Portfolio Construction When Regimes are Ambiguous

Investors sometimes have strong convictions that a distinctive economic regime will prevail in the period ahead and therefore would like to form a portfolio that reflects the expected returns, standard deviations, and correlations of assets during such a regime. To do so, they typically isolate a subsample of returns in which a regime indicator, such as the rate of economic growth, is above or below a chosen threshold and estimate expected returns, standard deviations, and correlations by equally weighting the observations within the subsample. This approach assumes that every observation within the regime subsample is equally important to forming the estimates whether an observation coincides with a growth rate that is far from the threshold or one that is only marginally distant from the threshold. Moreover, with this approach it is problematic to describe a regime by more than a single indicator because there is no non-arbitrary way to combine the indicators and because the addition of indicators increases the likelihood of producing an empty or overly sparse subsample. The authors apply a new concept called relevance to estimate regime-specific expected returns, standard deviations, and correlations. Their relevance-based approach explicitly accounts for the importance of an observation to forming an estimate, and it seamlessly enables the inclusion of multiple regime indicators in a principled way