Coefficient of determination in a simultaneous equation model: A pedagogic note

The simultaneity of the market for securities has been recognized by a number of finance authors. Simkowitz and Jones 10] advocate the use of a simultaneous equation system to capture some of the relationships among the securities in a homogeneous set. Simkowitz and Logue 11], and Jones and Simkowitz 6], have performed studies using a simultaneous equation system in a capital asset pricing framework. Marcis and Smith 9] call for the use of the simultaneous methodology when there is a strong residual correlation between securities. Simultaneous equation systems have been used in other areas of finance by authors such as Barnea 1], Herbst 5], and Logue and Lindvall 8]. This note explores how anomalies concerning the coefficient of determination (R²) mentioned in previous research could have occured. Conditions under which the (R²) does not have its usual properties and an example is given.