Measuring the Performance of Government Bond Portfolios with Index-Based Level, Slope, and Curvature Factors

Despite the nonlinearity in the relation between interest rate risk and expected return, bond fund performance regressions usually lever expected benchmark returnslinearly to the fund’srisk. This causes systematic miscalculations of expected passive style returns and active alphas. I propose a model which considers the nonlinearity via level, slope, and curvature of the expected return curve. The three priced factors are constructed from common US treasury indexes and represent passive, diversified investment alternatives. Using a wide range of treasury indexes as test assets, I confirm the efficiency of the model in avoiding the miscalculation. Then I apply it to active government bond mutual funds and separate accounts. Both vehicles show significantly negative alphas before and after fees on average. While separate accounts outperform funds on an alpha basis, they underperform considering their “value added” because they have nearly 2.5 times more assets under management than funds