This paper derives a new decomposition of stock returns using price extremes and proposes a conditional autoregressive shape (CARS) model with beta density to predict the direction of stock returns. The CARS model is continuously valued, which makes it different from binary classification...

We provide empirical evidence that CAPM-betas positively predict asset returns when market returns are predicted to be high, which occurs about every other month. Consequently, the product of beta and the predicted market return (CAPM) predicts asset returns by combining the out-of-sample...