Measuring Asset Association and Dependence
THE SAMPLE COVARIANCE MATRIX
Ascertaining the association between assets is one of the fundamental considerations of risk analysis. Security association is dependent on many factors, but estimating their covariance has historically been the objective for asset managers, pension owners, banks, insurers, and firms that hold assets against liabilities of some sort. Regardless of the asset class, if one can ascertain a reliable estimate of the association between assets (assuming stationarity), one is at least halfway to determining the risk of a portfolio holding such assets.
Before we discuss measures of asset association, however, first we draw attention to the importance of stationarity. Stationarity is what makes risk estimates useful. Without it, the estimate itself is unreliable. It also implies that the correlation and nonlinear dependence structure between securities exists for a long enough period of time that an estimate of risk based on the historical period most recently experienced will persist as far into the future as the horizon is forecasted. This persistence through time for both idiosyncratic volatility and asset association is a necessary condition for risk modeling to be dependable.
It’s the structural dislocation of asset association that is the domain of so-called Black Swans. In simple terms, when major ...