Systematic Fixed Income: A Closer Look


This page includes sophisticated financial research and educational information that is intended only for investment professionals and other knowledgeable institutional investors who are capable of evaluating investment risks and making their own investment decisions. It should not be interpreted as investment advice or as a recommendation of an particular security, strategy or investment product.


Credit Risk Premium

Corporate bonds are an important component of many fixed income portfolios because they offer exposure to the credit risk premium—an additional source of returns beyond those from default-free government bonds. Yet though it seems intuitive to expect a higher return for bearing corporate default risk, past research has found limited evidence to support it. Why the disconnect? Is there a premium for investing in credit, and how large has it been?

Research on this topic has traditionally looked at the simple difference between long-term corporate bond returns and long-term government bond returns. But this simple difference misses a key fact: corporate bonds tend to have lower interest rate durations than government bonds. Correcting for this, we find strong evidence, across many decades and markets, of a credit risk premium whose risk-adjusted returns are in line with other major market risk premia.

Importantly for investors, we find the credit risk premium to be different from the commonly known term (or bond) premium and equity risk premium. That means the addition of corporate bonds—a source of return with unique risk characteristics—may help investors build more efficient portfolios.

Comparison of Risk Premia Sharpe Ratios and Correlations
Source: AQR, Ibbotson, Barclays. The U.S. Credit Risk Premium (Credit) is the excess return of U.S. corporate bonds over duration-matched U.S. Treasuries. The U.S. Term Risk Premium (Term) is the excess return of U.S. Treasuries over 30-day T-bills. The U.S Equity Risk Premium (Equity) is the excess return of U.S. large cap equities over 30-day T-bills. See below for more details on the construction of the three return series. Sharpe ratios are based on these monthly excess returns and their volatilities. Diversification does not eliminate the risk of experiencing investment losses. Past performance is not a guarantee of future performance. The U.S. corporate bond excess returns are based on Ibbotson’s data from January 1936 through July 1988 and Barclays’ data from August 1988 through December 2014. This measure of credit excess returns is with respect to duration matched government bond returns. The U.S. Treasuries excess returns are the difference between either Ibbotson’s U.S. Long-Term Government bonds for the January 1936 through December 1972 period or Barclays U.S. Treasury index for the January 1973 through December 2014 period and the U.S. 30-day Treasury Bill returns. The U.S. large cap equity excess returns are the difference between the returns of the S&P Composite index, which later becomes the S&P 500 index and the U.S. 30-day Treasury Bill returns. See “The Credit Risk Premium” by Asvanunt and Richardson (2016) for more details.

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Factors in Fixed Income Markets 

Momentum, value and other factors exist not only in equities—we also find evidence of their efficacy in government and corporate bonds. The notion of each factor in bonds shares much with its counterparts in equities.

Of course, the implementation will differ somewhat. Value in bonds aims to distinguish cheap versus expensive bonds by using a fundamental anchor to measure against, but the specific metrics differ from those used for equities. In government bonds, for example, value can use yield-based measures: observed yield relative to an “anchor” of inflation expectations. The intuition for corporates is similar: value might consider the credit spread (rather than pure yield) relative to a fundamental anchor such as default expectations.

Factors in fixed income markets have decades of evidence to support their inclusion in many portfolios. These factors also have delivered returns that are diversifying to one another, suggesting a multi-factor approach may lead to even better results. 

Chart of Global Government and U S Corporate Bonds Annual Excess Returns Sorted by Styles
Source: AQR, J.P. Morgan, Consensus Economics, Bank of America Merrill Lynch. Global government bond portfolios are based on a hypothetical country allocation strategy across 13 developed markets and three maturity buckets using one simple indicator per style, with monthly rebalancing. All bonds are ranked along each style and sorted into terciles. Value, momentum and carry are applied across countries; defensive is applied across maturities within each country. All returns are excess of local cash. Within each tercile, the bonds are equal-weighted. U.S. Corporate bond portfolios are formed by ranking 1,300 bonds (that roughly comprise the Bank of America Merrill Lynch investment grade and high yield corporate bond indices) along each of four styles, and then sorting into quintiles. The first, third, and fifth quintiles are shown here. Within each quintile, bonds are value-weighted. All returns are excess of key-rates-duration-matched treasury portfolios. Please see below for more details on the construction of these portfolios. Past performance is not a guarantee of future performance.These are not the returns of an actual portfolio AQR managed and are for illustrative purposes only. 

Description of Data and Styles Used


Data: Government bonds include 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 markets (Australia, Belgium, Canada, Denmark, France, Germany, Italy, Japan, Netherlands, Spain, Sweden, U.K., U.S.). It excludes securities with time-to-maturity (TTM) of less than 12 months, illiquid securities, and securities with embedded optionality (e.g., convertible bonds). The GBI is sub-divided into two country-maturity partitions. We use the first, more coarse partition in this analysis, which divides bonds into 1yr-5yr TTM, 5yr-10yr TTM, and 10yr-30yr TTM. We sort the bonds into terciles based on the style metrics described below. The portfolios go long the top tercile and short the bottom tercile. Bonds are equal-weighted in each tercile. The Bank of America Merrill Lynch U.S. Corporate Master Index includes publicly-issued, fixed-rate, nonconvertible investment grade dollar-denominated, SEC-registered corporate debt having at least one year to maturity and an outstanding par value of at least $250 million. The Bank of America Merrill Lynch U.S. High Yield Master Index tracks the performance of below-investment-grade U.S. dollar-denominated corporate bonds publicly issued in the U.S. domestic market.

Styles: Value: Real yield (nominal bond yield minus maturity-matched consensus inflation forecast) Momentum: Past 12-month excess return Carry: Term spread (bond yield minus short-term yield) Defensive: Short duration (within country, buy short-dated bonds and sell duration-equivalent amount of long-dated bonds).


