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We extend the parametric portfolio policies that exploit firm characteristics to optimize portfolios of stocks and are thus based on asset selection. In addition to this, our extension exploits market indicators for market timing purposes (i.e. optimal allocations between stocks and a risk-free asset). We demonstrate the mechanics of the proposed technique in simulation studies. Specifically, we show that the extended approach is able to produce portfolios based on selection and timing that outperform portfolios that only apply selection, when the applied market indicators have sufficient predictive power. In purely demonstrative empirical applications, we illustrate how investors can use our optimization approach using common market indicators.