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The primary role of an index fund manager is to track the fund’s designated benchmark. In practice, it is difficult to obtain near-zero tracking error, unless the manager holds every single security in the benchmark and perfectly synchronizes portfolio rebalancing activity with benchmark changes at minimal cost.
Holding every security in the benchmark can be challenging in liquid markets, such as exchange-traded equities. In less liquid markets, such as the over-the-counter bond markets, it is virtually impossible. Because of the discontinuous liquidity and wide bid/offer spreads often present in the OTC fixed-income markets, holding more securities may reduce tracking error in theory, but may also ultimately result in much higher transaction costs.
Many fixed-income index fund managers seek to address this problem by holding an optimized subset of available, liquid securities. This strategy strives to balance market risk and portfolio management costs using risk models and optimization techniques to locate the intersection of projected tracking error and projected transaction costs. In short, the manager will attempt to drive projected tracking error down to the point where any further decreases would be outweighed by increases in projected transaction costs.
However, this conventional solution does not account for the “short volatility” risk inherent in sampled portfolios. Optimized portfolios rely heavily on assumptions about asset volatilities, correlations and transaction costs. Rising volatility often leads to a destabilization of correlations, an increase in idiosyncratic risk and a widening in bid/offer spreads. The combined effects (and their correlation with each other) often result in higher-than-expected realized tracking error in an environment of rising volatility.
In this paper, we test and quantify trade-offs among portfolio solutions through historical market cycles to identify a portfolio construction and management approach that minimizes realized tracking error across a range of volatility regimes and market conditions.
Portfolio Construction And Management
Fixed-income index portfolio managers strive to minimize realized tracking error by targeting projected tracking error (PTE) and transaction costs. PTE is typically defined as the forecast standard deviation of the performance differential between a portfolio and its benchmark. This projected variation is based on a risk model and specific assumptions about market parameters such as correlations and volatility. PTE consists of common-factor risk (i.e., risk that is common to all securities and therefore cannot be diversified away on an absolute basis) and idiosyncratic (or, security-specific) risk. While common-factor risk relative to a benchmark may be eliminated by holding a relatively small sample of securities, reducing idiosyncratic risk relative to a benchmark is far more difficult and costly because a significantly larger sample set of securities may be necessary. The larger the sample size, the greater the proportion of less liquid securities, which, in turn, increases transaction costs.
Traditional optimized portfolio construction strategies rely heavily on the stability of correlations among portfolio constituents (e.g., constructing a portfolio to minimize tracking error based on a historical covariance matrix). The challenge with this approach is that shifts in correlation often invalidate the original optimized solution. As a result, the portfolio manager is forced to choose between incurring higher transaction costs in order to rebalance to the new optimized solution or facing higher potential tracking error by choosing not to rebalance.1 Overreliance on correlations—which the financial crisis proved is not an advisable practice—can be mitigated by employing rigorous stratified sampling techniques to construct index tracking portfolios. Stratified sampling seeks to identify and quantify index risk exposures that are not dependent on correlation assumptions and can be matched through judicious portfolio construction. A portfolio construction approach based on stratified sampling techniques will potentially be more stable and less vulnerable to sudden shifts in asset correlations during market dislocations.
Shifts in correlation often occur in an environment of rising volatility, which also may result in an increase in idiosyncratic risk due to an increase in sampling error. If a portfolio manager is holding a subset of securities relative to the benchmark in an optimized portfolio (and is therefore exposed to idiosyncratic risk because not all benchmark holdings are represented), higher volatility will likely result in higher sampling error. Conversely, at the limit, zero volatility should result in zero sampling error.
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2012