 Corporate bonds include 1,300 bonds that roughly comprise the Bank of America Merrill Lynch investment grade (U.S. Corporate Master) and high yield (U.S. High Yield Master) corporate bond indices. Of the 1,300, 600 are investment grade, and 700 are high yield bonds. We sort the bonds into quintiles based on the four style metrics described below. The portfolios go long the top quintile and short the bottom quintile. Bonds are value-weighted, not equal-weighted, within each quintile.

 Value: Averaging two indicators, both of which compare the current credit spread (see “OAS” under Carry) to a fundamental anchor. One anchor is a structural model which measures the bond’s “distance to default” (the number of standard deviations the asset value is away from the default threshold); another anchor is an empirical model (based on a regression of the spread on duration, rating and return volatility). Momentum: Averaging indicators based on the past six-month return of the corporate bond itself (in excess of Treasuries) and of the issuer’s equity. Carry: The option-adjusted spread (“OAS”) versus Treasuries, as estimated by Bank of America Merrill Lynch. Defensive: Averaging indicators based on profitability (gross profits over assets), short duration and low leverage (measured by the ratio of net debt to the sum of net debt and market equity).

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How Do Active Systematic Fixed Income Managers Invest?

Given multiple systematic sources of returns in fixed income markets, which do active bond managers actually harvest?

The answer varies across categories and from manager to manager, but we find exposure to credit tends to explain a lot. Taking the Core-Plus bond category as an example, we find about 95 percent of active returns can be attributed to exposure to high-yield credit over the past 10 years.

What this means for many investors is that seemingly diversified allocations across multiple fixed income funds might result in one active bet on credit and much smaller exposures, if any, on other factors such as value or momentum—ones that may be as diversifying and have as much evidence supporting their efficacy. In our view, these investors may be missing out on an opportunity to outperform.

Core Plus Median Excess Return vs. High Yield Index Excess Return
Source: AQR, eVestment Alliance. Core-Plus refer to eVestment’s categories, and manager returns are pulled from their database. eVestment data is input by the respective managers in each category. Returns are shown in USD. The HY Index is the Bloomberg Barclays US Corporate High Yield Index, which measures the USD-denominated, high yield, fixed-rate corporate bond market. Securities are classified as high yield if the middle rating of Moody’s, Fitch and S&P is Ba1/BB+/BB+ or below. These are not the returns of an actual portfolio AQR managed and are for illustrative purposes only. Past performance is not a guarantee of future performance.

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Journal Article

Style Investing in Fixed Income Markets

A disciplined, systematic approach to over/underweight securities based on well-known factors, or styles, such as value, momentum, carry and defensive (sometimes called “quality”), can offer alternative sources of outperformance not only within equities, where these ideas have long been studied and applied, but also within fixed income markets.

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This information is for informational purposes only and not intended to, and does not relate specifically to any investment strategy or product that AQR offers. It is being provided merely to provide a framework to assist in the implementation of an investor’s own analysis and an investor’s own view on the topic discussed herein.


Past performance is not a guarantee of future results. Diversification does not eliminate the risk of experiencing investment loss. Broad-based securities indices are unmanaged and are not subject to fees and expenses typically associated with managed accounts or investment funds. Investments cannot be made directly in an index.


HYPOTHETICAL PERFORMANCE RESULTS HAVE MANY INHERENT LIMITATIONS, SOME OF WHICH, BUT NOT ALL, ARE DESCRIBED HEREIN. NO REPRESENTATION IS BEING MADE THAT ANY FUND OR ACCOUNT WILL OR IS LIKELY TO ACHIEVE PROFITS OR LOSSES SIMILAR TO THOSE SHOWN HEREIN. IN FACT, THERE ARE FREQUENTLY SHARP DIFFERENCES BETWEEN HYPOTHETICAL PERFORMANCE RESULTS AND THE ACTUAL RESULTS SUBSEQUENTLY REALIZED BY ANY PARTICULAR TRADING PROGRAM. ONE OF THE LIMITATIONS OF HYPOTHETICAL PERFORMANCE RESULTS IS THAT THEY ARE GENERALLY PREPARED WITH THE BENEFIT OF HINDSIGHT. IN ADDITION, HYPOTHETICAL TRADING DOES NOT INVOLVE FINANCIAL RISK, AND NO HYPOTHETICAL TRADING RECORD CAN COMPLETELY ACCOUNT FOR THE IMPACT OF FINANCIAL RISK IN ACTUAL TRADING. FOR EXAMPLE, THE ABILITY TO WITHSTAND LOSSES OR TO ADHERE TO A PARTICULAR TRADING PROGRAM IN SPITE OF TRADING LOSSES ARE MATERIAL POINTS THAT CAN ADVERSELY AFFECT ACTUAL TRADING RESULTS. THERE ARE NUMEROUS OTHER FACTORS RELATED TO THE MARKETS IN GENERAL OR TO THE IMPLEMENTATION OF ANY SPECIFIC TRADING PROGRAM WHICH CANNOT BE FULLY ACCOUNTED FOR IN THE PREPARATION OF HYPOTHETICAL PERFORMANCE RESULTS, ALL OF WHICH CAN ADVERSELY AFFECT ACTUAL TRADING RESULTS. The hypothetical performance results contained herein represent the application of the quantitative models as currently in effect on the date first written above and there can be no assurance that the models will remain the same in the future or that an application of the current models in the future will produce similar results because the relevant market and economic conditions that prevailed during the hypothetical performance period will not necessarily recur.  There are numerous other factors related to the markets in general or to the implementation of any specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results, all of which can adversely affect actual trading results. Discounting factors may be applied to reduce suspected anomalies.  This backtest’s return, for this period, may vary depending on the date it is run.


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