In any canonical Gaussian dynamic term structure model (GDTSM), the conditional forecasts of the pricing factors are invariant to the imposition of no-arbitrage restrictions. This invariance is maintained even in the presence of a variety of restrictions on the factor structure of bond yields. To establish these results, we develop a novel canonical GDTSM in which the pricing factors are observable portfolios of yields. For our normalization, standard maximum likelihood algorithms converge to the global optimum almost instantaneously. We present empirical estimates and out-of-sample forecasts for several GDTSMs using data on U.S. Treasury bond yields. The Author 2011. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: [email protected]., Oxford University Press.

This paper provides theory and evidence that a low-dimensional term structure model can simultaneously price bonds and related options. It shows that a component of volatility risk largely unrelated to the shape of the yield curve is a determinant of expected excess returns for holding long maturity bonds. It also finds evidence for this return relationship both in the model and directly in the data through regression analysis. The paper also identifies a link between corporate earnings performance and interest rate volatility, providing a channel driving interest rate volatility. The structure of risk in the model that gives rise to these features of volatility is distinct from that inherent in recent models with unspanned stochastic volatility.

This paper explores the implications of filtering and no-arbitrage for the maximum likelihood estimates of the entire conditional distribution of the risk factors and bond yields in Gaussian macro-finance term structure model (MTSM) when all yields are priced imperfectly. For typical yield curves and macro-variables studied in this literature, the estimated joint distribution within a canonical MTSM is nearly identical to the estimate from an economic-model-free factor vector-autoregression (factor-VAR), even when measurement errors are large. It follows that a canonical MTSM offers no new insights into economic questions regarding the historical distribution of the macro risk factors and yields, over and above what is learned from a factor-VAR. These results are rotation-invariant and, therefore, apply to many of the specifications in the literature.

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