Optimizing the Tracking Error of Fixed-Income Index Funds
Authors: Stephen Laipply, Christopher Woida
Source: Journal of Indexes
Date: January/February 2012
This article investigates how to best optimise the tracking-error of fixed-income index funds. It is generally not possible to hold all securities that constitute the reference index within the funds, particularly given that bond markets are often less liquid than equity markets. Most fixed-income index funds are thus made up of a subset of securities, identified as liquid and available, and optimised to minimise the tracking-error. However, the authors note that traditional portfolio optimisation strategies are based on a historical covariance matrix, assuming that the correlations between the portfolio constituents are stable over time. The recent financial crisis has illustrated the sudden change of volatility that may occur, causing an unexpected increase in index funds' tracking error.
In such a context of rising volatility, index fund managers were confronted with the dilemma of bearing higher transaction costs if choosing to rebalance their portfolio, or facing potentially higher tracking-error if they decided not to rebalance. This situation shows the need to adapt index replicating methodology. In this paper, the authors propose a portfolio construction approach that should minimise the realised tracking error for various volatility regimes and market conditions. The authors suggest that increasing ex post the size of the optimised sample of securities in a context of increasing volatility appears to be costly. On the other hand, holding a larger than prescribed optimised sample in a low volatility context may appear as a protection against a potential rise in market volatility. Similar to buying an insurance policy, this strategy has a cost if the volatility remains low, but it saves money in the case of rising volatility.
In order to illustrate their approach, the authors present two index fund replications in detail. The first index fund replicates the Barclays Capital U.S 1-3 Year Credit Index, which is made up of 600 securities. The backtest horizon covers the period from 2007 to 2010. The second example presents a fund benchmarked to the Barclays Capital U.S. Treasury 7-10 Year Bond Index, which is made up of roughly 20 securities. Replicating portfolios were simulated over the 2005-2010 period. The authors display the curve representing the portfolio transaction costs as a function of the portfolio projected tracking error for different size of optimised sample. This graphic should help the manager to select an optimal portfolio along the curve for different volatility regimes. With the first index, they take the example of a manager selecting a portfolio with 9 bps per year of mean projected tracking error. Then, they compare the cumulative realised tracking error of this portfolio with that of the full replication portfolio. It appears that the portfolio selected by the manager exhibits a lower cumulative realised tracking error than the portfolio that fully replicates the index. This result is explained by a good trade-off between transaction costs and projected tracking-error. The portfolio selected also appears to display a positive differential of performance with regards to its reference index. In the second case, the authors also reach the conclusion that selecting portfolios that offer a good compromise between transaction costs and projected tracking-error makes it possible to obtain an optimised index fund that better meets the tracking objectives than the fully replicating fund.
In conclusion, the authors argue that fixed-income index fund replication should take into account the various potential volatility regimes and their impact on fund tracking-error and transaction costs. According to the authors, such an approach can be compared to an insurance-based strategy that makes it possible to obtain the tightest realised tracking-error within the context of market conditions that may change over time. The choice of the optimal replicating portfolio is made by taking into account the projected tracking error (based on forecasts), the historical realised tracking error for different simulated portfolios (based on empirical data) and the transaction costs (based on both forecasts and empirical data). This approach differs from traditional optimisation, which is mainly based on historical correlations and static assumptions about idiosyncratic risk and transaction costs.