Equities

Estimating VARs for equity positions has one fundamental difference compared with estimating VARs for interest rate and foreign exchange positions in that there is no underlying risk factor that can be simply used for aggregation purposes.
A bank may have holdings in very many different debt instruments of similar duration whose price changes can be determined in a linear way from a single underlying risk factor, such as a yield taken from a specific point on the yield curve. Foreign exchange positions change with foreign exchange rates. In more formal terms we can say that the changes in the value of vanilla interest rate and foreign exchange products have perfect, or close to perfect, correlations with changes in their underlying risk factor.
This is not the case with equity positions, where stock price changes are not perfectly correlated with the market. If we take our two stocks, Blue Sky’s returns have a relatively high correlation with market returns while that of Bore Inc.’s is low.