Derivative-Free Replication of a Bond Benchmark with a Fraction of the Portfolio

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. Our main contribution lies in the derivative-free approach to replication. The constraints can, however, be adapted to accommodate the use of interest rate and bond futures. The methodology proposed here responds to the particular needs of the asset management industry where clients unwilling to invest in derivatives can still benefit from replicating a traditional investment in a bond index with a fraction of the portfolio according to their 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 1st January, 2008 to 3rd 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%. These results highlight our contribution of a generic and intuitive yet robust approach that is still not employed as the industry standard