Swedroe: Factors In Fixed Income

A look at how factors manifest in the world of bonds.

Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

Since Eugene Fama and Kenneth French’s 1992 publication of the paper “The Cross-Section of Expected Stock Returns,” factor-based (style) investing has been applied in equity markets. Not only has it become increasingly popular, with massive flows into “smart beta” products, it has also been extended to long/short, market-neutral applications and across bonds, currencies and commodities.

Despite style investing’s popularity, comparatively little has appeared in the literature, or been put into practice by publicly available funds, as it relates to the enormous bond markets.

Jordan Brooks, Diogo Palhares and Scott Richardson of AQR Capital Management add to our understanding in this area with the study “Style Investing in Fixed Income,” which will appear in a forthcoming issue of the Journal of Portfolio Management. They applied the value, momentum, carry and defensive style premiums to country and maturity selection across global government bond markets and to individual issuer selection across U.S. investment-grade and high-yield corporate credits.


Value is the tendency for relatively cheap assets to outperform relatively expensive assets. To determine value, the authors measured market “prices” as yields in the case of government bonds and as credit spreads in the case of corporate bonds.

For government bonds, they used a “real yield” metric, comparing nominal yields against maturity-matched inflation expectations from survey-based forecasts from Consensus Economics. Government bonds with higher (lower) real yields relative to their peers are cheap (expensive).

For corporate bonds, they compared credit-option-adjusted spreads against two fundamental anchors designed to capture the “risk” that the company may migrate to a poorer credit quality.

The first fundamental anchor is a structural model that measures the bond’s “distance to default,” which reflects the number of standard deviations the asset value is away from the default threshold. The second fundamental anchor is an empirical model based on a regression of the spread on duration, rating and return volatility. In both cases, a corporate bond is deemed cheap (expensive) when the credit spread is high (low) relative to the respective fundamental anchor.


Momentum is the tendency for an asset’s recent performance to continue in the near future. For government bonds, Brooks, Palhares and Richardson used the prior 12-month excess return. For corporate bonds, they used an equal-weighted combination of the bond’s prior six-month credit excess returns and, for public issuers, the bond’s prior 12-month returns. While the results were not sensitive to the choice of lagged 12-month excess credit returns, the authors chose the prior six-month period to increase data coverage.


Carry is the tendency for higher-yielding assets to outperform lower-yielding assets. It assumes a return if relative prices do not change.


Defensive (quality) is the tendency of safer, lower-risk assets to deliver higher risk-adjusted returns than their low-quality, higher-risk counterparts. For government bonds, within each country, the authors’ position goes long short-dated bonds and shorts a duration-equivalent amount of long-dated bonds. For corporate bonds, they also favor low duration, but include two additional indicators based on profitability (gross profits over assets) and leverage (measured by the ratio of net debt to the sum of net debt and market equity).


More Methodology

Brooks, Palhares and Richardson’s sample of government bonds includes all bonds covered by the J.P. Morgan Government Bond Index (GBI). The GBI is a market-cap-weighted index of all liquid government bonds across 13 developed markets (Australia, Belgium, Canada, Denmark, France, Germany, Italy, Japan, Netherlands, Spain, Sweden, U.K. and the U.S.). They partitioned bonds in each country into three time-to-maturity buckets: one- to five-year (short-term), five- to 10-year (medium-term) and 10- to 30-year (long-term), weighting individual bonds by market cap within each.

The authors apply the value, momentum and carry styles across countries, while defensive is a pure maturity bet. Value (likewise momentum and carry) favors countries with relatively high real yields; the defensive strategy favors shorter-maturity bonds across all countries.

For value, momentum and carry, the authors formed “country assets” by taking an equal-duration-weighted average across the three maturity buckets within each country. They then scaled all country assets to the same duration. For each country-maturity bucket, they computed real yield (yield minus maturity-matched inflation expectations), term spread (yield net of financing) and price momentum (past 12-month excess return). For each style, they combined the measures across maturities to come up with a country-level style factor, with each country-level style factor having the same overall duration.

At the beginning of each month, for each style, the authors formed tercile portfolios of country assets based on their respective country style metrics and created a position that goes long the most-attractive third tercile and shorts the least-attractive first tercile. For the defensive style—which, again, is a pure maturity bet—the position goes long the third-tercile short maturities and short the first-tercile long maturities, equal-weighting countries. Their “COMBO” government bond portfolios are equally weighted across all four styles and scaled to the same duration so the long/short portfolios each target similar levels of risk ex-ante.

