The author considers two bond futures return prediction models that use fewer factors than the five used in previous research. To make the models more parsimonious (from a statistical perspective) than previous models, the bond futures returns (2-year US Treasury note, 5-year US Treasury note, 10-year US Treasury note, and US Treasury bond) are analyzed monthly rather than annually, with three US Treasury one-month forward rates (1-year, 5-year, and 10-year maturities) used as predictors. The model using the three forward rates generates better trading performance than a two-factor model that uses the differences between the 1-year and 5-year forward rates and between the 5-year and 10-year forward rates, despite the fact that the two-factor model has better statistical attributes. The author thus suggests that prediction models must be evaluated on the basis of statistical and economic merits.

Practitioners benefit from being able to consider bond futures return prediction models that have fewer model factors (i.e., three or fewer) than what has previously been demonstrated in the literature. Furthermore, the analysis that led to the two- and three-factor models is useful; the author addresses multicollinearity and autocorrelation issues.

The author’s suggestion that models be evaluated using dual criteria of economic and statistical performance is a key insight. Statistically, it is important for model factors to be reasonably stable with accurate estimation, but economic performance is often not considered, even though it is potentially more important than statistical parsimony.

The author uses monthly US Treasury futures and forward data between 1991 and 2011. He first regresses annual futures returns calculated each month against five different annual forward rate returns calculated each month to demonstrate the prediction model that currently exists in the literature. After demonstrating that the five-factor model suffers from multicollinearity and autocorrelation, the author takes steps to address the two statistical issues that lead to two- and three-factor prediction models using monthly returns rather than annual returns calculated on a monthly basis.

For two- and three-factor models, regressions are performed for 15- and 20-year windows, which demonstrates the stability of the coefficients of the prediction factors (but the R², compared with that of the five-factor model, is greatly reduced). Trading strategies using model coefficients are implemented on a rolling 60-month basis. Also, using coefficients based on the first 15 years of data, the author applies a similar trading strategy to the last 5 years of data. In both trials, both models added value when compared with a benchmark, but the three-factor model performed better, despite having less desirable statistical properties than the two-factor model.

Although the reduction in model factors is an important contribution, I think the use of dual criteria (economic and statistical performance) is possibly a greater revelation.