Long/Short Extensions: How Much is Enough?
32 Pages Posted: 23 Jul 2007
Date Written: September 2007
Long/short ratios like 130/30 are an increasingly common way for the investment management industry to describe portfolios that are released from the long-only constraint. The ratio of a portfolio's long and short positions to net notional value is often the primary description of the strategy, replacing more traditional measures such as active risk. Unfortunately, managers and their clients may not understand the underlying parameters associated with the value of the long/short ratio, beyond the general recognition that the size of the extensions (e.g., 30 percent) and active risk are positively related. We develop a mathematical model to identify the factors that determine the size of the long/short extension, and illustrate the relationships using historical data on the S&P 500 benchmark, as well as current data on a variety of domestic and international equity benchmarks. The model confirms the basic intuition that the size of the long/short extension increases with the active risk target chosen by the manager, and decreases with the estimated costs of shorting. In addition, the model shows that the expected short extension for an unconstrained portfolio depends on average security risk, average pair-wise security correlation, the security weight concentration of the benchmark, the number of investable securities, and the assumed accuracy of security return forecasts. The model provides important perspectives on long/short strategies as the investment management industry continues to move away from more traditional long-only portfolios.
Keywords: Portfolio Management, Short Selling, Portfolio Optimization
JEL Classification: G11, G23
Suggested Citation: Suggested Citation