In this paper, we introduce a new risk-based, long-run portfolio that bridges the gap between the multi-regime distribution of assets and risk-parity investing. Building on the seminal idea of the risk-parity portfolio, we relate regime-level information and portfolio allocation. When returns are influenced by latent regimes such as recession-expansion phases or inflation shocks, these non-stationarities can affect the unconditional distribution underlying the portfolio construction, leading the risk-parity allocation to load too much risk on the hedging asset. Our solution is the regime-parity portfolio, which is a linear combination between regime-specific risk-parity portfolios. We propose to weigh these regime-specific portfolios according to the steady-state probabilities of each regime, thus making use of the entire regime-level information. This new portfolio shows interesting features, notably better resistance to rare, yet adverse, regimes. We present the model and its salient features before showcasing different practical applications, highlighting the empirical interest of the approach.