Asset Correlation Estimation for Inhomogeneous Exposure Pools

A possible data source for the estimation of asset correlations is default time series. This study investigates the systematic error that is made if the exposure pool underlying a default time series is assumed to be homogeneous when in reality it is not. We find that the asset correlation will always be underestimated if homogeneity with respect to the probability of default (PD) is wrongly assumed, and the error is the larger the more spread out the PD is within the exposure pool. If the exposure pool is inhomogeneous with respect to the asset correlation itself then the error may be going in both directions, but for most PD- and asset correlation ranges relevant in practice the asset correlation is systematically underestimated. Both effects stack up and the error tends to become even larger if in addition a negative correlation between asset correlation and PD is assumed, which is plausible in many circumstances and consistent with the Basel RWA formula. It is argued that the generic inhomogeneity effect described is one of the reasons why asset correlations measured from default data tend to be lower than asset correlations derived from asset value data.