Long-term investing under uncertain parameter instability

The relationship between excess returns and the dividend price ratio is known to be unstable. However, there is no consensus on the type of instability, i.e., few or many breaks. Differences in parameter instability affect in particular the long-term investor, because misspecification errors are exacerbated as the investment horizon increases. The consequences of different types of break processes for a long-term investor are therefore assessed. The break process is inferred using a mixture innovation model using Bayesian methods. This allows for estimation of the break risk and the uncertainty around it. The estimated parameters show substantial instability, with an average break probability of 14.0%. Assuming constant parameters can lead to large losses in certainty equivalent return for the long-term investor, even when the break probability is small. The costs of ignoring uncertainty regarding the instability are smaller, but non-negligible.