In Search of the Perfect Hedge Underlying

This report attempts to answer the question: What underlying portfolio should one use to hedge an active fund? We introduce a framework which allows us to conduct analysis on simulated realistic active portfolios in order to build intuition as to how hedge mismatch error affects the level of protection from a given hedge. We show that for typical market conditions, hedge effectiveness improves dramatically when using a hedge portfolio that more accurately reflects the underlying portfolio. This has clear consequences for using generic index options to hedge highly active portfolios. We also showcase several active return and tracking error decompositions that allow one to precisely quantify and thus manage the sources of risk and rewards within a given portfolio. We then discuss a mixed integer quadratic programming formulation that enables us to search across a large investment universe in order to find the subset of stocks that most closely replicates a given portfolio's performance, whilst simultaneously complying with realistic market constraints. Motivated by these three elements, we introduce several alternative hedging methods for the fund manager to implement a better hedge for their active portfolio. In this report, we focus specifically on the use of long-only and long/short custom basket options as a means of creating an appropriate portfolio hedge