The performances of the competing predictors are also compared using an out-of-sample trading strategy based on predictive regressions, which combines the stock market and the risk-free asset (one-month Treasury bill) (Ferreira and Santa-Clara, 2011). For each period, predictions of market excess returns are used to calculate the Markowitz optimal weight on the stock market:(9)where λ is the risk aversion and is the corresponding sample variance of market return.13 Portfolio decisions can be made in real time with data available when decisions are made. The ex post portfolio excess return is then calculated at the end of month as