Combining alpha streams with costs

ABSTRACT In this paper, we discuss investment allocation to multiple alpha streams traded on the same execution platform with internal trade crossing. We then point out the differences between such a case and investment allocation when alpha streams are traded on separate execution platforms with no crossing. In the latter case, allocation weights are nonnegative; in the former, they can be negative. The effects of linear and nonlinear (impact) costs are different in these two cases due to turnover reduction when the trades are crossed. 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 is required. 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, which is useful in often-occurring cases with a singular alpha covariance matrix.