Defining Residual Risk-Sharing Opportunities: Pooling World Income Components

We construct a new method of decomposing the variance of national incomes into components in such a way as to indicate the most important 'residual' risk-sharing opportunities among peoples of the world. The risk-sharing opportunities we study are nonsystematic risk-sharing opportunities. These are the risk-sharing opportunities that remain if systematic risk were already shared, see Athanasoulis and Shiller (2000). The new method developed here uses a simpler approach to deriving the components based on pure variance reduction. With the new method, the income component securities are derived in terms of eigenvectors of a transformed variance matrix of world incomes, but with this method the transformation is to use the residuals when incomes are regressed on world income instead of deviations of incomes from average world income as in Athanasoulis and Shiller (2001). The method is applied using Summers-Heston (1991)data on national incomes for large countries 1950-1990, using two different methods of estimating variances.