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 the long-term investor in particular, as misspecification errors are exacerbated as the investment horizon increases. Therefore, we investigate the consequences of different types of break processes for a long-term investor. The break process is inferred with a mixture innovation model using Bayesian methods. This allows us to estimate the break risk and the uncertainty around it. The estimated parameters show substantial instability, with an average break probability of 20.6%. Assuming constant parameters can lead to losses of up to 16.3% in certainty equivalent return for the long-term investor, even if the break probability is small in reality. The costs of ignoring uncertainty regarding the instability are smaller, but non-negligible.