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We explore the stability properties of interest rate rules granting an explicit response to stock prices in a New Keynesian DSGE model where the presence of non‐Ricardian households makes stock prices nonredundant for the business cycle. We find that responding to stock prices enlarges the policy space for which the equilibrium is both determinate and E‐stable (learnable). In particular, the Taylor principle ceases to be necessary, and determinacy/E‐stability is granted also by mildly passive policy rules. Our results appear to be more prominent in economies featuring a lower elasticity of substitution across differentiated products and/or more rigid labor markets.