Integrated Simulation and Optimization Models for Tracking Indices of Fixed-Income Securities

Abstract

Increasing performance pressures on fixed-income managers have led to a search for new and creative ways to add to portfolio returns. The largest pension plan sponsors, insurance companies, foundations, and money management firms are using indexed portfolios as their fixed-income assets management strategies since the late 1970s. Tracking a fixed-income index is a difficult task due to transaction costs, portfolio size and diversification restrictions, liquidity requirements, bid/ask spreads, etc. This paper develops an integrated simulation and optimization approach for tracking fixed-income indices. The model was implemented at Metropolitan Life Insurance Company. We introduce a simulation model for generating scenarios of holding period returns of the securities in the index. Then we develop optimization models to select a portfolio that tracks the index. The models penalize downside deviations of the portfolio return from the index. The developed framework is used to track the Salomon Brothers Mortgage Index. In backtesting over the period 1989–1991, the models outperformed the index by 50bp. Underperformance never exceeded more than −5bp in any single month. A small tracking error was also observed during the recent months that the model has been in use.