatilities:

correlation

Properties of correlation

  • Correlation has the same sign (+/-) as covariance
  • Correlation measures the linear relationship between two variables
  • Between -1.0 and +1.0, inclusive
  • The correlation is a unit-less metric
  • If two variables are independent, the have zero covariance and this implies (→) zero correlation. But the converse not necessarily true: a correlation of zero does not imply independence. For example, Y=X^2 is nonlinear
  • Correlation (or dependence) is not causation.

For example, in a basket credit default swap, the correlation (dependence) between the obligors is a key input. But we do not assume there is mutual causation (e.g., that one default causes another). Rather, more likely, different obligors are similarly sensitive to economic conditions. So, economic deterioration may the the external cause that all obligors have in common. Consequently, their default exhibit dependence. But the causation is not internal.

Tips for FRM candidates:

  • Dependence is a broader (more encompassing) term than correlation. Obligors can be dependent due to shared, non-linear exposure to similar risk factors. But correlation signifies statistically linear relationship.
  • Many people forget that correlation is direct function of volatilities.  Last year, the New York Fed showed why recently high correlations among hedge fund returns were driven primarily by lower volatilities (in the denominator) rather than higher covariances.

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