The Federal Reserve holds two main sets of monetary policy meetings, the “Federal Open Market Committee” (FOMC) and the “Board Meetings”, which gather with sixweek and two week cadence respectively. Cieslak, Morse, and Vissing-Jorgensen (2019) show that the cadence of these meetings is associated with cycles of corresponding frequencies in stock markets. These can be fruitfully exploited through a portfolio strategy that invests in the whole market at alternate weeks (the even-week strategy). This simple investment rule is based on the cycles identified empirically but, so far, lacks a theoretical foundation. In this paper, we provide a rigorous framework to detect cycles in the stock market, and to determine optimal portfolio choices which profit from such cycles. We use the filtering approach for stationary time series of Ortu, Severino, Tamoni, and Tebaldi (2020) to isolate uncorrelated components of stock returns that are precisely associated with two- and six-week cycles. Then, we replicate these components using tradable assets from the U.S. market, and design an optimal portfolio strategy that maximizes the investor’s wealth and outperforms the even-week strategy.