Brooks, Palhares and Richardson’s data sample of investment-grade bonds are the constituents of the Bank of America Merrill Lynch U.S. Corporate Master Index, and their sample of high-yield bonds are the constituents of the Bank of America Merrill Lynch U.S. High Yield Master Index. The data sample covers the period January 1996 through June 2017.

Unpacking The Findings

Following is a summary of the authors’ findings:

  • There are consistent monotonic patterns between bottom/middle/top-ranked countries for all styles within government as well as corporate bonds.
  • With the single exception of carry in corporate bonds, there is a clear monotonic pattern in Sharpe ratios as you move from the least- to most-attractive style portfolio, and particularly so for the COMBO portfolio. Despite higher returns for corporate bonds with the widest credit spreads, the volatility of credit excess returns dampens the risk-adjusted return earned by an investor for this carry exposure.
  • In government bonds, all styles performed well, whether measured by Sharpe ratio or alpha to the cap-weighted J.P. Morgan government bond index. The exception was an insignificant alpha for the momentum style portfolio. The results were similar for corporate bonds, with the exception of an insignificant alpha for carry, which is not surprising, as carry is directly related to the credit risk premium. However, once again, the COMBO portfolio—which includes carry—produced the highest Sharpe ratio.
  • Consistent with past research documenting the diversification benefit of investing across styles and asset classes, there is strong evidence of low correlation across style portfolios both within and across government and corporate bonds. The COMBO portfolio produced the highest Sharpe ratios.
  • Demonstrating portfolio diversification benefits, the COMBO portfolio has no significant exposure to any traditional equity or bond risk premiums—whether credit risk premium, equity risk premium or term premium—nor does it provide much exposure to equity factors such as size, value, momentum or quality.
  • Fixed-income style portfolios exhibit little sensitivity to various macroeconomic state variables about which investors typically are concerned (such as shocks to inflation, shocks to economic growth, shocks to real yields, shocks to liquidity and shocks to volatility), and are meaningfully less sensitive to these variables than the underlying asset classes themselves.

The bottom line is that Brooks, Palhares and Richardson demonstrated that applying the style premiums—value, momentum, carry and defensive—identified in other asset classes would have enhanced returns in various fixed-income markets over the past two decades.


They concluded: “Our empirical analysis suggests a powerful role for style based investing in fixed income.” They add: “Style investing can be applied through long-only tilts or through long/short strategies. Both can make sense. Long/short strategies provide better diversification but investor constraints and limited shorting ability/capacity may make the long-only path more realistic for many investors.”

It’s important to note, as the authors did, that their results are gross of trading costs and fees. This is especially important for corporate bonds, as trading costs are relatively high, and shorting can be hard.

They observe, however, that in the August 2017 update of the study “Common Factors in Corporate Bond Returns,” Palhares and Richardson, along with co-author Ronen Israel, examined whether a long-only portfolio can be constructed with optimal exposure to styles while respecting the challenges of trading corporate bonds.

They found that even after explicitly accounting for trade sizes, turnover constraints and expected costs to trade, a long-only corporate bond portfolio yields an active return of 2.20% annualized, with a Sharpe ratio of 1.03, net of assumed, realistic trading costs.


While factor-based, style investing in equities has become popular, its adoption has been much slower in other asset classes, including fixed income. Brooks, Palhares and Richardson demonstrate that style investing in bonds can also be applied. Thanks to the documented low or negative correlations between style premiums and market premiums, and low sensitivity to macroeconomic and financial market environments, fixed-income style investing can provide diversification benefits—as well as potentially enhance returns—for traditional, long-only stock and bond portfolios.

AQR implements style investing in fixed income in its Style Premia Alternative Fund (QSPRX) and its Alternative Risk Premia Fund (QRPRX), the latter of which is tax-managed and, thus, generally more appropriate for holding in taxable accounts. QSPRX provides exposure to the value, momentum, defensive and carry factors across four asset classes (stocks, bonds, commodities and currencies). QRPRX provides exposure to six factors (adding time-series momentum, also called trend, and the variance risk premium) across three asset classes (stocks, bonds and currencies).* (Full disclosure: My firm, Buckingham Strategic Wealth, recommends AQR funds in constructing client portfolios.)


* Discussion of QSPRX and QRPRX is provided for informational purposes only and is not intended to serve as specific investment or financial advice. This discussion does not constitute a recommendation to purchase a single specific security, and it should not be assumed that the securities referenced herein were or will prove to be profitable. Prior to making any investment, an investor should carefully consider the fund’s risks and investment objectives and evaluate all offering materials and other documents associated with the investment.


Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.

Larry Swedroe is a principal and the director of research for Buckingham Strategic Wealth, an independent member of the BAM Alliance. Previously, he was vice chairman of Prudential Home Mortgage.