Popular factors for government bond investment are “carry”, “momentum”, “value” and “defensive”. “Carry” depends on the steepness of the yield curve, which to some extent reflects aversion to risk and volatility. “Momentum” relates to medium-term directional trends, which in the case of fixed income are often propagated by fundamental economic changes. “Value” compares yields against a fundamental anchor, albeit some approaches are as rough as medium-term mean reversion. Finally, “defensive” seeks to benefit from some bonds’ status as a “safe haven” in crisis times. A historic analysis over the past 50 years suggests that all of these factors have been relevant in some form. Yet, without more precise and compelling macroeconomic rationale factor investing may lack stability of performance in the medium term. The scope for theory-guided improvement seems vast.

The below are excerpts from the paper. Headings and text in italics and brackets have been added.

The post ties in with this site’s summary of macro information efficiency.

### The popular bond factors

“We find evidence for four main investment styles [since 1969]… namely __carry, momentum, value and defensive__…Carry is ubiquitous and strongly linked with momentum…Value and reversal may provide further diversification…Defensive investing [refers to the feature that] bonds can provide a useful safe haven.”

*Carry and curve*

“The __spread between the yield of a government bond and the money market__ is a key source of carry…we refer to as `**simple carry**‘…[one should] also consider the additional benefits of rolling down the curve…Steepness and curvature are principal components of bond returns…Simple carry is an indicator of steepness and roll-down captures the shape on the long end.”

“Carry is a form of reward for holding a long-dated security…Long-term rates can be split into three components…[expected future short rates, risk premia and convexity premia]…__Steepness in the curve reflects expectations about short-term rates, aversion to risk and volatility__. If investors were not averse to risk and expected rates to remain stable, the curve would be slightly inverted and negatively convex due to a convexity premium.”

*On the subject of fixed income carry as trading signal view post here.*

*Momentum*

“Momentum…is __classically defined as the returns from the past 12 months__…[More recent research focuses on] average cross-over signals from various horizons [and] reviews different ways to measure trends efficiently.”

“With quantitative easing, central banks have played an increasing role in long-term interest rates. These changes are likely to have had a major impact on momentum patterns. The __wild fluctuations that occurred during the Great Inflation and the subsequent decrease in rates were not seen again__ and may not be as long as inflation expectations remain anchored.”

*Value, reversal, and fundamentals*

“Value involves setting market prices against a fundamental anchor. Surprising as it may be for an equity analyst, __there is no agreement in the fixed income community as to the right rate of return to apply for a fundamental assessment of value__. Relative value analysis is a more common approach and involves averages across sectors or buckets.”

“[A common approach is to] define value as the __change in yields over the last 5 years__, a classic reversal signal…Arguably, a measure of value is supposed to set a market price against a fundamental anchor [such as] inflation and economic growth.”

“With a __variety of approaches to the equilibrium and fair value of rates__, our data set covers the most classic ones, such as time patterns in yields, 10-year real rates and real rates versus growth. We also consider CPI inflation, GDP growth and unemployment, which are key ingredients for the main macro-finance models. These fundamental indicators are sometimes compared to reference levels, typically potential growth, non-accelerating rate of unemployment, or target inflation.”

*Defensive*

“__The counter-cyclicality in bond returns is a well-known phenomenon__…The liquidity premium in Treasury bonds is related to a flight to quality, which occurs when consumer confidence drops, foreign investors buy more Treasury bonds and investors broadly shift funds out of equities into money markets.”

“[Often] equity market shocks are associated with flight-to-quality effects, whereas both bonds and equities fall in a bond market shock. Therefore, the stock market volatility looks like a good guide for defensive bond investors.”

“The table [below] sums up the list of indicators for each style [and sub-styles].”

### Relevant indicators of the past

“[Our empirical analysis uses] __50 years of data__…Our first data set…`Great Moderation’ data set…starts in 1992 with daily quotes. We consider 10 year government bond futures for 6 countries, namely Australia, Canada, Germany, Japan, the UK and the US. These markets were selected for their high level of liquidity…Our second data set starts in 1969 for the same list of countries [excluding] Japan…We consider monthly data until 1992.”

“We broaden the range of possible factors and look to inductively select the most relevant ones…__We use a machine learning algorithm for selecting the best combination of variables__. Rather than measuring the explanatory power of a given set of variables, we infer from the data which combination of variables best forecasts bond returns.”

“[The figure below] displays the most relevant connections between the main variables. One group of variables is related to the market factor and another combines the fundamental variables. Carry is connected to the former group through growth gap and to the latter through momentum.”

“The __Lasso [least absolute shrinkage and selection operator] has been widely used for selecting variables__ and can be conveniently solved with a fast algorithm. The Lasso penalizes the fitting error by the sum of all betas, taken in absolute value. Our version of the adaptive Lasso adjusts each beta for its estimate in a simple linear regression model. This simple change allows the model to focus on the most significant variables. The penalty term is then weighted by a certain tuning parameter, which is selected by minimizing an adjusted Bayesian Information Criterion.”

“We find that __carry matters in time series for all horizons, while value and fundamentals have a stronger impact in the longer term.__ We also find that momentum plays a lesser statistical role, owing to its greater variability. Reversal is more visible after one year, roughly the amount of time it takes for time series to revert to the mean.”

“Similar patterns are observed in the cross-section. Momentum is a driver of quarterly returns, alongside the short end of the curve. __Flight to quality, as measured by equity volatility, seems to play a key role on all horizons__.”

“Indicators are then ranked based on the percentage of betas they represent [see table below]. __Carry is key__. __Flight to quality is the main driver of cross-sectional returns and plays no role in time series__. The short end of the curve, which reflects expectations about monetary policy, is another important source of information. __Reversal and value are key factors in time series but are not selected in the cross section__. Fundamental variables play a key role in forecasting both types of returns.”