A Fundamentally Weighted Broad-Based Fixed-Income Index

December 30, 2011

A Fundamentally Weighted Broad-Based Fixed-Income Index

At the bare minimum, a benchmark index should measure the performance of an investment strategy or asset class. But as far as investors are concerned, although most fixed-income indexes meet this threadbare requirement, they fail miserably on most other counts. For starters, cap-weighted fixed-income indexes deliver suboptimal portfolio allocations, impairing performance. Many bond indexes also fail to provide adequate investability and liquidity. In addition, many bond indexes also show extremely high turnover, lack of adequate diversification and unstable risk characteristics. Finally, it is difficult to properly determine the weight of many issues in a given index because bonds are traded over the counter, oftentimes at infrequent intervals. Thus a key variable for the index weight—the price of the bond—is not known with precision.

In this paper we show that, in the presence of real-world frictions and imperfect capital markets, a cap-weighted aggregate global bond portfolio leads to suboptimal allocations and performance. In contrast, a simulated global broad bond index that is fundamentally weighted (“fundamentally weighted portfolio”) and that selects in a liquid, representative fashion, creates superior performance over time, based on simulated performance data since 1997. The six components of our broad bond index all show outperformance in the range of 75 bps to over 400 bps annually, and the broad portfolio provides 110 bps outperformance over a cap-weighted benchmark of the same bonds, and 161 bps annual outperformance over the Barclays Capital Global Aggregate Index.1 Additionally, these fundamentally weighted portfolios provide improved liquidity and investability, thus representing achievable returns.

Theoretical Overview
If the bond markets are less than perfectly efficient, the resulting mispricings will result in a return drag embedded in the cap-weighted bond indexes. This phenomenon has been shown in the equity markets by Arnott, Hsu and Moore (2005); Hsu (2006); and in the fixed-income markets by Arnott, Hsu, Li and Shepherd (2010). The optimality of cap-weighted indexes as investment options depends crucially on the assumptions of perfectly efficient capital markets and rational investors with mean-variance utility preferences. As we begin to weaken these assumptions, market mispricings enter into the prices we observe in the marketplace. Because a cap-weighted portfolio bases its constituent weights on price, there will be a systematic correlation between pricing errors and portfolio weights that leads to suboptimal allocations and performance.

Additionally, traditional fixed-income indexes are exposed to the “bums” problem, as noted by Enderle, Pope and Siegel (2003). As a corporation or country issues more and more debt, it becomes a bigger and bigger part of the index. Because traditional indexes are weighted by size of issuance, these heavily indebted “bums” will dominate the index weights. From a benchmarking standpoint, that may not be a concern: The indexes are, after all, reflecting the current opportunity set. However, from the investor’s perspective, why should we allocate a higher portion of our portfolio to big debtors just because they wish to borrow more?

We view uncertainty about default risk and inflation rates as the primary source of market inefficiencies.2 If market participants have properly estimated the amount of default risk to which they are exposed by holding a bond, then the current yield exactly compensates them for holding that risk. However, if they underestimate the default risk, then they end up holding a bond with too low of a yield (and, thus, too high of a price); if they overestimate the risk of default, they hold a bond with an overly high yield and too low of a price. Now we see how the return drag enters into standard indexes.

Because returns are calculated based on the relative dollar value of each holding, those bonds that trade too rich will have a higher price and, thus, a higher weight, while those bonds that trade cheaply will have a lower price and, therefore, a lower weight. The cap-weighted index will have a perfect correlation between the pricing errors and its portfolio weights, systematically overweighting overvalued bonds and underweighting undervalued bonds. The index is overexposed to bonds where the default risk outweighs the yield, and underexposed to bonds where the premium yield exceeds the default risk. We may not know which bonds these are a priori, but if these mispriced bonds exist in the marketplace, this systematic correlation will always hold.



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