Term Glossary

Metrics, Models & Concepts

Correlation


Correlation is a normalized measure of asset return co-movement based on return covariance. \begin{equation} \rho_{ij}=\frac{cov(r_{i},r_{j})}{\sigma_{i}\sigma_{j}} \end{equation}

\(r_i\)
i-th asset return
\(\sigma_i\)
i-th asset standard deviation of returns (square root of variance)

Correlation coefficients are between -1 and 1, inclusive, by definition. Two assets are positively correlated if high return values of one are likely to be associated with high return values of the other. They are negatively correlated if high returns of one are likely to be associated with low returns of the other.

Assuming co-movement of all assets is due to one common factor, as in SIM, excess returns can be decomposed to: \begin{equation} \rho_{ij}=\frac{\beta_{j}\beta_{i}\sigma_{M}^{2}}{\sigma_{i}\sigma_{j}} \end{equation}

\(r_i\)
i-th asset return
\(\beta_i\)
i-th asset return beta
\(\sigma_i\)
i-th asset return standard deviation (square root of variance)


Function Reference
position_correlationMatrix, position_correlation