Long-short extensions: How much is enough?

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.