Non-fully invested derivative-free bond index replication

Abstract

The problem we address here is the replication of a bond benchmark when only a fraction of the portfolio is invested for the replication. Our methodology is based on a minimization of the tracking error subject to a set of constraints, namely (1) the fraction invested for the replication, (2) a no short selling constraint, and (3) a null active duration constraint, where the last one can be relaxed. The constraints can also be adapted to accommodate the use of interest rate and bond futures. Our main contribution, however, lies in the derivative-free approach to replication. It is very useful for managing assets when the use of derivatives is prohibited, for instance by certain investors. We can thus still benefit from replicating a traditional investment in a bond index with a fraction of the portfolio according to our risk appetite. The rest of the portfolio can be invested in alpha-portable strategies. An analysis without the use of derivatives over a period spanning from 1 January 2008 to 3 October 2011 shows that for 70% to 90% invested for the replication the annualized ex-ante tracking error can range from 0.41% to 0.07%. We use principal component analysis to extract the main drivers of the size of the tracking error, namely the volatility of and the differential between the yields in the objective function's covariance matrix of spot rates. These results highlight our contribution of a generic and intuitive yet robust approach to bond index replication.