A Spectral Model of Turnover Reduction

We give a simple explicit formula for turnover reduction when a large number of alphas are traded on the same execution platform and trades are crossed internally. We model turnover reduction via alpha correlations. Then, for a large number of alphas, turnover reduction is related to the largest eigenvalue and the corresponding eigenvector of the alpha correlation matrix.Comment: 15 pages; a trivial typo corrected in Eq. (43), no other change

Combining Alpha Streams with Costs

We discuss investment allocation to multiple alpha streams traded on the same execution platform with internal crossing of trades and point out differences with allocating investment when alpha streams are traded on separate execution platforms with no crossing. First, in the latter case allocation weights are non-negative, while in the former case they can be negative. Second, the effects of both linear and nonlinear (impact) costs are different in these two cases due to turnover reduction when the trades are crossed. Third, the turnover reduction depends on the universe of traded alpha streams, so if some alpha streams have zero allocations, turnover reduction needs to be recomputed, hence an iterative procedure. We discuss an algorithm for finding allocation weights with crossing and linear costs. We also discuss a simple approximation when nonlinear costs are added, making the allocation problem tractable while still capturing nonlinear portfolio capacity bound effects. We also define "regression with costs" as a limit of optimization with costs, useful in often-occurring cases with singular alpha covariance matrix.Comment: 21 pages; minor misprints corrected; to appear in The Journal of Ris

Notes on Alpha Stream Optimization

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.Comment: 42 pages; clarifying remarks added, minor misprints corrected; to appear in The Journal of Investment Strategie