Long–short extension strategies, such as 130–30, allow portfolio
managers to reduce the implementation inefficiencies associated with the
long-only constraint. Ample research using benchmark-specific and time
period–specific numerical analyses indicates that long–short
extensions increase expected information ratios. What is lacking is a general
theory or mathematical model of long–short extensions based on underlying
assumptions about benchmark composition, the security covariance matrix, and the
portfolio optimization process. The analytical model developed here identifies
the roles various parameters play in determining the size of the
long–short extension. The impact of changes in the model parameters over
time and across markets is illustrated with the use of historical and current
equity benchmark data.