  We explore the statistical and economic importance of restrictions on the
dynamics of risk compensation from the perspective of a real-time Bayesian
learner who predicts bond excess returns using dynamic term structure models
(DTSMs). The question on whether potential statistical predictability offered
by such models can generate economically significant portfolio benefits
out-of-sample, is revisited while imposing restrictions on their risk premia
parameters. To address this question, we propose a methodological framework
that successfully handles sequential model search and parameter estimation over
the restriction space in real time, allowing investors to revise their beliefs
when new information arrives, thus informing their asset allocation and
maximising their expected utility. Empirical results reinforce the argument of
sparsity in the market price of risk specification since we find strong
evidence of out-of-sample predictability only for those models that allow for
level risk to be priced and, additionally, only one or two of these risk premia
parameters to be different than zero. Most importantly, such statistical
evidence is turned into economically significant utility gains, across
prediction horizons, different time periods and portfolio specifications. In
addition to identifying successful DTSMs, the sequential version of the
stochastic search variable selection (SSVS) scheme developed can be applied on
its own and also offer useful diagnostics monitoring key quantities over time.
Connections with predictive regressions are also provided.
