Numeraire Portfolio Tests of International Government Bond Market Integration and Redundancy

September 2002

This paper proposes a new way to test whether international government bond markets are integrated and to measure the economic gains from diversifying across them. Most earlier studies call markets integrated when a standard asset pricing model cannot be rejected for assets from all of them, an approach that both depends on the currency chosen to measure returns and tends to reject integration whenever the pricing model fits poorly. This paper instead defines markets as integrated when, ignoring frictions, they offer no arbitrage opportunities, and it detects arbitrage using a numeraire portfolio, a portfolio whose returns can be used to price every asset in the set. A central advantage of this approach is that its tests do not depend on the currency in which returns are denominated, nor on whether returns are real or nominal. Applying the method to government bond markets in the United States, the United Kingdom, and Germany, the paper tests integration, measures how redundant each market is given access to the others, and estimates the gains a diversifying investor would realize. It is written for a technical audience of researchers, allocators, and quantitatively minded fixed income investors.

What This Paper Examines

• A definition of market integration based on the absence of arbitrage, rather than on a specific asset pricing model.
• How a numeraire portfolio provides a currency-independent test of integration.
• Whether the US, UK, and German government bond markets are integrated with one another.
• How redundant each market is given access to the others, measured through implied transaction-cost thresholds.
• How large the diversification gains from costless access to foreign bond markets are for a log-utility investor.

Key Findings

• The US, UK, and German government bond markets are integrated. A numeraire portfolio can price the bonds across all three markets and every combination of them, which means the analysis detects no arbitrage opportunities.
• The tests do not depend on the choice of currency. Because the measures are built from ratios of returns, they are invariant to the currency of denomination and to real-versus-nominal choices, unlike conventional integration tests.
• Small transaction costs can induce a complete home bias. For a log-utility bond investor, trading costs of only a few basis points would be enough to make holding foreign bonds unattractive, which helps rationalize observed home bias.
• Yet costless access to foreign bond markets offers economically large gains. A log-utility investor would realize meaningful, if only marginally significant, utility gains from free access to the foreign markets, because capturing them requires large leveraged positions.
• The numeraire-based discount factor is well-behaved where linear ones are not. By construction it stays positive, so it can rule out arbitrage, whereas conventional linear discount factors estimated from the same bonds can turn negative and cannot.

The Authors

This paper is part of the long lineage of quantitative research that Versor’s founders began earlier in their careers and continue to build on at the firm today.

Ludger Hentschel, Founding Partner, Investment Advisor

Ludger Hentschel joined Versor Investments as a Founding Partner and is based in New York. Ludger has over 20 years of experience in quantitative research and investing.

Versor’s founders co-authored this research with Jangkoo Kang and John B. Long Jr., a colleague at the firm where this work was originally conducted.

Disclaimer: Past performance is not necessarily indicative of future results. Not an offer to sell or a solicitation of any type with respect to any securities or financial products.

Methodology: The paper defines integration as the absence of arbitrage and tests it by searching for a numeraire portfolio, following Long (1990), whose gross return is always positive and under which each asset’s expected numeraire-denominated gross return equals one. A penalty-based numerical procedure enforces the positivity requirement during estimation.

The data are monthly returns from January 1974 to December 1993 on artificial zero-coupon bonds with maturities from one month to ten years, constructed from all outstanding government bonds in the United States, the United Kingdom, and Germany. Two currency-independent measures follow from the same framework: numeraire-denominated excess returns, interpreted as the implied bid-ask spread that would keep a log-utility investor out of a foreign bond, and certainty-equivalent wealth gains from access to larger markets. Inference uses Newey-West adjusted standard errors and joint GMM tests.