In these notes we discuss investment allocation to multiple alpha streams traded on the same execution platform, including when trades are crossed internally resulting in turnover reduction. We discuss approaches to alpha weight optimization where one maximizes P&L subject to bounds on volatility (or Sharpe ratio). The presence of negative alpha weights, which are allowed when alpha streams are traded on the same execution platform, complicates the optimization problem. By using factor model approach to alpha covariance matrix, the original optimization problem can be viewed as a 1-dimensional root searching problem plus an optimization problem that requires a finite number of iterations. We discuss this approach without costs and with linear costs, and also with nonlinear costs in a certain approximation, which makes the allocation problem tractable without forgoing nonlinear portfolio capacity bound effects.
