In this paper we model conditional distributions of intraday maximum and minimum REIT prices with extreme value theory (`EVT') techniques. We condition the parameters of these distributions on continuously evolving risk decomposition values derived from the CMBX market. These risk decompositions are interpreted as dynamic state variables, and serve as signals for changing likelihoods of daily REIT extrema. By assessing the model at fifteen-second intervals, intraday, our model generates high-confidence signals of single optimal stopping times for long/short trades for REITs in our study and extraordinary profits with positive and significant alphas in some 90% of our tests.